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config.json

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+{
+  "architectures": [
+    "TransformerForCausalLM"
+  ],
+  "attn_impl": "parallel_attn",
+  "bos_token_id": 1,
+  "elementwise_affine": true,
+  "eos_token_id": 2,
+  "fuse_cross_entropy": true,
+  "fuse_norm": true,
+  "fuse_swiglu": true,
+  "hidden_act": "swish",
+  "hidden_ratio": 4,
+  "hidden_size": 2048,
+  "initializer_range": 0.006,
+  "intermediate_size": null,
+  "max_position_embeddings": 8192,
+  "model_type": "transformer",
+  "norm_eps": 1e-06,
+  "num_heads": 32,
+  "num_hidden_layers": 32,
+  "num_kv_heads": null,
+  "pad_token_id": 2,
+  "qk_norm": false,
+  "qkv_bias": false,
+  "rope_theta": 10000.0,
+  "tie_word_embeddings": false,
+  "torch_dtype": "float32",
+  "transformers_version": "4.51.3",
+  "use_cache": true,
+  "vocab_size": 32000,
+  "window_size": null
+}

fla/layers/__init__.py

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+# -*- coding: utf-8 -*-
+# Copyright (c) 2023-2025, Songlin Yang, Yu Zhang
+
+from .abc import ABCAttention
+from .attn import Attention
+from .based import BasedLinearAttention
+from .bitattn import BitAttention
+from .delta_net import DeltaNet
+from .forgetting_attn import ForgettingAttention
+from .gated_deltanet import GatedDeltaNet
+from .gated_deltaproduct import GatedDeltaProduct
+from .gla import GatedLinearAttention
+from .gsa import GatedSlotAttention
+from .hgrn import HGRNAttention
+from .hgrn2 import HGRN2Attention
+from .lightnet import LightNetAttention
+from .linear_attn import LinearAttention
+from .multiscale_retention import MultiScaleRetention
+from .nsa import NativeSparseAttention
+from .rebased import ReBasedLinearAttention
+from .rwkv6 import RWKV6Attention
+from .rwkv7 import RWKV7Attention
+
+__all__ = [
+    'ABCAttention',
+    'Attention',
+    'BasedLinearAttention',
+    'BitAttention',
+    'DeltaNet',
+    'ForgettingAttention',
+    'GatedDeltaNet',
+    'GatedDeltaProduct',
+    'GatedLinearAttention',
+    'GatedSlotAttention',
+    'HGRNAttention',
+    'HGRN2Attention',
+    'LightNetAttention',
+    'LinearAttention',
+    'MultiScaleRetention',
+    'NativeSparseAttention',
+    'ReBasedLinearAttention',
+    'RWKV6Attention',
+    'RWKV7Attention',
+]

fla/layers/attn.py

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+# -*- coding: utf-8 -*-
+# Copyright (c) 2023-2025, Songlin Yang, Yu Zhang
+
+from __future__ import annotations
+
+import warnings
+from typing import TYPE_CHECKING, Optional, Tuple
+
+import torch
+import torch.nn as nn
+import torch.nn.functional as F
+import torch.utils.checkpoint
+from einops import rearrange
+from transformers.utils import logging
+
+from fla.modules import RMSNorm, RotaryEmbedding
+from fla.ops import parallel_attn, parallel_rectified_attn, parallel_softpick_attn, naive_attn, naive_rectified_attn, naive_softpick_attn
+
+if TYPE_CHECKING:
+    from fla.models.utils import Cache
+
+try:
+    from flash_attn import flash_attn_func, flash_attn_varlen_func
+    from flash_attn.bert_padding import index_first_axis, pad_input, unpad_input
+except ImportError:
+    warnings.warn(
+        "Flash Attention is not installed. Please install it via `pip install flash-attn --no-build-isolation`",
+        category=ImportWarning
+    )
+    flash_attn_func = None
+
+logger = logging.get_logger(__name__)
+
+
+class Attention(nn.Module):
+
+    def __init__(
+        self,
+        hidden_size: int = 2048,
+        num_heads: int = 32,
+        num_kv_heads: Optional[int] = None,
+        qkv_bias: bool = False,
+        qk_norm: bool = False,
+        window_size: Optional[int] = None,
+        rope_theta: Optional[float] = 10000.,
+        max_position_embeddings: Optional[int] = None,
+        layer_idx: int = None,
+        attn_impl: str = "flash_attn",
+    ):
+        super().__init__()
+
+        self.hidden_size = hidden_size
+        self.num_heads = num_heads
+        if num_kv_heads is None:
+            self.num_kv_heads = self.num_heads
+        else:
+            self.num_kv_heads = num_kv_heads
+        self.num_kv_groups = num_heads // self.num_kv_heads
+        self.head_dim = self.hidden_size // self.num_heads
+        self.kv_dim = self.num_kv_heads * self.head_dim
+        self.qkv_bias = qkv_bias
+        self.qk_norm = qk_norm
+
+        self.window_size = window_size
+        self.rope_theta = rope_theta
+        self.max_position_embeddings = max_position_embeddings
+        self.layer_idx = layer_idx
+        self.attn_impl = attn_impl
+
+        self.q_proj = nn.Linear(self.hidden_size, self.hidden_size, bias=self.qkv_bias)
+        self.k_proj = nn.Linear(self.hidden_size, self.kv_dim, bias=self.qkv_bias)
+        self.v_proj = nn.Linear(self.hidden_size, self.kv_dim, bias=self.qkv_bias)
+        self.o_proj = nn.Linear(self.hidden_size, self.hidden_size, bias=False)
+
+        if "scaled" in self.attn_impl:
+            self.s = nn.Parameter(torch.empty(self.num_heads, 1))
+            self.register_buffer("logn", torch.log(torch.arange(2, self.max_position_embeddings*4+2, dtype=self.s.dtype)[:, None, None]))
+
+        if qk_norm:
+            self.q_norm = RMSNorm(self.head_dim)
+            self.k_norm = RMSNorm(self.head_dim)
+
+        self.rotary = RotaryEmbedding(dim=self.head_dim, base=self.rope_theta)
+
+    def reset_parameters(self):
+        if "scaled" in self.attn_impl:
+            nn.init.constant_(self.s, 0.3)
+            self.logn.copy_(torch.log(torch.arange(2, self.max_position_embeddings*4+2, dtype=self.s.dtype)[:, None, None]))
+
+    def forward(
+        self,
+        hidden_states: torch.Tensor,
+        attention_mask: Optional[torch.LongTensor] = None,
+        past_key_values: Optional[Cache] = None,
+        output_attentions: bool = False,
+        use_cache: bool = False,
+        **kwargs,
+    ) -> Tuple[torch.Tensor, Optional[torch.Tensor], Optional[Tuple[torch.Tensor]]]:
+        if attention_mask is not None:
+            assert len(attention_mask.shape) == 2, (
+                "Expected attention_mask as a 0-1 matrix with shape [batch_size, seq_len] "
+                "for padding purposes (0 indicating padding). "
+                "Arbitrary attention masks of shape [batch_size, seq_len, seq_len] are not allowed."
+            )
+
+        batch_size, q_len, _ = hidden_states.size()
+
+        q, k, v = self.q_proj(hidden_states), self.k_proj(hidden_states), self.v_proj(hidden_states)
+
+        q = rearrange(q, '... (h d) -> ... h d', d=self.head_dim)
+        k = rearrange(k, '... (h d) -> ... h d', d=self.head_dim)
+        v = rearrange(v, '... (h d) -> ... h d', d=self.head_dim)
+
+        if self.qk_norm:
+            q, k = self.q_norm(q), self.k_norm(k)
+
+        # equivalent to cu_seqlens in `flash_attn`
+        cu_seqlens = kwargs.get('cu_seqlens', None)
+
+        seqlen_offset, max_seqlen = 0, q_len
+        if past_key_values is not None:
+            seqlen_offset = past_key_values.get_seq_length(self.layer_idx)
+            max_seqlen = q.shape[1] + seqlen_offset
+
+            if attention_mask is not None:
+                # to deliminate the offsets of padding tokens
+                seqlen_offset = seqlen_offset + attention_mask.sum(-1) - attention_mask.shape[-1]
+                max_seqlen = q.shape[1] + max(seqlen_offset)
+
+        if self.max_position_embeddings is not None:
+            max_seqlen = max(max_seqlen, self.max_position_embeddings)
+        q, k = self.rotary(q, k, seqlen_offset=seqlen_offset, max_seqlen=max_seqlen, cu_seqlens=cu_seqlens)
+
+        if past_key_values is not None:
+            cache_has_content = past_key_values.get_seq_length(self.layer_idx) > 0
+            k_cached, v_cached = past_key_values.update(
+                attn_state=(k.flatten(-2, -1), v.flatten(-2, -1)),
+                layer_idx=self.layer_idx,
+                offset=q_len,
+                cache_kwargs=dict(window_size=self.window_size)
+            )['attn_state']
+            if cache_has_content:
+                k, v = k_cached, v_cached
+                k = rearrange(k, '... (h d) -> ... h d', d=self.head_dim)
+                v = rearrange(v, '... (h d) -> ... h d', d=self.head_dim)
+
+        # if flash_attn_func is None:
+        #     raise ImportError("Please install Flash Attention via `pip install flash-attn --no-build-isolation` first")
+
+        if "scaled" in self.attn_impl:
+            k_len = k.shape[1]
+            q = q * self.s.to(q.dtype) * self.logn[k_len-q_len:k_len].to(q.dtype)
+
+        # Contains at least one padding token in the sequence
+        if self.attn_impl == "flash_attn":
+            if attention_mask is not None:
+                q, k, v, indices_q, cu_seq_lens, max_seq_lens = self._upad_input(q, k, v, attention_mask, q_len)
+                cu_seqlens_q, cu_seqlens_k = cu_seq_lens
+                max_seqlen_q, max_seqlen_k = max_seq_lens
+                o = flash_attn_varlen_func(
+                    q, k, v,
+                    cu_seqlens_q=cu_seqlens_q,
+                    cu_seqlens_k=cu_seqlens_k,
+                    max_seqlen_q=max_seqlen_q,
+                    max_seqlen_k=max_seqlen_k,
+                    causal=True,
+                    window_size=(-1, -1) if self.window_size is None else (self.window_size-1, 0)
+                )
+                o = pad_input(o, indices_q, batch_size, q_len)
+            elif cu_seqlens is not None:
+                o = flash_attn_varlen_func(
+                    q.squeeze(0), k.squeeze(0), v.squeeze(0),
+                    cu_seqlens_q=cu_seqlens,
+                    cu_seqlens_k=cu_seqlens,
+                    max_seqlen_q=max_seqlen,
+                    max_seqlen_k=max_seqlen,
+                    causal=True,
+                    window_size=(-1, -1) if self.window_size is None else (self.window_size-1, 0)
+                ).unsqueeze(0)
+            else:
+                o = flash_attn_func(
+                    q, k, v,
+                    causal=True,
+                    window_size=(-1, -1) if self.window_size is None else (self.window_size-1, 0)
+                )
+        elif self.attn_impl == "parallel_attn":
+            o = parallel_attn(q, k, v, scale=self.head_dim**-0.5, cu_seqlens=cu_seqlens)
+        elif self.attn_impl == "parallel_scaled_attn":
+            o = parallel_attn(q, k, v, scale=self.head_dim**-0.5, cu_seqlens=cu_seqlens)
+        elif self.attn_impl == "parallel_rectified_attn":
+            o = parallel_rectified_attn(q, k, v, scale=self.head_dim**-0.5, cu_seqlens=cu_seqlens)
+        elif self.attn_impl == "parallel_softpick_attn":
+            o = parallel_softpick_attn(q, k, v, scale=self.head_dim**-0.5, cu_seqlens=cu_seqlens)
+        elif self.attn_impl == "parallel_scaled_softpick_attn":
+            o = parallel_softpick_attn(q, k, v, scale=self.head_dim**-0.5, cu_seqlens=cu_seqlens)
+        elif self.attn_impl == "naive_attn":
+            o, attentions = naive_attn(q, k, v, scale=self.head_dim**-0.5, cu_seqlens=cu_seqlens)
+        elif self.attn_impl == "naive_scaled_attn":
+            o, attentions = naive_attn(q, k, v, scale=self.head_dim**-0.5, cu_seqlens=cu_seqlens)
+        elif self.attn_impl == "naive_rectified_attn":
+            o, attentions = naive_rectified_attn(q, k, v, scale=self.head_dim**-0.5, cu_seqlens=cu_seqlens)
+        elif self.attn_impl == "naive_softpick_attn":
+            o, attentions = naive_softpick_attn(q, k, v, scale=self.head_dim**-0.5, cu_seqlens=cu_seqlens)
+        elif self.attn_impl == "naive_scaled_softpick_attn":
+            o, attentions = naive_softpick_attn(q, k, v, scale=self.head_dim**-0.5, cu_seqlens=cu_seqlens)
+        else:
+            raise ValueError(f"Unknown attention implementation: {self.attn_impl}")
+
+        o = o.reshape(batch_size, q_len, -1)
+        o = self.o_proj(o)
+
+        if not output_attentions or "parallel" in self.attn_impl or "flash" in self.attn_impl:
+            attentions = None
+
+        return o, attentions, past_key_values
+
+    def _upad_input(self, q, k, v, attention_mask, q_len):
+        batch_size, seq_len, num_key_value_heads, head_dim = k.shape
+        cache_mask = attention_mask[:, -seq_len:]
+        seqlens = cache_mask.sum(-1, dtype=torch.int32)
+        indices_k = torch.nonzero(cache_mask.flatten(), as_tuple=False).flatten()
+        max_seqlen_k = seqlens.max().item()
+        cu_seqlens_k = F.pad(torch.cumsum(seqlens, dim=0, dtype=torch.int32), (1, 0))
+
+        k = index_first_axis(k.reshape(batch_size * seq_len, num_key_value_heads, head_dim), indices_k)
+        v = index_first_axis(v.reshape(batch_size * seq_len, num_key_value_heads, head_dim), indices_k)
+        if q_len == seq_len:
+            q = index_first_axis(q.reshape(batch_size * seq_len, self.num_heads, head_dim), indices_k)
+            cu_seqlens_q = cu_seqlens_k
+            max_seqlen_q = max_seqlen_k
+            indices_q = indices_k
+        elif q_len == 1:
+            max_seqlen_q = 1
+            # There is a memcpy here, that is very bad.
+            cu_seqlens_q = torch.arange(batch_size + 1, dtype=torch.int32, device=q.device)
+            indices_q = cu_seqlens_q[:-1]
+            q = q.squeeze(1)
+        else:
+            # The -q_len: slice assumes left padding.
+            attention_mask = attention_mask[:, -q_len:]
+            q, indices_q, cu_seqlens_q, max_seqlen_q = unpad_input(q, attention_mask)
+
+        return q, k, v, indices_q, (cu_seqlens_q, cu_seqlens_k), (max_seqlen_q, max_seqlen_k)

fla/layers/bitattn.py

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+# -*- coding: utf-8 -*-
+# Copyright (c) 2023-2025, Songlin Yang, Yu Zhang
+
+from __future__ import annotations
+
+import warnings
+from typing import TYPE_CHECKING, Optional, Tuple
+
+import torch
+import torch.nn as nn
+import torch.nn.functional as F
+import torch.utils.checkpoint
+from einops import rearrange
+from transformers.utils import logging
+
+from fla.modules import RotaryEmbedding
+from fla.modules.fused_bitlinear import FusedBitLinear
+
+if TYPE_CHECKING:
+    from fla.models.utils import Cache
+
+try:
+    from flash_attn import flash_attn_func, flash_attn_varlen_func
+    from flash_attn.bert_padding import index_first_axis, pad_input, unpad_input
+except ImportError:
+    warnings.warn(
+        "Flash Attention is not installed. Please install it via `pip install flash-attn --no-build-isolation`",
+        category=ImportWarning
+    )
+    flash_attn_func = None
+
+logger = logging.get_logger(__name__)
+
+
+class BitAttention(nn.Module):
+
+    def __init__(
+        self,
+        hidden_size: int = 2048,
+        num_heads: int = 32,
+        num_kv_heads: Optional[int] = None,
+        window_size: Optional[int] = None,
+        rope_theta: Optional[float] = 10000.,
+        max_position_embeddings: Optional[int] = None,
+        norm_eps: float = 1e-5,
+        layer_idx: int = None
+    ):
+        super().__init__()
+
+        self.num_heads = num_heads
+        if num_kv_heads is None:
+            self.num_kv_heads = self.num_heads
+        else:
+            self.num_kv_heads = num_kv_heads
+        self.num_kv_groups = num_heads // self.num_kv_heads
+        self.hidden_size = hidden_size
+        self.head_dim = self.hidden_size // self.num_heads
+        self.kv_dim = self.num_kv_heads * self.head_dim
+        self.kv_dim = self.num_kv_heads * self.head_dim
+        self.window_size = window_size
+        self.rope_theta = rope_theta
+        self.max_position_embeddings = max_position_embeddings
+        self.layer_idx = layer_idx
+
+        self.q_proj = FusedBitLinear(self.hidden_size, self.hidden_size, bias=False)
+        self.k_proj = FusedBitLinear(self.hidden_size, self.kv_dim, bias=False)
+        self.v_proj = FusedBitLinear(self.hidden_size, self.kv_dim, bias=False)
+        self.o_proj = FusedBitLinear(self.hidden_size, self.hidden_size, bias=False)
+
+        self.rotary = RotaryEmbedding(dim=self.head_dim, base=self.rope_theta)
+
+    def forward(
+        self,
+        hidden_states: torch.Tensor,
+        attention_mask: Optional[torch.LongTensor] = None,
+        past_key_values: Optional[Cache] = None,
+        output_attentions: bool = False,
+        use_cache: bool = False,
+        **kwargs,
+    ) -> Tuple[torch.Tensor, Optional[torch.Tensor], Optional[Tuple[torch.Tensor]]]:
+        if attention_mask is not None:
+            assert len(attention_mask.shape) == 2, (
+                "Expected attention_mask as a 0-1 matrix with shape [batch_size, seq_len] "
+                "for padding purposes (0 indicating padding). "
+                "Arbitrary attention masks of shape [batch_size, seq_len, seq_len] are not allowed."
+            )
+
+        batch_size, q_len, _ = hidden_states.size()
+
+        q = rearrange(self.q_proj(hidden_states), '... (h d) -> ... h d', d=self.head_dim)
+        k = rearrange(self.k_proj(hidden_states), '... (h d) -> ... h d', d=self.head_dim)
+        v = rearrange(self.v_proj(hidden_states), '... (h d) -> ... h d', d=self.head_dim)
+
+        # equivalent to cu_seqlens in `flash_attn`
+        cu_seqlens = kwargs.get('cu_seqlens', None)
+
+        seqlen_offset, max_seqlen = 0, q_len
+        if past_key_values is not None:
+            seqlen_offset = past_key_values.get_seq_length(self.layer_idx)
+            max_seqlen = q.shape[1] + seqlen_offset
+
+            if attention_mask is not None:
+                # to deliminate the offsets of padding tokens
+                seqlen_offset = seqlen_offset + attention_mask.sum(-1) - attention_mask.shape[-1]
+                max_seqlen = q.shape[1] + max(seqlen_offset)
+
+        if self.max_position_embeddings is not None:
+            max_seqlen = max(max_seqlen, self.max_position_embeddings)
+        q, k = self.rotary(q, k, seqlen_offset=seqlen_offset, max_seqlen=max_seqlen, cu_seqlens=cu_seqlens)
+
+        if past_key_values is not None:
+            cache_has_content = past_key_values.get_seq_length(self.layer_idx) > 0
+            k_cached, v_cached = past_key_values.update(
+                attn_state=(k.flatten(-2, -1), v.flatten(-2, -1)),
+                layer_idx=self.layer_idx,
+                offset=q_len,
+                cache_kwargs=dict(window_size=self.window_size)
+            )['attn_state']
+            if cache_has_content:
+                k, v = k_cached, v_cached
+                k = rearrange(k, '... (h d) -> ... h d', d=self.head_dim)
+                v = rearrange(v, '... (h d) -> ... h d', d=self.head_dim)
+
+        if flash_attn_func is None:
+            raise ImportError("Please install Flash Attention via `pip install flash-attn --no-build-isolation` first")
+
+        # Contains at least one padding token in the sequence
+        if attention_mask is not None:
+            q, k, v, indices_q, cu_seq_lens, max_seq_lens = self._upad_input(q, k, v, attention_mask, q_len)
+            cu_seqlens_q, cu_seqlens_k = cu_seq_lens
+            max_seqlen_q, max_seqlen_k = max_seq_lens
+            o = flash_attn_varlen_func(
+                q, k, v,
+                cu_seqlens_q=cu_seqlens_q,
+                cu_seqlens_k=cu_seqlens_k,
+                max_seqlen_q=max_seqlen_q,
+                max_seqlen_k=max_seqlen_k,
+                causal=True,
+                window_size=(-1, -1) if self.window_size is None else (self.window_size-1, 0)
+            )
+            o = pad_input(o, indices_q, batch_size, q_len)
+        elif cu_seqlens is not None:
+            o = flash_attn_varlen_func(
+                q.squeeze(0), k.squeeze(0), v.squeeze(0),
+                cu_seqlens_q=cu_seqlens,
+                cu_seqlens_k=cu_seqlens,
+                max_seqlen_q=max_seqlen,
+                max_seqlen_k=max_seqlen,
+                causal=True,
+                window_size=(-1, -1) if self.window_size is None else (self.window_size-1, 0)
+            ).unsqueeze(0)
+        else:
+            o = flash_attn_func(
+                q, k, v,
+                causal=True,
+                window_size=(-1, -1) if self.window_size is None else (self.window_size-1, 0)
+            )
+        o = o.reshape(batch_size, q_len, -1)
+        o = self.o_proj(o)
+
+        if not output_attentions:
+            attentions = None
+
+        return o, attentions, past_key_values
+
+    def _upad_input(self, q, k, v, attention_mask, q_len):
+        batch_size, seq_len, num_key_value_heads, head_dim = k.shape
+        cache_mask = attention_mask[:, -seq_len:]
+        seqlens = cache_mask.sum(-1, dtype=torch.int32)
+        indices_k = torch.nonzero(cache_mask.flatten(), as_tuple=False).flatten()
+        max_seqlen_k = seqlens.max().item()
+        cu_seqlens_k = F.pad(torch.cumsum(seqlens, dim=0, dtype=torch.int32), (1, 0))
+
+        k = index_first_axis(k.reshape(batch_size * seq_len, num_key_value_heads, head_dim), indices_k)
+        v = index_first_axis(v.reshape(batch_size * seq_len, num_key_value_heads, head_dim), indices_k)
+        if q_len == seq_len:
+            q = index_first_axis(q.reshape(batch_size * seq_len, self.num_heads, head_dim), indices_k)
+            cu_seqlens_q = cu_seqlens_k
+            max_seqlen_q = max_seqlen_k
+            indices_q = indices_k
+        elif q_len == 1:
+            max_seqlen_q = 1
+            # There is a memcpy here, that is very bad.
+            cu_seqlens_q = torch.arange(batch_size + 1, dtype=torch.int32, device=q.device)
+            indices_q = cu_seqlens_q[:-1]
+            q = q.squeeze(1)
+        else:
+            # The -q_len: slice assumes left padding.
+            attention_mask = attention_mask[:, -q_len:]
+            q, indices_q, cu_seqlens_q, max_seqlen_q = unpad_input(q, attention_mask)
+
+        return q, k, v, indices_q, (cu_seqlens_q, cu_seqlens_k), (max_seqlen_q, max_seqlen_k)

fla/layers/gated_deltaproduct.py

@@ -0,0 +1,351 @@
+from __future__ import annotations
+
+import math
+from typing import TYPE_CHECKING, Dict, Optional, Tuple
+
+import torch
+import torch.nn as nn
+import torch.nn.functional as F
+from einops import rearrange
+
+from fla.modules import FusedRMSNormSwishGate, RMSNorm, ShortConvolution
+from fla.ops.delta_rule import chunk_delta_rule
+from fla.ops.gated_delta_rule import chunk_gated_delta_rule
+
+if TYPE_CHECKING:
+    from transformers.processing_utils import Unpack
+
+    from fla.models.utils import Cache
+
+
+def elu_p1(x):
+    return (F.elu(x, 1.0, False) + 1.0).to(x)
+
+
+def sum_norm(x):
+    return (x / x.sum(-1, keepdim=True)).to(x)
+
+
+def interleave_multiple_sequences(*sequences):
+    """
+    Interleave multiple sequences together.
+    For example, with sequences [A1, A2], [B1, B2], [C1, C2],
+    returns [A1, B1, C1, A2, B2, C2]
+    """
+    if isinstance(sequences[0], (list, tuple)):
+        sequences = sequences[0]
+
+    if len(sequences) == 1:
+        return sequences[0]
+
+    # All sequences should have the same shape
+    assert all(s.shape == sequences[0].shape for s in sequences)
+
+    # Get the original shape
+    batch_size, seq_len, *rest = sequences[0].shape
+
+    # Stack sequences along a new dimension
+    stacked = torch.stack(sequences, dim=2)
+
+    # Reshape to interleave
+    reshaped = stacked.view(batch_size, seq_len * len(sequences), *rest)
+
+    return reshaped
+
+
+class GatedDeltaProduct(nn.Module):
+    """
+    Generalized version of GatedDoubleDeltaNet that supports arbitrary number of householder transformations.
+    """
+
+    def __init__(
+            self,
+            hidden_size: int = 2048,
+            expand_v: float = 2,
+            head_dim: int = 256,
+            num_heads: int = 6,
+            num_householder: int = 2,  # New parameter for number of householder transformations
+            mode: str = "chunk",
+            use_gate: bool = True,
+            use_forget_gate: bool = True,  # when true Gated DeltaProduct, when false DeltaProduct
+            use_short_conv: bool = True,
+            conv_size: int = 4,
+            conv_bias: bool = False,
+            layer_idx: int | None = None,
+            norm_eps: float = 1e-5,
+            allow_neg_eigval: bool = False,  # when true (Gated) DeltaProduct [-1, 1], when false (Gated) DeltaProduct [0, 1]
+            **kwargs,
+    ) -> None:
+        super().__init__()
+
+        self.mode = mode
+        self.hidden_size = hidden_size
+        self.expand_v = expand_v
+        self.use_gate = use_gate
+        self.use_short_conv = use_short_conv
+        self.conv_size = conv_size
+        self.conv_bias = conv_bias
+        self.head_dim = head_dim
+        self.num_heads = num_heads
+        self.num_householder = num_householder
+        self.allow_neg_eigval = allow_neg_eigval
+        self.use_forget_gate = use_forget_gate
+        self.key_dim = self.num_heads * self.head_dim
+        self.value_dim = int(self.key_dim * self.expand_v)
+        self.head_qk_dim = head_dim
+        self.head_v_dim = int(head_dim * self.expand_v)
+        self.layer_idx = layer_idx
+        self.silu = nn.SiLU()
+        assert mode in ["chunk", "fused_recurrent"], f"Not supported mode `{mode}`."
+        # Create multiple projection layers for each householder transformation
+        self.q_proj = nn.Linear(hidden_size, self.key_dim, bias=False)
+
+        self.k_projs = nn.ModuleList(
+            [
+                nn.Linear(hidden_size, self.key_dim, bias=False)
+                for _ in range(num_householder)
+            ]
+        )
+        self.v_projs = nn.ModuleList(
+            [
+                nn.Linear(hidden_size, self.value_dim, bias=False)
+                for _ in range(num_householder)
+            ]
+        )
+        self.b_projs = nn.ModuleList(
+            [
+                nn.Linear(hidden_size, self.num_heads, bias=False)
+                for _ in range(num_householder)
+            ]
+        )
+        if use_short_conv:
+            self.q_conv1ds = nn.ModuleList(
+                [
+                    ShortConvolution(
+                        hidden_size=self.key_dim,
+                        kernel_size=conv_size,
+                        activation="silu",
+                    )
+                    for _ in range(num_householder)
+                ]
+            )
+            self.k_conv1ds = nn.ModuleList(
+                [
+                    ShortConvolution(
+                        hidden_size=self.key_dim,
+                        kernel_size=conv_size,
+                        activation="silu",
+                    )
+                    for _ in range(num_householder)
+                ]
+            )
+            self.v_conv1ds = nn.ModuleList(
+                [
+                    ShortConvolution(
+                        hidden_size=self.value_dim,
+                        kernel_size=conv_size,
+                        activation="silu",
+                    )
+                    for _ in range(num_householder)
+                ]
+            )
+
+        if self.use_forget_gate:
+            self.a_proj = nn.Linear(hidden_size, self.num_heads, bias=False)
+            A = torch.empty(self.num_heads, dtype=torch.float32).uniform_(0, 16)
+            A_log = torch.log(A)
+            self.A_log = nn.Parameter(A_log)
+            self.A_log._no_weight_decay = True
+
+            # Initialize dt parameters
+            dt_min = 0.001
+            dt_max = 0.1
+            dt_init_floor = 1e-4
+            dt = torch.exp(
+                torch.rand(self.num_heads) * (math.log(dt_max) - math.log(dt_min))
+                + math.log(dt_min)
+            )
+            dt = torch.clamp(dt, min=dt_init_floor)
+            inv_dt = dt + torch.log(-torch.expm1(-dt))
+            self.dt_bias = nn.Parameter(inv_dt)
+            self.dt_bias._no_weight_decay = True
+
+        if use_gate:
+            self.g_proj = nn.Linear(hidden_size, self.value_dim, bias=False)
+            self.o_norm = FusedRMSNormSwishGate(self.head_v_dim, eps=norm_eps)
+        else:
+            self.o_norm = RMSNorm(self.head_v_dim, eps=norm_eps)
+        self.o_proj = nn.Linear(self.value_dim, hidden_size, bias=False)
+        self.k_id = torch.nn.Identity()
+        self.apply(self._initialize_weights)
+
+    def _initialize_weights(self, module: nn.Module):
+        if getattr(module, "_is_hf_initialized", False):
+            return
+        if isinstance(module, nn.Linear):
+            nn.init.xavier_uniform_(module.weight, gain=2 ** -2.5)
+            if module.bias is not None:
+                nn.init.zeros_(module.bias)
+        module._is_hf_initialized = True
+
+    def forward(
+            self,
+            hidden_states: torch.Tensor,
+            attention_mask: Optional[torch.Tensor] = None,
+            past_key_values: Optional[Cache] = None,
+            use_cache: Optional[bool] = False,
+            output_attentions: Optional[bool] = False,
+            **kwargs: Unpack[Dict],
+    ) -> Tuple[torch.Tensor, Optional[torch.Tensor], Optional[Cache]]:
+        if attention_mask is not None:
+            assert len(attention_mask.shape) == 2, (
+                "Expected attention_mask as a 0-1 matrix with shape [batch_size, seq_len] "
+                "for padding purposes (0 indicating padding)."
+            )
+
+        mode = (
+            "chunk"  # 'fused_recurrent' if hidden_states.shape[1] <= 64 else self.mode
+        )
+        if self.training:
+            assert mode == "chunk", "Only chunk mode is supported in training."
+
+        last_state = None
+        if past_key_values is not None and len(past_key_values) > self.layer_idx:
+            last_state = past_key_values[self.layer_idx]
+
+        # Process each householder transformation
+        ks, vs, betas = [], [], []
+        conv_states = []
+
+        for i in range(self.num_householder):
+            if self.use_short_conv:
+                conv_state_q, conv_state_k, conv_state_v = None, None, None
+                if last_state is not None:
+                    conv_state_q, conv_state_k, conv_state_v = last_state["conv_state"][
+                        i
+                    ]
+                conv_mask = (
+                    attention_mask[:, -hidden_states.shape[1]:]
+                    if attention_mask is not None
+                    else None
+                )
+
+                k, conv_state_k = self.k_conv1ds[i](
+                    x=self.k_projs[i](hidden_states),
+                    mask=conv_mask,
+                    cache=conv_state_k,
+                    output_final_state=use_cache,
+                )
+                v, conv_state_v = self.v_conv1ds[i](
+                    x=self.v_projs[i](hidden_states),
+                    mask=conv_mask,
+                    cache=conv_state_v,
+                    output_final_state=use_cache,
+                )
+                conv_states.append((conv_state_q, conv_state_k, conv_state_v))
+            else:
+                k = self.silu(self.k_projs[i](hidden_states))
+                v = self.silu(self.v_projs[i](hidden_states))
+
+            ks.append(k)
+            vs.append(v)
+
+            beta = self.b_projs[i](
+                hidden_states
+            ).sigmoid()  # bs, sequence_length, num_heads
+            if attention_mask is not None:
+                beta = beta.mul(attention_mask[:, -hidden_states.shape[1]:, None])
+            if self.allow_neg_eigval:
+                beta = beta * 2
+            betas.append(beta)
+
+        if self.use_short_conv:
+            q, conv_state_q = self.q_conv1ds[0](
+                x=self.q_proj(hidden_states),
+                mask=conv_mask,
+                cache=conv_state_q,
+                output_final_state=use_cache,
+            )
+        else:
+            q = self.silu(self.q_proj(hidden_states))
+        q = interleave_multiple_sequences(
+            [torch.zeros_like(q)] * (self.num_householder - 1) + [q]
+        )
+        # Interleave all sequences
+        k = interleave_multiple_sequences(ks)
+        v = interleave_multiple_sequences(vs)
+        beta = interleave_multiple_sequences(betas)
+
+        q, k, v = (
+            rearrange(x, "b t (h d) -> b t h d", h=self.num_heads) for x in (q, k, v)
+        )
+
+        recurrent_state = (
+            last_state["recurrent_state"] if last_state is not None else None
+        )
+        offsets = kwargs.get("offsets")
+
+        if mode == "chunk":
+            if self.use_forget_gate:
+                g = -self.A_log.float().exp() * F.softplus(
+                    self.a_proj(hidden_states).float() + self.dt_bias
+                )
+                if attention_mask is not None:
+                    g = g.mul(attention_mask[:, -g.shape[-2]:, None])
+
+                # Interleave g with zeros for non-first transformations
+                g = interleave_multiple_sequences(
+                    [g] + [torch.zeros_like(g)] * (self.num_householder - 1)
+                )
+
+                o, recurrent_state = chunk_gated_delta_rule(
+                    q=q,
+                    k=k,
+                    v=v,
+                    g=g,
+                    beta=beta,
+                    initial_state=recurrent_state,
+                    output_final_state=use_cache,
+                    cu_seqlens=offsets,
+                    head_first=False,
+                    use_qk_l2norm_in_kernel=True
+                )
+            else:
+                o, recurrent_state = chunk_delta_rule(
+                    q=q,
+                    k=k,
+                    v=v,
+                    beta=beta,
+                    initial_state=recurrent_state,
+                    output_final_state=use_cache,
+                    cu_seqlens=offsets,
+                    head_first=False,
+                    use_qk_l2norm_in_kernel=True
+                )
+        else:
+            raise NotImplementedError(f"Not supported mode `{mode}`.")
+
+        # Take every nth element for n householder transformations
+        o = o[:, self.num_householder - 1:: self.num_householder, :]
+
+        if past_key_values is not None:
+            past_key_values.update(
+                recurrent_state=recurrent_state,
+                conv_state=conv_states if self.use_short_conv else None,
+                layer_idx=self.layer_idx,
+                offset=q.shape[2],
+            )
+
+        if self.use_gate:
+            g = rearrange(
+                self.g_proj(hidden_states),
+                "... (h d) -> ... h d",
+                h=self.num_heads,
+            )
+            o = self.o_norm(o, g)
+        else:
+            o = self.o_norm(o)
+        o = rearrange(o, "b t h d -> b t (h d)")
+        o = self.o_proj(o)
+
+        return o, None, past_key_values

fla/layers/hgrn.py

@@ -0,0 +1,168 @@
+# -*- coding: utf-8 -*-
+# Copyright (c) 2023-2025, Songlin Yang, Yu Zhang
+
+# "Hierarchically Gated Recurrent Neural Network for Sequence Modeling" [https://arxiv.org/abs/2311.04823]
+
+from __future__ import annotations
+
+from typing import TYPE_CHECKING, Dict, Optional, Tuple
+
+import torch
+import torch.nn as nn
+import torch.nn.functional as F
+
+from fla.modules import FusedRMSNormGated, ShortConvolution
+from fla.modules.activations import swiglu
+from fla.ops.hgrn import chunk_hgrn, fused_recurrent_hgrn
+
+if TYPE_CHECKING:
+    from transformers.processing_utils import Unpack
+
+    from fla.models.utils import Cache
+
+
+class HGRNAttention(nn.Module):
+
+    def __init__(
+        self,
+        mode: str = 'chunk',
+        hidden_size: int = 1024,
+        expand_ratio: Optional[int] = 1,
+        use_short_conv: bool = False,
+        conv_size: int = 4,
+        conv_bias: bool = False,
+        elementwise_affine: Optional[bool] = True,
+        norm_eps: float = 1e-5,
+        layer_idx: int = None
+    ) -> HGRNAttention:
+        super().__init__()
+
+        self.mode = mode
+        self.hidden_size = hidden_size
+        self.expand_ratio = expand_ratio
+        self.input_dim = int(hidden_size * expand_ratio)
+
+        self.use_short_conv = use_short_conv
+        self.conv_size = conv_size
+        self.conv_bias = conv_bias
+
+        self.layer_idx = layer_idx
+
+        assert mode in ['chunk', 'fused_recurrent'], f"Not suppoerted mode `{mode}`."
+
+        self.i_proj = nn.Linear(hidden_size, self.input_dim, bias=False)
+        self.f_proj = nn.Linear(hidden_size, self.input_dim, bias=False)
+        self.g_proj = nn.Linear(hidden_size, self.input_dim, bias=False)
+
+        if use_short_conv:
+            self.conv_size = conv_size
+            self.q_conv1d = ShortConvolution(self.input_dim, conv_size, activation=None)
+            self.f_conv1d = ShortConvolution(self.input_dim, conv_size, activation=None)
+            self.i_conv1d = ShortConvolution(self.input_dim, conv_size, activation=None)
+
+        self.g_norm = FusedRMSNormGated(
+            hidden_size=self.input_dim,
+            elementwise_affine=elementwise_affine,
+            eps=norm_eps
+        )
+        self.o_proj = nn.Linear(self.input_dim, hidden_size, bias=False)
+
+    def forward(
+        self,
+        hidden_states: torch.Tensor,
+        attention_mask: Optional[torch.Tensor] = None,
+        past_key_values: Optional[Cache] = None,
+        use_cache: Optional[bool] = False,
+        output_attentions: Optional[bool] = False,
+        lower_bound: Optional[torch.Tensor] = None,
+        **kwargs: Unpack[Dict]
+    ) -> Tuple[torch.Tensor, Optional[torch.Tensor], Optional[Cache]]:
+        if attention_mask is not None:
+            assert len(attention_mask.shape) == 2, (
+                "Expected attention_mask as a 0-1 matrix with shape [batch_size, seq_len] "
+                "for padding purposes (0 indicating padding). "
+                "Arbitrary attention masks of shape [batch_size, seq_len, seq_len] are not allowed."
+            )
+
+        # launching the triton kernel for just one token will actually be slower
+        mode = 'fused_recurrent' if not self.training and hidden_states.shape[1] <= 64 else self.mode
+
+        last_state = None
+        if past_key_values is not None and len(past_key_values) > self.layer_idx:
+            last_state = past_key_values[self.layer_idx]
+
+        cu_seqlens = kwargs.get('cu_seqlens', None)
+        if self.use_short_conv:
+            conv_state_i, conv_state_f = None, None
+            if last_state is not None:
+                conv_state_i, conv_state_f = last_state['conv_state']
+            conv_mask = attention_mask[:, -hidden_states.shape[1]:] if attention_mask is not None else None
+            i, conv_state_i = self.i_conv1d(
+                x=self.i_proj(hidden_states),
+                mask=conv_mask,
+                cache=conv_state_i,
+                output_final_state=use_cache,
+                cu_seqlens=cu_seqlens
+            )
+            f, conv_state_f = self.f_conv1d(
+                x=self.f_proj(hidden_states),
+                mask=conv_mask,
+                cache=conv_state_f,
+                output_final_state=use_cache,
+                cu_seqlens=cu_seqlens
+            )
+        else:
+            i = self.i_proj(hidden_states)
+            f = self.f_proj(hidden_states)
+
+        # the lower bound for the first layer is zero
+        if lower_bound is None or self.layer_idx == 0:
+            i, f = swiglu(i, 1 - f.sigmoid()), F.logsigmoid(f)
+        else:
+            g = lower_bound + (1 - lower_bound) * f.sigmoid()
+            i, f = swiglu(i, 1 - g), g.log()
+
+        # dealing with left-padding
+        if attention_mask is not None:
+            i = i.mul_(attention_mask[:, -i.shape[-2]:, None])
+
+        recurrent_state = last_state['recurrent_state'] if last_state is not None else None
+        if mode == 'chunk':
+            if cu_seqlens is not None:
+                raise NotImplementedError("Chunk mode does not support variable-length sequences.")
+            o, recurrent_state = chunk_hgrn(
+                x=i,
+                g=f,
+                initial_state=recurrent_state,
+                output_final_state=use_cache,
+            )
+        elif mode == 'fused_recurrent':
+            o, recurrent_state = fused_recurrent_hgrn(
+                x=i,
+                g=f,
+                initial_state=recurrent_state,
+                output_final_state=use_cache,
+                cu_seqlens=cu_seqlens
+            )
+        else:
+            raise NotImplementedError(f"Not supported mode `{mode}`.")
+
+        if past_key_values is not None:
+            past_key_values.update(
+                recurrent_state=recurrent_state,
+                conv_state=(conv_state_i, conv_state_f) if self.use_short_conv else None,
+                layer_idx=self.layer_idx,
+                offset=i.shape[2]
+            )
+
+        o = self.g_norm(o, self.g_proj(hidden_states))
+        o = self.o_proj(o)
+
+        return o, None, past_key_values
+
+    def state_size(self, **kwargs) -> int:
+        state_size = self.hidden_size
+        for module in self.children():
+            if isinstance(module, ShortConvolution):
+                state_size += module.state_size
+        return state_size

fla/layers/hgrn2.py

@@ -0,0 +1,211 @@
+# -*- coding: utf-8 -*-
+# Copyright (c) 2023-2025, Songlin Yang, Yu Zhang
+
+# "HGRN2: Gated Linear RNNs with State Expansion"[https://arxiv.org/abs/2404.07904]
+
+from __future__ import annotations
+
+from typing import TYPE_CHECKING, Dict, Optional, Tuple
+
+import torch
+import torch.nn as nn
+import torch.nn.functional as F
+from einops import rearrange
+
+from fla.modules import RMSNorm, ShortConvolution
+from fla.modules.activations import swish
+from fla.modules.layernorm import rms_norm_linear
+from fla.ops.gla import chunk_gla, fused_chunk_gla, fused_recurrent_gla
+
+if TYPE_CHECKING:
+    from transformers.processing_utils import Unpack
+
+    from fla.models.utils import Cache
+
+
+class HGRN2Attention(nn.Module):
+
+    def __init__(
+        self,
+        mode: str = 'chunk',
+        hidden_size: int = 1024,
+        num_heads: Optional[int] = None,
+        expand_ratio: Optional[int] = 128,
+        use_short_conv: bool = False,
+        conv_size: int = 4,
+        conv_bias: bool = False,
+        elementwise_affine: Optional[bool] = True,
+        norm_eps: float = 1e-5,
+        layer_idx: int = None
+    ) -> HGRN2Attention:
+        super().__init__()
+
+        self.mode = mode
+        self.hidden_size = hidden_size
+
+        if expand_ratio is None and num_heads is not None:
+            expand_ratio = hidden_size // num_heads
+        elif expand_ratio is not None and num_heads is None:
+            num_heads = hidden_size // expand_ratio
+        elif expand_ratio is None and num_heads is None:
+            raise RuntimeError("One of `expand_ratio` or `num_heads` should be provided.")
+        self.num_heads = num_heads
+        self.expand_ratio = expand_ratio
+
+        self.use_short_conv = use_short_conv
+        self.conv_size = conv_size
+        self.conv_bias = conv_bias
+
+        self.forget_dim = int(self.num_heads * self.expand_ratio)
+        self.input_dim = hidden_size
+        self.layer_idx = layer_idx
+
+        assert mode in ['chunk', 'fused_recurrent', 'fused_chunk'], f"Not suppoerted mode `{mode}`."
+        assert self.forget_dim % num_heads == 0, f"forget dim must be divisible by num_heads of {num_heads}"
+        assert self.input_dim % num_heads == 0, f"input dim must be divisible by num_heads of {num_heads}"
+
+        self.head_f_dim = self.expand_ratio
+        self.head_i_dim = self.hidden_size // num_heads
+
+        self.q_proj = nn.Linear(hidden_size, self.forget_dim, bias=False)
+        self.f_proj = nn.Linear(hidden_size, self.forget_dim, bias=False)
+        self.i_proj = nn.Linear(hidden_size, self.input_dim, bias=False)
+
+        if use_short_conv:
+            self.conv_size = conv_size
+            self.q_conv1d = ShortConvolution(self.forget_dim, conv_size, activation=None)
+            self.f_conv1d = ShortConvolution(self.forget_dim, conv_size, activation=None)
+            self.i_conv1d = ShortConvolution(self.input_dim, conv_size, activation=None)
+
+        self.g_norm = RMSNorm(hidden_size=self.hidden_size, elementwise_affine=elementwise_affine, eps=norm_eps)
+        self.o_proj = nn.Linear(self.input_dim, hidden_size, bias=False)
+
+    def forward(
+        self,
+        hidden_states: torch.Tensor,
+        attention_mask: Optional[torch.Tensor] = None,
+        past_key_values: Optional[Cache] = None,
+        use_cache: Optional[bool] = False,
+        output_attentions: Optional[bool] = False,
+        lower_bound: Optional[torch.Tensor] = None,
+        **kwargs: Unpack[Dict]
+    ) -> Tuple[torch.Tensor, Optional[torch.Tensor], Optional[Cache]]:
+        if attention_mask is not None:
+            assert len(attention_mask.shape) == 2, (
+                "Expected attention_mask as a 0-1 matrix with shape [batch_size, seq_len] "
+                "for padding purposes (0 indicating padding). "
+                "Arbitrary attention masks of shape [batch_size, seq_len, seq_len] are not allowed."
+            )
+
+        # launching the triton kernel for just one token will actually be slower
+        mode = 'fused_recurrent' if hidden_states.shape[1] <= 64 else self.mode
+
+        last_state = None
+        if past_key_values is not None and len(past_key_values) > self.layer_idx:
+            last_state = past_key_values[self.layer_idx]
+
+        cu_seqlens = kwargs.get('cu_seqlens', None)
+        if self.use_short_conv:
+            conv_state_q, conv_state_f, conv_state_i = None, None, None
+            if last_state is not None:
+                conv_state_q, conv_state_f, conv_state_i = last_state['conv_state']
+            conv_mask = attention_mask[:, -hidden_states.shape[1]:] if attention_mask is not None else None
+            q, conv_state_q = self.q_conv1d(
+                x=self.q_proj(hidden_states),
+                mask=conv_mask,
+                cache=conv_state_q,
+                output_final_state=use_cache,
+                cu_seqlens=cu_seqlens
+            )
+            f, conv_state_f = self.f_conv1d(
+                x=self.f_proj(hidden_states),
+                mask=conv_mask,
+                cache=conv_state_f,
+                output_final_state=use_cache,
+                cu_seqlens=cu_seqlens
+            )
+            i, conv_state_i = self.i_conv1d(
+                x=self.i_proj(hidden_states),
+                mask=conv_mask,
+                cache=conv_state_i,
+                output_final_state=use_cache,
+                cu_seqlens=cu_seqlens
+            )
+        else:
+            q = self.q_proj(hidden_states)
+            f = self.f_proj(hidden_states)
+            i = self.i_proj(hidden_states)
+
+        # dealing with left-padding
+        if attention_mask is not None:
+            i = i.mul_(attention_mask[:, -i.shape[-2]:, None])
+
+        q = swish(q)
+
+        # improve precision
+        f = f.float()
+
+        # the lower bound for the first layer is zero
+        if lower_bound is None or self.layer_idx == 0:
+            k, g = 1 - f.sigmoid(), F.logsigmoid(f)
+        else:
+            g = lower_bound + (1 - lower_bound) * f.sigmoid()
+            k, g = 1 - g, g.log()
+
+        q, k, g = map(lambda x: rearrange(x, '... (h d) -> ... h d', d=self.head_f_dim), (q, k.to(i), g))
+        i = rearrange(i, '... (h d) -> ... h d', d=self.head_i_dim)
+
+        recurrent_state = last_state['recurrent_state'] if last_state is not None else None
+        if mode == 'fused_recurrent':
+            o, recurrent_state = fused_recurrent_gla(
+                q=q,
+                k=k,
+                v=i,
+                gk=g,
+                initial_state=recurrent_state,
+                output_final_state=use_cache,
+                cu_seqlens=cu_seqlens,
+                head_first=False
+            )
+        elif mode == 'fused_chunk':
+            o, recurrent_state = fused_chunk_gla(
+                q=q,
+                k=k,
+                v=i,
+                g=g,
+                initial_state=recurrent_state,
+                output_final_state=use_cache,
+                head_first=False
+            )
+        elif mode == 'chunk':
+            o, recurrent_state = chunk_gla(
+                q=q,
+                k=k,
+                v=i,
+                g=g,
+                initial_state=recurrent_state,
+                output_final_state=use_cache,
+                cu_seqlens=cu_seqlens,
+                head_first=False
+            )
+        else:
+            raise NotImplementedError(f"Not supported mode `{mode}`.")
+
+        if past_key_values is not None:
+            past_key_values.update(
+                recurrent_state=recurrent_state,
+                conv_state=(conv_state_q, conv_state_f, conv_state_i) if self.use_short_conv else None,
+                layer_idx=self.layer_idx,
+                offset=q.shape[1]
+            )
+
+        o = rearrange(o, '... h d -> ... (h d)')
+        o = rms_norm_linear(o, self.g_norm.weight, self.g_norm.bias, self.o_proj.weight, self.o_proj.bias)
+        return o, None, past_key_values
+
+    def state_size(self, **kwargs) -> int:
+        state_size = self.forget_dim * self.head_i_dim
+        for module in self.children():
+            if isinstance(module, ShortConvolution):
+                state_size += module.state_size
+        return state_size

fla/layers/lightnet.py

@@ -0,0 +1,210 @@
+# -*- coding: utf-8 -*-
+# Copyright (c) 2023-2025, Songlin Yang, Yu Zhang
+
+# ["You Only Scan Once: Efficient Multi-dimension Sequential Modeling with LightNet"](https://arxiv.org/abs/2405.21022)
+
+from __future__ import annotations
+
+from typing import TYPE_CHECKING, Dict, Optional, Tuple
+
+import torch
+import torch.nn as nn
+import torch.nn.functional as F
+from einops import rearrange
+
+from fla.modules import FusedRMSNormGated, ShortConvolution
+from fla.modules.fused_norm_gate import rms_norm_swish_gate_linear
+from fla.ops.gla import chunk_gla, fused_recurrent_gla
+
+if TYPE_CHECKING:
+    from transformers.processing_utils import Unpack
+
+    from fla.models.utils import Cache
+
+
+class LightNetAttention(nn.Module):
+
+    def __init__(
+        self,
+        mode: str = 'chunk',
+        hidden_size: int = 1024,
+        num_heads: Optional[int] = None,
+        expand_ratio: Optional[int] = 128,
+        use_short_conv: bool = False,
+        conv_size: int = 4,
+        conv_bias: bool = False,
+        gate_low_rank_dim: int = 128,
+        elementwise_affine: Optional[bool] = True,
+        norm_eps: float = 1e-5,
+        layer_idx: int = None
+    ) -> LightNetAttention:
+        super().__init__()
+
+        self.mode = mode
+        self.hidden_size = hidden_size
+
+        if expand_ratio is None and num_heads is not None:
+            expand_ratio = hidden_size // num_heads
+        elif expand_ratio is not None and num_heads is None:
+            num_heads = hidden_size // expand_ratio
+        elif expand_ratio is None and num_heads is None:
+            raise RuntimeError("One of `expand_ratio` or `num_heads` should be provided.")
+        self.num_heads = num_heads
+        self.expand_ratio = expand_ratio
+
+        self.use_short_conv = use_short_conv
+        self.conv_size = conv_size
+        self.conv_bias = conv_bias
+
+        self.key_dim = int(self.num_heads * self.expand_ratio)
+        self.value_dim = hidden_size
+        self.gate_low_rank_dim = gate_low_rank_dim
+        self.layer_idx = layer_idx
+
+        assert mode in ['chunk', 'fused_chunk'], f"Not suppoerted mode `{mode}`."
+        assert self.key_dim % num_heads == 0, f"key dim must be divisible by num_heads of {num_heads}"
+        assert self.value_dim % num_heads == 0, f"value dim must be divisible by num_heads of {num_heads}"
+
+        self.head_f_dim = self.expand_ratio
+        self.head_i_dim = self.hidden_size // num_heads
+
+        self.q_proj = nn.Linear(hidden_size, self.key_dim, bias=False)
+        self.k_proj = nn.Linear(hidden_size, self.key_dim, bias=False)
+        self.v_proj = nn.Linear(hidden_size, self.value_dim, bias=False)
+
+        if use_short_conv:
+            self.conv_size = conv_size
+            self.q_conv1d = ShortConvolution(self.key_dim, conv_size, activation=None)
+            self.k_conv1d = ShortConvolution(self.key_dim, conv_size, activation=None)
+            self.v_conv1d = ShortConvolution(self.value_dim, conv_size, activation=None)
+
+        self.g_proj = nn.Sequential(
+            nn.Linear(hidden_size, gate_low_rank_dim, bias=False),
+            nn.Linear(gate_low_rank_dim, hidden_size, bias=False)
+        )
+        self.g_norm = FusedRMSNormGated(
+            hidden_size=hidden_size,
+            elementwise_affine=elementwise_affine,
+            eps=norm_eps
+        )
+        self.o_proj = nn.Linear(self.value_dim, hidden_size, bias=False)
+
+    def forward(
+        self,
+        hidden_states: torch.Tensor,
+        attention_mask: Optional[torch.Tensor] = None,
+        past_key_values: Optional[Cache] = None,
+        use_cache: Optional[bool] = False,
+        output_attentions: Optional[bool] = False,
+        **kwargs: Unpack[Dict]
+    ) -> Tuple[torch.Tensor, Optional[torch.Tensor], Optional[Cache]]:
+        if attention_mask is not None:
+            assert len(attention_mask.shape) == 2, (
+                "Expected attention_mask as a 0-1 matrix with shape [batch_size, seq_len] "
+                "for padding purposes (0 indicating padding). "
+                "Arbitrary attention masks of shape [batch_size, seq_len, seq_len] are not allowed."
+            )
+
+        # launching the triton kernel for just one token will actually be slower
+        mode = 'fused_recurrent' if hidden_states.shape[1] <= 64 else self.mode
+
+        last_state = None
+        if past_key_values is not None and len(past_key_values) > self.layer_idx:
+            last_state = past_key_values[self.layer_idx]
+
+        cu_seqlens = kwargs.get('cu_seqlens', None)
+        if self.use_short_conv:
+            conv_state_q, conv_state_k, conv_state_v = None, None, None
+            if last_state is not None:
+                conv_state_q, conv_state_k, conv_state_v = last_state['conv_state']
+            conv_mask = attention_mask[:, -hidden_states.shape[1]:] if attention_mask is not None else None
+            q, conv_state_q = self.q_conv1d(
+                x=self.q_proj(hidden_states),
+                mask=conv_mask,
+                cache=conv_state_q,
+                output_final_state=use_cache,
+                cu_seqlens=cu_seqlens
+            )
+            k, conv_state_k = self.k_conv1d(
+                x=self.k_proj(hidden_states),
+                mask=conv_mask,
+                cache=conv_state_k,
+                output_final_state=use_cache,
+                cu_seqlens=cu_seqlens
+            )
+            v, conv_state_v = self.v_conv1d(
+                x=self.v_proj(hidden_states),
+                mask=conv_mask,
+                cache=conv_state_v,
+                output_final_state=use_cache,
+                cu_seqlens=cu_seqlens
+            )
+        else:
+            q = self.q_proj(hidden_states)
+            k = self.k_proj(hidden_states)
+            v = self.v_proj(hidden_states)
+
+        # dealing with left-padding
+        if attention_mask is not None:
+            v = v.mul_(attention_mask[:, -v.shape[-2]:, None])
+
+        q = F.silu(q)
+        q, k = map(lambda x: rearrange(x, '... (h d) -> ... h d', d=self.head_f_dim), (q, k))
+        v = rearrange(v, '... (h d) -> ... h d', d=self.head_i_dim)
+        # TODO: this 2 steps took huge amount of time, which should be optimized
+        z = k.float().logcumsumexp(1)
+
+        if cu_seqlens is not None:
+            raise NotImplementedError("LightNet does not support variable-length sequences for now.")
+        k, g = torch.exp(k - z).to(k.dtype), (torch.cat((z[:, :1], z[:, :-1]), 1) - z).to(k.dtype)
+
+        recurrent_state = last_state['recurrent_state'] if last_state is not None else None
+        if mode == 'fused_recurrent':
+            o, recurrent_state = fused_recurrent_gla(
+                q=q,
+                k=k,
+                v=v,
+                gk=g,
+                initial_state=recurrent_state,
+                output_final_state=use_cache,
+                cu_seqlens=cu_seqlens,
+                head_first=False
+            )
+        elif mode == 'chunk':
+            o, recurrent_state = chunk_gla(
+                q=q,
+                k=k,
+                v=v,
+                g=g,
+                initial_state=recurrent_state,
+                output_final_state=use_cache,
+                cu_seqlens=cu_seqlens,
+                head_first=False
+            )
+        else:
+            raise NotImplementedError(f"Not supported mode `{mode}`.")
+
+        if past_key_values is not None:
+            past_key_values.update(
+                recurrent_state=recurrent_state,
+                conv_state=(conv_state_q, conv_state_k, conv_state_v) if self.use_short_conv else None,
+                layer_idx=self.layer_idx,
+                offset=q.shape[1]
+            )
+
+        o = rms_norm_swish_gate_linear(
+            rearrange(o, 'b t h d -> b t (h d)'),
+            self.g_proj(hidden_states),
+            self.g_norm.weight,
+            self.g_norm.bias,
+            self.o_proj.weight,
+            self.o_proj.bias
+        )
+        return o, None, past_key_values
+
+    def state_size(self, **kwargs) -> int:
+        state_size = self.key_dim * self.head_i_dim
+        for module in self.children():
+            if isinstance(module, ShortConvolution):
+                state_size += module.state_size
+        return state_size

fla/layers/linear_attn.py

@@ -0,0 +1,166 @@
+# -*- coding: utf-8 -*-
+# Copyright (c) 2023-2025, Songlin Yang, Yu Zhang
+
+from typing import Optional
+
+import torch
+import torch.nn as nn
+import torch.nn.functional as F
+from einops import rearrange, repeat
+
+from fla.modules import RMSNorm
+from fla.modules.feature_map import DPFPFeatureMap, HadamardFeatureMap, HedgehogFeatureMap, T2RFeatureMap
+from fla.ops.linear_attn import chunk_linear_attn, fused_chunk_linear_attn, fused_recurrent_linear_attn
+
+
+class LinearAttention(nn.Module):
+
+    def __init__(
+        self,
+        mode: str = 'chunk',
+        hidden_size: str = 1024,
+        expand_k: int = 1.0,
+        expand_v: int = 1.0,
+        num_heads: int = 8,
+        num_kv_heads: Optional[int] = None,
+        feature_map: str = 'elementwise_product',
+        tie_feature_map_qk: bool = False,
+        output_norm: str = 'rmsnorm',
+        norm_q: bool = False,
+        norm_k: bool = False,
+        do_feature_map_norm: bool = False,
+        elementwise_affine: bool = True,
+        norm_eps: float = 1e-5,
+        **kwargs
+    ):
+        super().__init__()
+
+        self.hidden_size = hidden_size
+        self.mode = mode
+        self.num_heads = num_heads
+        self.num_kv_heads = num_kv_heads if num_kv_heads is not None else num_heads
+        self.num_kv_groups = self.num_heads // self.num_kv_heads
+        self.key_dim = int(hidden_size * expand_k)
+        self.value_dim = int(hidden_size * expand_v)
+        self.key_dim_per_group = self.key_dim // self.num_kv_groups
+        self.value_dim_per_group = self.value_dim // self.num_kv_groups
+
+        assert mode in ['chunk', 'fused_chunk', 'fused_recurrent'], f"Not suppoerted mode `{mode}`."
+        assert self.key_dim % num_heads == 0, f"key dim must be divisible by num_heads of {num_heads}"
+        assert self.value_dim % num_heads == 0, f"value dim must be divisible by num_heads of {num_heads}"
+
+        self.head_k_dim = self.key_dim // num_heads
+        self.head_v_dim = self.value_dim // num_heads
+        self.do_feature_map_norm = do_feature_map_norm
+
+        if feature_map == 'hedgehog':
+            if tie_feature_map_qk:
+                self.feature_map_q = self.feature_map_k = HedgehogFeatureMap(head_dim=self.head_k_dim)
+            else:
+                self.feature_map_q = HedgehogFeatureMap(head_dim=self.head_k_dim)
+                self.feature_map_k = HedgehogFeatureMap(head_dim=self.head_k_dim)
+
+        elif feature_map == 't2r':
+            if tie_feature_map_qk:
+                self.feature_map_q = self.feature_map_k = T2RFeatureMap(head_dim=self.head_k_dim)
+            else:
+                self.feature_map_q = T2RFeatureMap(head_dim=self.head_k_dim)
+                self.feature_map_k = T2RFeatureMap(head_dim=self.head_k_dim)
+
+        elif feature_map == 'elementwise_product':
+            if tie_feature_map_qk:
+                self.feature_map_q = self.feature_map_k = HadamardFeatureMap(head_dim=self.head_k_dim)
+            else:
+                self.feature_map_q = HadamardFeatureMap(head_dim=self.head_k_dim)
+                self.feature_map_k = HadamardFeatureMap(head_dim=self.head_k_dim)
+
+        elif feature_map == 'dpfp':
+            self.feature_map_q = DPFPFeatureMap(head_dim=self.head_k_dim)
+            self.feature_map_k = DPFPFeatureMap(head_dim=self.head_k_dim)
+
+        elif feature_map == 'elu':
+            def elu(x):
+                return F.elu(x) + 1
+            self.feature_map_q = elu
+            self.feature_map_k = elu
+
+        elif feature_map == 'relu':
+            self.feature_map_q = nn.ReLU()
+            self.feature_map_k = nn.ReLU()
+
+        elif feature_map == 'identity':
+            self.feature_map_q = nn.Identity()
+            self.feature_map_k = nn.Identity()
+        else:
+            raise NotImplementedError(f"Not supported feature map `{feature_map}`.")
+
+        self.q_proj = nn.Linear(hidden_size, self.key_dim, bias=False)
+        self.k_proj = nn.Linear(hidden_size, self.key_dim_per_group, bias=False)
+        self.v_proj = nn.Linear(hidden_size, self.value_dim_per_group, bias=False)
+
+        if output_norm == 'rmsnorm':
+            self.norm = RMSNorm(hidden_size=self.head_v_dim, elementwise_affine=elementwise_affine, eps=norm_eps)
+        elif output_norm == 'identity':
+            self.norm = nn.Identity()
+        else:
+            raise NotImplementedError(f"Not supported output norm `{output_norm}`.")
+
+        self.o_proj = nn.Linear(self.value_dim, hidden_size, bias=False)
+
+        self.norm_q = norm_q
+        self.norm_k = norm_k
+
+    def forward(
+        self,
+        hidden_states: torch.Tensor,
+        **kwargs
+    ) -> torch.Tensor:
+        mode = self.mode
+        q = self.q_proj(hidden_states)
+        k = self.k_proj(hidden_states)
+        v = self.v_proj(hidden_states)
+
+        q = rearrange(q, '... (h d) -> ... h d', d=self.head_k_dim)
+        if self.num_kv_groups > 1:
+            k = repeat(k, '... (h d) -> ... (h g) d', d=self.head_k_dim, g=self.num_kv_groups)
+            v = repeat(v, '... (h d) -> ... (h g) d', d=self.head_v_dim, g=self.num_kv_groups)
+        else:
+            k = rearrange(k, '... (h d) -> ... h d', d=self.head_k_dim)
+            v = rearrange(v, '... (h d) -> ... h d', d=self.head_v_dim)
+
+        q = self.feature_map_q(q)
+        k = self.feature_map_k(k)
+
+        if self.norm_q:
+            q = q / (q.sum(-1, True) + 1e-4)
+        if self.norm_k:
+            k = k / (k.sum(-1, True) + 1e-4)
+
+        if mode == 'chunk':
+            o, final_state = chunk_linear_attn(
+                q=q,
+                k=k,
+                v=v,
+                normalize=self.do_feature_map_norm,
+                head_first=False
+            )
+        elif mode == 'fused_chunk':
+            o, final_state = fused_chunk_linear_attn(
+                q=q,
+                k=k,
+                v=v,
+                normalize=self.do_feature_map_norm,
+            )
+        elif mode == 'fused_recurrent':
+            o, final_state = fused_recurrent_linear_attn(
+                q=q,
+                k=k,
+                v=v,
+                normalize=self.do_feature_map_norm,
+            )
+        else:
+            raise NotImplementedError
+        o = self.norm(o)
+        o = rearrange(o, '... h d -> ... (h d)')
+        o = self.o_proj(o)
+        return o

fla/layers/multiscale_retention.py

@@ -0,0 +1,298 @@
+# -*- coding: utf-8 -*-
+# Copyright (c) 2023-2025, Songlin Yang, Yu Zhang
+
+from __future__ import annotations
+
+from typing import TYPE_CHECKING, Optional, Tuple
+
+import torch
+import torch.nn as nn
+from einops import rearrange, repeat
+from transformers.activations import ACT2FN
+
+from fla.modules import FusedRMSNormGated, RMSNorm, ShortConvolution
+from fla.modules.rotary import RotaryEmbedding
+from fla.ops.retention import chunk_retention, fused_chunk_retention, fused_recurrent_retention, parallel_retention
+
+if TYPE_CHECKING:
+    from fla.models.utils import Cache
+
+
+class MultiScaleRetention(nn.Module):
+    r"""
+    The layer implementaion for [Retentive Network: A Successor to Transformer for Large Language Models](https://arxiv.org/pdf/2307.08621.pdf).  # noqa
+
+    Args:
+        mode (str, Optional):
+            Which Retention kernel to use.
+            Currently available: `chunk`, `fused_recurrent`, `parallel`, and `fused_chunk`.
+            Default: `chunk`.
+        hidden_size (int, Optional):
+            The hidden size of the input. Default: 1024.
+        expand_k (float, Optional):
+            The expansion ratio for the key dim. Default: 1.0.
+        expand_v (float, Optional):
+            The expansion ratio for the value dim. Default: 2.0.
+        num_heads (int, Optional):
+            The number of heads. Default: 8.
+        num_kv_heads (int, Optional):
+            The number of key/value heads, used for MQA. Default: None.
+        feature_map (str, Optional):
+            Feature map function applied to queries/keys. Default: None.
+        use_short_conv (bool, Optional):
+            Whether to use short convolutions. Default: `False`.
+        conv_size (int, Optional):
+            The kernel size of the short convolution, only used when `use_short_conv` is `True`. Default: 4.
+        conv_bias (bool, Optional):
+            Whether to use bias in the short convolution, only used when `use_short_conv` is `True`. Default: `False`.
+        use_output_gate (bool, Optional):
+            Whether to use output gate. Default: `True`.
+        gate_fn (str, Optional):
+            The activation function for the output gate. Default: `swish`.
+        elementwise_affine (bool, Optional):
+            If `True`, applies elementwise affine to LayerNorm with learnable parameters. Default: `True`.
+        norm_eps (float, Optional):
+            The epsilon value for the layernorm/rmsnorm layer. Default: 1e-5.
+        fuse_norm (bool, Optional):
+            Whether to fuse the norm and the output gate for better memory footprint. Default: `True`.
+        layer_idx (int, Optional):
+            The index of the layer. Default: None.
+    """
+
+    def __init__(
+        self,
+        mode: str = 'chunk',
+        hidden_size: int = 1024,
+        expand_k: float = 1.0,
+        expand_v: float = 2.0,
+        num_heads: int = 8,
+        num_kv_heads: Optional[int] = None,
+        feature_map: Optional[str] = None,
+        use_short_conv: bool = False,
+        conv_size: int = 4,
+        conv_bias: bool = False,
+        use_output_gate: bool = True,
+        gate_fn: str = 'swish',
+        elementwise_affine: Optional[bool] = True,
+        norm_eps: float = 1e-5,
+        fuse_norm: bool = True,
+        layer_idx: int = None,
+        **kwargs
+    ) -> MultiScaleRetention:
+        super().__init__()
+
+        self.mode = mode
+        self.hidden_size = hidden_size
+        self.expand_k = expand_k
+        self.expand_v = expand_v
+        self.num_heads = num_heads
+        self.num_kv_heads = num_kv_heads if num_kv_heads is not None else num_heads
+        self.num_kv_groups = self.num_heads // self.num_kv_heads
+        self.feature_map_fn = ACT2FN[feature_map] if feature_map is not None else None
+
+        self.use_short_conv = use_short_conv
+        self.conv_size = conv_size
+        self.conv_bias = conv_bias
+        self.use_output_gate = use_output_gate
+
+        self.key_dim = int(hidden_size * expand_k)
+        self.value_dim = int(hidden_size * expand_v)
+        self.key_dim_per_group = self.key_dim // self.num_kv_groups
+        self.value_dim_per_group = self.value_dim // self.num_kv_groups
+        self.layer_idx = layer_idx
+
+        assert mode in ['chunk', 'fused_chunk', 'parallel', 'fused_recurrent'], f"Not suppoerted mode `{mode}`."
+        assert self.key_dim % num_heads == 0, f"key dim must be divisible by num_heads of {num_heads}"
+        assert self.value_dim % num_heads == 0, f"value dim must be divisible by num_heads of {num_heads}"
+
+        self.head_k_dim = self.key_dim // num_heads
+        self.head_v_dim = self.value_dim // num_heads
+
+        self.q_proj = nn.Linear(hidden_size, self.key_dim, bias=False)
+        self.k_proj = nn.Linear(hidden_size, self.key_dim_per_group, bias=False)
+        self.v_proj = nn.Linear(hidden_size, self.value_dim_per_group, bias=False)
+        if self.use_output_gate:
+            self.g_proj = nn.Linear(hidden_size, self.value_dim, bias=False)
+
+        if use_short_conv:
+            self.conv_size = conv_size
+            self.q_conv1d = ShortConvolution(self.key_dim, conv_size, activation='silu')
+            self.k_conv1d = ShortConvolution(self.key_dim_per_group, conv_size, activation='silu')
+            self.v_conv1d = ShortConvolution(self.value_dim_per_group, conv_size, activation='silu')
+
+        self.o_proj = nn.Linear(self.value_dim, hidden_size, bias=False)
+
+        if gate_fn == 'swish' and fuse_norm and use_output_gate:
+            self.g_norm_swish_gate = FusedRMSNormGated(
+                hidden_size=self.head_v_dim,
+                elementwise_affine=elementwise_affine,
+                eps=norm_eps
+            )
+            self.fuse_norm_and_gate = True
+        else:
+            self.fuse_norm_and_gate = False
+            self.g_norm = RMSNorm(
+                hidden_size=self.head_v_dim,
+                elementwise_affine=elementwise_affine,
+                eps=norm_eps
+            )
+            self.gate_fn = ACT2FN[gate_fn]
+
+        # TODO: fix this issue
+        # https://github.com/Dao-AILab/flash-attention/blob/main/flash_attn/ops/triton/rotary.py#L180
+        # Ideally, we would want to support arbitrary d_head_qk
+        assert self.head_k_dim <= 256, "head_k_dim must be less than or equal to 256"
+        self.rotary = RotaryEmbedding(dim=self.head_k_dim)
+
+    def forward(
+        self,
+        hidden_states: torch.Tensor,
+        attention_mask: Optional[torch.Tensor] = None,
+        past_key_values: Optional[Cache] = None,
+        use_cache: Optional[bool] = False,
+        output_attentions: Optional[bool] = False,
+        **kwargs
+    ) -> Tuple[torch.Tensor, Optional[torch.Tensor], Optional[Cache]]:
+        if attention_mask is not None:
+            assert len(attention_mask.shape) == 2, (
+                "Expected attention_mask as a 0-1 matrix with shape [batch_size, seq_len] "
+                "for padding purposes (0 indicating padding). "
+                "Arbitrary attention masks of shape [batch_size, seq_len, seq_len] are not allowed."
+            )
+
+        # launching the triton kernel for just one token will actually be slower
+        mode = 'fused_recurrent' if hidden_states.shape[1] <= 64 else self.mode
+
+        last_state = None
+        if past_key_values is not None and len(past_key_values) > self.layer_idx:
+            last_state = past_key_values[self.layer_idx]
+
+        cu_seqlens = kwargs.get('cu_seqlens', None)
+        if self.use_short_conv:
+            conv_state_q, conv_state_k, conv_state_v = None, None, None
+            if last_state is not None:
+                conv_state_q, conv_state_k, conv_state_v = last_state['conv_state']
+            conv_mask = attention_mask[:, -hidden_states.shape[1]:] if attention_mask is not None else None
+            q, conv_state_q = self.q_conv1d(
+                x=self.q_proj(hidden_states),
+                mask=conv_mask,
+                cache=conv_state_q,
+                output_final_state=use_cache,
+                cu_seqlens=cu_seqlens
+            )
+            k, conv_state_k = self.k_conv1d(
+                x=self.k_proj(hidden_states),
+                mask=conv_mask,
+                cache=conv_state_k,
+                output_final_state=use_cache,
+                cu_seqlens=cu_seqlens
+            )
+            v, conv_state_v = self.v_conv1d(
+                x=self.v_proj(hidden_states),
+                mask=conv_mask,
+                cache=conv_state_v,
+                output_final_state=use_cache,
+                cu_seqlens=cu_seqlens
+            )
+        else:
+            q = self.q_proj(hidden_states)
+            k = self.k_proj(hidden_states)
+            v = self.v_proj(hidden_states)
+
+        # dealing with left-padding
+        if attention_mask is not None:
+            v = v.mul_(attention_mask[:, -v.shape[-2]:, None])
+        q = rearrange(q, '... (h d) -> ... h d', d=self.head_k_dim)
+        k = rearrange(k, '... (h d) -> ... h d', d=self.head_k_dim)
+        if self.feature_map_fn is not None:
+            q, k = map(self.feature_map_fn, (q, k))
+
+        seqlen_offset, max_seqlen = 0, q.shape[1]
+        if past_key_values is not None:
+            seqlen_offset = past_key_values.get_seq_length(self.layer_idx)
+            max_seqlen = q.shape[1] + seqlen_offset
+
+            if attention_mask is not None:
+                # to deliminate the offsets of padding tokens
+                seqlen_offset = seqlen_offset + attention_mask.sum(-1) - attention_mask.shape[-1]
+                max_seqlen = q.shape[1] + max(seqlen_offset)
+
+        q, k = self.rotary(q, k, seqlen_offset=seqlen_offset, max_seqlen=max_seqlen, cu_seqlens=cu_seqlens)
+
+        if self.num_kv_groups > 1:
+            k = repeat(k, 'b t h d -> b t (h g) d', g=self.num_kv_groups)
+            v = repeat(v, 'b t (h d) -> b t (h g) d', d=self.head_v_dim, g=self.num_kv_groups)
+        else:
+            v = rearrange(v, 'b t (h d) -> b t h d', d=self.head_v_dim)
+
+        recurrent_state = last_state['recurrent_state'] if last_state is not None else None
+        if mode == 'chunk':
+            o, recurrent_state = chunk_retention(
+                q=q,
+                k=k,
+                v=v,
+                initial_state=recurrent_state,
+                output_final_state=use_cache,
+                cu_seqlens=cu_seqlens,
+                head_first=False
+            )
+        elif mode == 'fused_chunk':
+            o, recurrent_state = fused_chunk_retention(
+                q=q,
+                k=k,
+                v=v,
+                initial_state=recurrent_state,
+                output_final_state=use_cache,
+                cu_seqlens=cu_seqlens,
+                head_first=False
+            )
+        elif mode == 'parallel':
+            o, recurrent_state = parallel_retention(
+                q=q,
+                k=k,
+                v=v,
+                cu_seqlens=cu_seqlens,
+                head_first=False
+            )
+        elif mode == 'fused_recurrent':
+            o, recurrent_state = fused_recurrent_retention(
+                q=q,
+                k=k,
+                v=v,
+                initial_state=recurrent_state,
+                output_final_state=use_cache,
+                cu_seqlens=cu_seqlens,
+                head_first=False
+            )
+        else:
+            raise NotImplementedError(f"Not supported mode `{mode}`.")
+
+        if past_key_values is not None:
+            past_key_values.update(
+                recurrent_state=recurrent_state,
+                conv_state=(conv_state_q, conv_state_k, conv_state_v) if self.use_short_conv else None,
+                layer_idx=self.layer_idx,
+                offset=q.shape[1]
+            )
+
+        if self.use_output_gate:
+            g = self.g_proj(hidden_states)
+            if self.fuse_norm_and_gate:
+                g = rearrange(g, 'b t (h d) -> b t h d', d=self.head_v_dim)
+                o = self.g_norm_swish_gate(o, g)
+                o = rearrange(o, 'b t h d -> b t (h d)')
+            else:
+                o = rearrange(self.g_norm(o), 'b t h d -> b t (h d)')
+                o = o * self.gate_fn(g)
+        else:
+            o = rearrange(self.g_norm(o), 'b t h d -> b t (h d)')
+        o = self.o_proj(o)
+
+        return o, None, past_key_values
+
+    def state_size(self, **kwargs) -> int:
+        state_size = self.key_dim * self.head_v_dim
+        for module in self.children():
+            if isinstance(module, ShortConvolution):
+                state_size += module.state_size
+        return state_size

fla/layers/nsa.py

@@ -0,0 +1,138 @@
+# -*- coding: utf-8 -*-
+# Copyright (c) 2023-2025, Songlin Yang, Yu Zhang
+
+from __future__ import annotations
+
+from typing import TYPE_CHECKING, Optional, Tuple, Union
+
+import torch
+import torch.nn as nn
+from einops import rearrange
+from transformers.utils import logging
+
+from fla.modules import RotaryEmbedding
+from fla.ops.nsa.parallel import parallel_nsa
+
+if TYPE_CHECKING:
+    from fla.models.utils import Cache
+
+logger = logging.get_logger(__name__)
+
+
+class NativeSparseAttention(nn.Module):
+
+    def __init__(
+        self,
+        hidden_size: int = 2048,
+        num_heads: int = 64,
+        num_kv_heads: Optional[int] = 4,
+        head_dim: int = 64,
+        qkv_bias: bool = False,
+        block_size: Optional[int] = 64,
+        block_counts: Optional[Union[torch.LongTensor, int]] = 16,
+        window_size: Optional[int] = 512,
+        rope_theta: Optional[float] = 10000.,
+        max_position_embeddings: Optional[int] = None,
+        layer_idx: int = None
+    ):
+        super().__init__()
+
+        self.hidden_size = hidden_size
+        self.num_heads = num_heads
+        if num_kv_heads is None:
+            self.num_kv_heads = self.num_heads
+        else:
+            self.num_kv_heads = num_kv_heads
+        self.num_kv_groups = num_heads // self.num_kv_heads
+        self.head_dim = head_dim
+        self.kv_dim = self.num_kv_heads * self.head_dim
+        self.qkv_bias = qkv_bias
+
+        self.block_size = block_size
+        self.block_counts = block_counts
+        self.window_size = window_size
+        self.rope_theta = rope_theta
+        self.max_position_embeddings = max_position_embeddings
+        self.layer_idx = layer_idx
+
+        self.q_proj = nn.Linear(self.hidden_size, self.num_heads * self.head_dim, bias=self.qkv_bias)
+        self.k_proj = nn.Linear(self.hidden_size, self.kv_dim, bias=self.qkv_bias)
+        self.v_proj = nn.Linear(self.hidden_size, self.kv_dim, bias=self.qkv_bias)
+        self.g_proj = nn.Linear(self.hidden_size, self.num_heads * 3, bias=False)
+        self.o_proj = nn.Linear(self.num_heads * self.head_dim, self.hidden_size, bias=False)
+
+        self.rotary = RotaryEmbedding(dim=self.head_dim, base=self.rope_theta)
+
+    def forward(
+        self,
+        hidden_states: torch.Tensor,
+        attention_mask: Optional[torch.LongTensor] = None,
+        past_key_values: Optional[Cache] = None,
+        output_attentions: bool = False,
+        use_cache: bool = False,
+        **kwargs,
+    ) -> Tuple[torch.Tensor, Optional[torch.Tensor], Optional[Tuple[torch.Tensor]]]:
+        if attention_mask is not None:
+            assert len(attention_mask.shape) == 2, (
+                "Expected attention_mask as a 0-1 matrix with shape [batch_size, seq_len] "
+                "for padding purposes (0 indicating padding). "
+                "Arbitrary attention masks of shape [batch_size, seq_len, seq_len] are not allowed."
+            )
+
+        batch_size, seq_len, _ = hidden_states.size()
+
+        q = rearrange(self.q_proj(hidden_states), '... (h d) -> ... h d', d=self.head_dim)
+        k = rearrange(self.k_proj(hidden_states), '... (h d) -> ... h d', d=self.head_dim)
+        v = rearrange(self.v_proj(hidden_states), '... (h d) -> ... h d', d=self.head_dim)
+        g = rearrange(self.g_proj(hidden_states), '... (h d) -> ... h d', d=3)
+        g_cmp, g_slc, g_swa = g.sigmoid().unbind(-1)
+
+        cu_seqlens = kwargs.get('cu_seqlens', None)
+
+        seqlen_offset, max_seqlen = 0, seq_len
+        if past_key_values is not None:
+            seqlen_offset = past_key_values.get_seq_length(self.layer_idx)
+            max_seqlen = q.shape[1] + seqlen_offset
+
+            if attention_mask is not None:
+                # to deliminate the offsets of padding tokens
+                seqlen_offset = seqlen_offset + attention_mask.sum(-1) - attention_mask.shape[-1]
+                max_seqlen = q.shape[1] + max(seqlen_offset)
+
+        if self.max_position_embeddings is not None:
+            max_seqlen = max(max_seqlen, self.max_position_embeddings)
+        q, k = self.rotary(q, k, seqlen_offset=seqlen_offset, max_seqlen=max_seqlen, cu_seqlens=cu_seqlens)
+
+        if past_key_values is not None:
+            cache_has_content = past_key_values.get_seq_length(self.layer_idx) > 0
+            k_cached, v_cached = past_key_values.update(
+                attn_state=(k.flatten(-2, -1), v.flatten(-2, -1)),
+                layer_idx=self.layer_idx,
+                offset=seq_len,
+                cache_kwargs=dict(window_size=self.window_size)
+            )['attn_state']
+            if cache_has_content:
+                k, v = k_cached, v_cached
+                k = rearrange(k, '... (h d) -> ... h d', d=self.head_dim)
+                v = rearrange(v, '... (h d) -> ... h d', d=self.head_dim)
+
+        o = parallel_nsa(
+            q=q,
+            k=k,
+            v=v,
+            g_cmp=g_cmp,
+            g_slc=g_slc,
+            g_swa=g_swa,
+            block_size=self.block_size,
+            block_counts=self.block_counts,
+            window_size=self.window_size,
+            cu_seqlens=cu_seqlens,
+            head_first=False
+        )
+        o = o.reshape(batch_size, seq_len, -1)
+        o = self.o_proj(o)
+
+        if not output_attentions:
+            attentions = None
+
+        return o, attentions, past_key_values

fla/layers/rwkv6.py

@@ -0,0 +1,307 @@
+# -*- coding: utf-8 -*-
+# Copyright (c) 2023-2025, Songlin Yang, Yu Zhang
+
+# "Eagle and Finch: RWKV with Matrix-Valued States and Dynamic Recurrence"[https://arxiv.org/abs/2404.05892]
+
+from __future__ import annotations
+
+from typing import TYPE_CHECKING, Optional, Tuple
+
+import torch
+import torch.nn as nn
+from einops import rearrange
+
+from fla.modules import GroupNorm
+from fla.modules.activations import ACT2FN
+from fla.ops.rwkv6 import chunk_rwkv6, fused_recurrent_rwkv6
+
+if TYPE_CHECKING:
+    from fla.models.utils import Cache
+
+
+class RWKV6Attention(nn.Module):
+
+    def __init__(
+        self,
+        mode: str = 'chunk',
+        hidden_size: int = 1024,
+        expand_k: float = 0.5,
+        expand_v: float = 1.0,
+        num_heads: int = 4,
+        gate_fn: str = 'swish',
+        proj_low_rank_dim: int = 32,
+        gate_low_rank_dim: int = 64,
+        fuse_norm: bool = True,
+        elementwise_affine: Optional[bool] = True,
+        norm_eps: float = 1e-5,
+        layer_idx: int = None,
+        **kwargs
+    ) -> RWKV6Attention:
+        super().__init__()
+
+        self.mode = mode
+        self.hidden_size = hidden_size
+        self.expand_k = expand_k
+        self.expand_v = expand_v
+        self.num_heads = num_heads
+        self.proj_low_rank_dim = proj_low_rank_dim
+        self.gate_low_rank_dim = gate_low_rank_dim
+
+        self.key_dim = int(hidden_size * expand_k)
+        self.value_dim = int(hidden_size * expand_v)
+        self.layer_idx = layer_idx
+
+        assert mode in ['chunk', 'fused_recurrent'], f"Not suppoerted mode `{mode}`."
+        assert self.key_dim % num_heads == 0, f"key dim must be divisible by num_heads of {num_heads}"
+        assert self.value_dim % num_heads == 0, f"value dim must be divisible by num_heads of {num_heads}"
+
+        self.head_k_dim = self.key_dim // num_heads
+        self.head_v_dim = self.value_dim // num_heads
+
+        self.time_shift = nn.ZeroPad2d((0, 0, 1, -1))
+        self.x_proj = nn.Sequential(
+            LerpLinear(hidden_size, proj_low_rank_dim * 5),
+            nn.Tanh(),
+            nn.Linear(proj_low_rank_dim * 5, hidden_size, bias=False)
+        )
+        self.x_bias = nn.Parameter(torch.zeros(5, hidden_size))
+
+        self.r_proj = DDLerpLinear(hidden_size, self.key_dim)
+        self.w_proj = DDLerpLinear(hidden_size, self.key_dim, low_rank_dim=gate_low_rank_dim)
+        self.k_proj = DDLerpLinear(hidden_size, self.key_dim)
+        self.v_proj = DDLerpLinear(hidden_size, self.value_dim)
+        self.g_proj = DDLerpLinear(hidden_size, self.value_dim)
+        self.bonus = nn.Parameter(torch.zeros(num_heads, self.head_k_dim))
+
+        # TODO: fuse GroupNorm and output gate
+        self.g_norm = GroupNorm(self.num_heads, self.value_dim, elementwise_affine=elementwise_affine, bias=True, eps=norm_eps)
+        self.o_proj = nn.Linear(self.value_dim, hidden_size, bias=False)
+        self.gate_fn = ACT2FN[gate_fn]
+
+        self.apply(self._initialize_weights)
+
+    def _initialize_weights(self, module: nn.Module):
+        if getattr(module, "_is_hf_initialized", False):
+            return
+        if isinstance(module, nn.Linear):
+            nn.init.xavier_uniform_(module.weight, gain=2 ** -2.5)
+            if module.bias is not None:
+                nn.init.zeros_(module.bias)
+        if isinstance(module, nn.Parameter):
+            nn.init.xavier_uniform_(module, gain=2 ** -2.5)
+        module._is_hf_initialized = True
+
+    def forward(
+        self,
+        hidden_states: torch.Tensor,
+        attention_mask: Optional[torch.Tensor] = None,
+        past_key_values: Optional[Cache] = None,
+        use_cache: Optional[bool] = False,
+        output_attentions: Optional[bool] = False,
+        **kwargs
+    ) -> Tuple[torch.Tensor, Optional[torch.Tensor], Optional[Cache]]:
+        if attention_mask is not None:
+            assert len(attention_mask.shape) == 2, (
+                "Expected attention_mask as a 0-1 matrix with shape [batch_size, seq_len] "
+                "for padding purposes (0 indicating padding). "
+                "Arbitrary attention masks of shape [batch_size, seq_len, seq_len] are not allowed."
+            )
+
+        batch_size, seq_len, hidden_size = hidden_states.shape
+        # launching the triton kernel for just one token will actually be slower
+        mode = 'fused_recurrent' if hidden_states.shape[1] <= 64 else self.mode
+
+        last_state = None
+        if past_key_values is not None and len(past_key_values) > self.layer_idx:
+            last_state = past_key_values[self.layer_idx]
+
+        if attention_mask is not None:
+            hidden_states = hidden_states.mul_(attention_mask[:, -hidden_states.shape[-2]:, None])
+        if hidden_states.shape[1] == 1 and last_state is not None:
+            shifted = last_state['conv_state'].unsqueeze(1)
+        else:
+            shifted = self.time_shift(hidden_states)
+            if last_state is not None:
+                shifted[:, 0] = last_state['conv_state']
+
+        delta = shifted - hidden_states
+        x = self.x_proj[0](hidden_states, delta).view(batch_size, seq_len, -1, self.proj_low_rank_dim)
+        x = torch.einsum('b t n r, h n r-> b t n h', self.x_proj[1](x), self.x_proj[2].weight.view(hidden_size, 5, -1))
+
+        r, w, k, v, g = x.add_(self.x_bias).unbind(-2)
+        r = self.r_proj(hidden_states, r, delta)
+        w = self.w_proj(hidden_states, w, delta)
+        k = self.k_proj(hidden_states, k, delta)
+        v = self.v_proj(hidden_states, v, delta)
+        g = self.g_proj(hidden_states, g, delta)
+
+        # dealing with left-padding
+        if attention_mask is not None:
+            v = v.mul_(attention_mask[:, -v.shape[-2]:, None])
+        r, w, k = map(lambda x: rearrange(x, 'b t (h d) -> b t h d', d=self.head_k_dim), (r, w, k))
+        v = rearrange(v, 'b t (h d) -> b t h d', d=self.head_v_dim)
+        w = -torch.exp(w)
+        u = self.bonus
+
+        recurrent_state = last_state['recurrent_state'] if last_state is not None else None
+        cu_seqlens = kwargs.get('cu_seqlens', None)
+        if mode == 'fused_recurrent':
+            o, recurrent_state = fused_recurrent_rwkv6(
+                r=r,
+                k=k,
+                v=v,
+                w=w,
+                u=u,
+                scale=1.,
+                initial_state=recurrent_state,
+                output_final_state=use_cache,
+                cu_seqlens=cu_seqlens,
+                head_first=False
+            )
+        elif mode == 'chunk':
+            o, recurrent_state = chunk_rwkv6(
+                q=r,
+                k=k,
+                v=v,
+                g=w,
+                u=u,
+                scale=1.,
+                initial_state=recurrent_state,
+                output_final_state=use_cache,
+                cu_seqlens=cu_seqlens,
+                head_first=False
+            )
+        else:
+            raise NotImplementedError(f"Not supported mode `{mode}`.")
+
+        if past_key_values is not None:
+            past_key_values.update(
+                recurrent_state=recurrent_state,
+                conv_state=hidden_states[:, -1],
+                layer_idx=self.layer_idx,
+                offset=r.shape[2]
+            )
+
+        o = self.g_norm(rearrange(o, '... h d -> ... (h d)')) * self.gate_fn(g)
+        o = self.o_proj(o)
+
+        return o, None, past_key_values
+
+
+class LoRA(nn.Module):
+
+    def __init__(
+        self,
+        input_dim: int,
+        output_dim: int,
+        low_rank_dim: int,
+        bias: Optional[bool] = True,
+        activation: Optional[str] = 'tanh'
+    ):
+        super().__init__()
+
+        self.input_dim = input_dim
+        self.output_dim = output_dim
+        self.low_rank_dim = low_rank_dim
+        self.bias = bias
+
+        if activation is None:
+            self.activation = nn.Identity()
+        elif activation == 'sigmoid':
+            self.activation = nn.Sigmoid()
+        elif activation == 'tanh':
+            self.activation = nn.Tanh()
+        elif activation == 'relu':
+            self.activation = nn.ReLU()
+        else:
+            raise ValueError(f"Not supported activation `{activation}`.")
+
+        self.lora = nn.Sequential(
+            nn.Linear(input_dim, low_rank_dim, bias=False),
+            self.activation,
+            nn.Linear(low_rank_dim, output_dim, bias=bias)
+        )
+
+    def __repr__(self) -> str:
+        s = f"{self.__class__.__name__}("
+        s += f"input_dim={self.input_dim}, low_rank_dim={self.low_rank_dim}, output_dim={self.output_dim}"
+        if not self.bias:
+            s += f", bias={self.bias}"
+        s += ")"
+        return s
+
+    def forward(self, x: torch.Tensor) -> torch.Tensor:
+        return self.lora(x)
+
+
+class LerpLinear(nn.Module):
+
+    def __init__(
+        self,
+        input_dim: int,
+        output_dim: int,
+        low_rank_dim: Optional[int] = None
+    ):
+        super().__init__()
+
+        self.input_dim = input_dim
+        self.output_dim = output_dim
+        self.low_rank_dim = low_rank_dim
+
+        self.time_shift = nn.ZeroPad2d((0, 0, 1, -1))
+        if low_rank_dim is None:
+            self.linear = nn.Linear(input_dim, output_dim, bias=False)
+        else:
+            self.linear = LoRA(input_dim, output_dim, low_rank_dim)
+        self.mu = nn.Parameter(torch.zeros(input_dim))
+
+    def __repr__(self) -> str:
+        s = f"{self.__class__.__name__}({self.input_dim}, {self.output_dim}"
+        if self.low_rank_dim is not None:
+            s += f", low_rank_dim={self.low_rank_dim}"
+        s += ")"
+        return s
+
+    def forward(self, x: torch.Tensor, delta: Optional[torch.Tensor] = None) -> torch.Tensor:
+        if delta is None:
+            shifted = self.time_shift(x)
+            if len(shifted.shape) == 2:
+                shifted = shifted.unsqueeze(1)
+            delta = shifted - x
+        return self.linear(x + delta * self.mu)
+
+
+class DDLerpLinear(nn.Module):
+
+    def __init__(
+        self,
+        input_dim: int,
+        output_dim: int,
+        low_rank_dim: Optional[int] = None
+    ):
+        super().__init__()
+
+        self.input_dim = input_dim
+        self.output_dim = output_dim
+        self.low_rank_dim = low_rank_dim
+
+        self.time_shift = nn.ZeroPad2d((0, 0, 1, -1))
+        if low_rank_dim is None:
+            self.linear = nn.Linear(input_dim, output_dim, bias=False)
+        else:
+            self.linear = LoRA(input_dim, output_dim, low_rank_dim)
+
+    def __repr__(self) -> str:
+        s = f"{self.__class__.__name__}({self.input_dim}, {self.output_dim}"
+        if self.low_rank_dim is not None:
+            s += f", low_rank_dim={self.low_rank_dim}"
+        s += ")"
+        return s
+
+    def forward(self, x: torch.Tensor, mu: torch.Tensor, delta: Optional[torch.Tensor] = None) -> torch.Tensor:
+        if delta is None:
+            shifted = self.time_shift(x)
+            if len(shifted.shape) == 2:
+                shifted = shifted.unsqueeze(1)
+            delta = shifted - x
+        return self.linear(x + delta * mu)

fla/layers/simple_gla.py

@@ -0,0 +1,261 @@
+# -*- coding: utf-8 -*-
+# Copyright (c) 2023-2025, Songlin Yang, Yu Zhang
+
+from __future__ import annotations
+
+from typing import TYPE_CHECKING, Optional, Tuple
+
+import torch
+import torch.nn as nn
+import torch.nn.functional as F
+from einops import rearrange, repeat
+
+from fla.modules import FusedRMSNormGated, RMSNorm, ShortConvolution
+from fla.modules.activations import ACT2FN
+from fla.ops.simple_gla import chunk_simple_gla, fused_recurrent_simple_gla
+
+if TYPE_CHECKING:
+    from fla.models.utils import Cache
+
+
+class SimpleGatedLinearAttention(nn.Module):
+    r"""
+    The layer implementaion for [Gated Linear Attention Transformers with Hardware-Efficient Training](https://arxiv.org/abs/2312.06635).  # noqa
+    This layer calls the simplified GLA kernel in which the gating is head-wise instead of elementwise.
+
+    Args:
+        mode (str, Optional):
+            Which GLA kernel to use.
+            Currently available: `chunk`.
+            Default: `chunk`.
+        hidden_size (int, Optional):
+            The hidden size of the input. Default: 1024.
+        expand_k (float, Optional):
+            The expansion ratio for the key dim. Default: 1.0.
+        expand_v (float, Optional):
+            The expansion ratio for the value dim. Default: 1.0.
+        num_heads (int, Optional):
+            The number of heads. Default: 4.
+        num_kv_heads (int, Optional):
+            The number of key/value heads, used for MQA. Default: None.
+        feature_map (str, Optional):
+            Feature map function applied to queries/keys. Default: None.
+        use_short_conv (bool, Optional):
+            Whether to use short convolutions. Default: `False`.
+        conv_size (int, Optional):
+            The kernel size of the short convolution, only used when `use_short_conv` is `True`. Default: 4.
+        conv_bias (bool, Optional):
+            Whether to use bias in the short convolution, only used when `use_short_conv` is `True`. Default: `False`.
+        gate_fn (str, Optional):
+            The activation function for the output gate. Default: `swish`.
+        elementwise_affine (bool, Optional):
+            If `True`, applies elementwise affine to LayerNorm with learnable parameters. Default: `True`.
+        norm_eps (float, Optional):
+            The epsilon value for the layernorm/rmsnorm layer. Default: 1e-5.
+        gate_logit_normalizer (int, Optional):
+            The normalizer for the gate logits, appied after `logsigmoid`. Default: 16.
+        fuse_norm (bool, Optional):
+            Whether to fuse the norm and the output gate for better memory footprint. Default: `True`.
+        layer_idx (int, Optional):
+            The index of the layer. Default: None.
+    """
+
+    def __init__(
+        self,
+        mode: str = 'chunk',
+        hidden_size: int = 1024,
+        expand_k: float = 1.,
+        expand_v: float = 1.,
+        num_heads: int = 4,
+        num_kv_heads: Optional[int] = None,
+        feature_map: Optional[str] = None,
+        use_short_conv: bool = True,
+        conv_size: int = 4,
+        conv_bias: bool = False,
+        gate_fn: str = 'swish',
+        elementwise_affine: Optional[bool] = True,
+        norm_eps: float = 1e-5,
+        gate_logit_normalizer: int = 16,
+        fuse_norm: bool = True,
+        layer_idx: int = None,
+    ) -> SimpleGatedLinearAttention:
+        super().__init__()
+
+        self.mode = mode
+        self.hidden_size = hidden_size
+        self.expand_k = expand_k
+        self.expand_v = expand_v
+        self.num_heads = num_heads
+        self.num_kv_heads = num_kv_heads if num_kv_heads is not None else num_heads
+        self.num_kv_groups = self.num_heads // self.num_kv_heads
+        self.feature_map_fn = ACT2FN[feature_map] if feature_map is not None else None
+
+        self.use_short_conv = use_short_conv
+        self.conv_size = conv_size
+        self.conv_bias = conv_bias
+
+        self.key_dim = int(hidden_size * expand_k)
+        self.value_dim = int(hidden_size * expand_v)
+        self.key_dim_per_group = self.key_dim // self.num_kv_groups
+        self.value_dim_per_group = self.value_dim // self.num_kv_groups
+        self.layer_idx = layer_idx
+
+        assert mode in ['chunk', "fused_recurrent"], f"Not suppoerted mode `{mode}`."
+        assert self.key_dim % num_heads == 0, f"key dim must be divisible by num_heads of {num_heads}"
+        assert self.value_dim % num_heads == 0, f"value dim must be divisible by num_heads of {num_heads}"
+
+        self.head_k_dim = self.key_dim // num_heads
+        self.head_v_dim = self.value_dim // num_heads
+
+        self.q_proj = nn.Linear(hidden_size, self.key_dim, bias=False)
+        self.k_proj = nn.Linear(hidden_size, self.key_dim_per_group, bias=False)
+        self.v_proj = nn.Linear(hidden_size, self.value_dim_per_group, bias=False)
+        self.g_proj = nn.Linear(hidden_size, self.value_dim, bias=False)
+
+        if use_short_conv:
+            self.conv_size = conv_size
+            self.q_conv1d = ShortConvolution(self.key_dim, conv_size, activation='silu')
+            self.k_conv1d = ShortConvolution(self.key_dim_per_group, conv_size, activation='silu')
+            self.v_conv1d = ShortConvolution(self.value_dim_per_group, conv_size, activation='silu')
+
+        self.gk_proj = nn.Linear(hidden_size, self.num_heads)
+
+        if gate_fn == 'swish' and fuse_norm:
+            self.g_norm_swish_gate = FusedRMSNormGated(
+                hidden_size=self.head_v_dim,
+                elementwise_affine=elementwise_affine,
+                eps=norm_eps
+            )
+            self.fuse_norm_and_gate = True
+        else:
+            self.fuse_norm_and_gate = False
+            self.g_norm = RMSNorm(
+                hidden_size=self.head_v_dim,
+                elementwise_affine=elementwise_affine,
+                eps=norm_eps
+            )
+            self.gate_fn = ACT2FN[gate_fn]
+        self.o_proj = nn.Linear(self.value_dim, hidden_size, bias=False)
+
+        self.gate_logit_normalizer = gate_logit_normalizer
+
+    def forward(
+        self,
+        hidden_states: torch.Tensor,
+        attention_mask: Optional[torch.Tensor] = None,
+        past_key_values: Optional[Cache] = None,
+        use_cache: Optional[bool] = False,
+        output_attentions: Optional[bool] = False,
+        **kwargs
+    ) -> Tuple[torch.Tensor, Optional[torch.Tensor], Optional[Cache]]:
+        if attention_mask is not None:
+            assert len(attention_mask.shape) == 2, (
+                "Expected attention_mask as a 0-1 matrix with shape [batch_size, seq_len] "
+                "for padding purposes (0 indicating padding). "
+                "Arbitrary attention masks of shape [batch_size, seq_len, seq_len] are not allowed."
+            )
+
+        # launching the triton kernel for just one token will actually be slower
+        mode = 'fused_recurrent' if hidden_states.shape[1] <= 64 else self.mode
+
+        last_state = None
+        if past_key_values is not None and len(past_key_values) > self.layer_idx:
+            last_state = past_key_values[self.layer_idx]
+
+        cu_seqlens = kwargs.get('cu_seqlens', None)
+        if self.use_short_conv:
+            conv_state_q, conv_state_k, conv_state_v = None, None, None
+            if last_state is not None:
+                conv_state_q, conv_state_k, conv_state_v = last_state['conv_state']
+            conv_mask = attention_mask[:, -hidden_states.shape[1]:] if attention_mask is not None else None
+            q, conv_state_q = self.q_conv1d(
+                x=self.q_proj(hidden_states),
+                mask=conv_mask,
+                cache=conv_state_q,
+                output_final_state=use_cache,
+                cu_seqlens=cu_seqlens
+            )
+            k, conv_state_k = self.k_conv1d(
+                x=self.k_proj(hidden_states),
+                mask=conv_mask,
+                cache=conv_state_k,
+                output_final_state=use_cache,
+                cu_seqlens=cu_seqlens
+            )
+            v, conv_state_v = self.v_conv1d(
+                x=self.v_proj(hidden_states),
+                mask=conv_mask,
+                cache=conv_state_v,
+                output_final_state=use_cache,
+                cu_seqlens=cu_seqlens
+            )
+        else:
+            q = self.q_proj(hidden_states)
+            k = self.k_proj(hidden_states)
+            v = self.v_proj(hidden_states)
+        gk = self.gk_proj(hidden_states)
+
+        if self.feature_map_fn is not None:
+            q, k = map(self.feature_map_fn, (q, k))
+        # dealing with left-padding
+        if attention_mask is not None:
+            v = v.mul_(attention_mask[:, -v.shape[-2]:, None])
+        q = rearrange(q, '... (h d) -> ... h d', h=self.num_heads)
+        if self.num_kv_groups > 1:
+            k, v = (repeat(x, '... (h d) -> ... (h g) d', h=self.num_kv_heads, g=self.num_kv_groups) for x in (k, v))
+        else:
+            k, v = (rearrange(x, '... (h d) -> ... h d', h=self.num_kv_heads) for x in (k, v))
+        gk = F.logsigmoid(gk) / self.gate_logit_normalizer
+
+        recurrent_state = last_state['recurrent_state'] if last_state is not None else None
+        if mode == 'chunk':
+            o, recurrent_state = chunk_simple_gla(
+                q=q,
+                k=k,
+                v=v,
+                gk=gk,
+                initial_state=recurrent_state,
+                output_final_state=use_cache,
+                cu_seqlens=cu_seqlens,
+                head_first=False
+            )
+        elif mode == 'fused_recurrent':
+            o, recurrent_state = fused_recurrent_simple_gla(
+                q=q,
+                k=k,
+                v=v,
+                gk=gk,
+                initial_state=recurrent_state,
+                output_final_state=use_cache,
+                cu_seqlens=cu_seqlens,
+                head_first=False
+            )
+        else:
+            raise NotImplementedError(f"Not supported mode `{mode}`.")
+
+        if past_key_values is not None:
+            past_key_values.update(
+                recurrent_state=recurrent_state,
+                conv_state=(conv_state_q, conv_state_k, conv_state_v) if self.use_short_conv else None,
+                layer_idx=self.layer_idx,
+                offset=q.shape[1]
+            )
+
+        g = self.g_proj(hidden_states)
+        if self.fuse_norm_and_gate:
+            g = rearrange(g, 'b t (h d) -> b t h d', h=self.num_heads)
+            o = self.g_norm_swish_gate(o, g)
+            o = rearrange(o, 'b t h d -> b t (h d)')
+        else:
+            o = rearrange(self.g_norm(o), 'b t h d -> b t (h d)')
+            o = o * self.gate_fn(g)
+        o = self.o_proj(o)
+
+        return o, None, past_key_values
+
+    def state_size(self, **kwargs) -> int:
+        state_size = self.key_dim * self.head_v_dim
+        for module in self.children():
+            if isinstance(module, ShortConvolution):
+                state_size += module.state_size
+        return state_size

fla/models/__init__.py

@@ -0,0 +1,51 @@
+# -*- coding: utf-8 -*-
+
+from fla.models.abc import ABCConfig, ABCForCausalLM, ABCModel
+from fla.models.bitnet import BitNetConfig, BitNetForCausalLM, BitNetModel
+from fla.models.delta_net import DeltaNetConfig, DeltaNetForCausalLM, DeltaNetModel
+from fla.models.forgetting_transformer import (
+    ForgettingTransformerConfig,
+    ForgettingTransformerForCausalLM,
+    ForgettingTransformerModel
+)
+from fla.models.gated_deltanet import GatedDeltaNetConfig, GatedDeltaNetForCausalLM, GatedDeltaNetModel
+from fla.models.gated_deltaproduct import GatedDeltaProductConfig, GatedDeltaProductForCausalLM, GatedDeltaProductModel
+from fla.models.gla import GLAConfig, GLAForCausalLM, GLAModel
+from fla.models.gsa import GSAConfig, GSAForCausalLM, GSAModel
+from fla.models.hgrn import HGRNConfig, HGRNForCausalLM, HGRNModel
+from fla.models.hgrn2 import HGRN2Config, HGRN2ForCausalLM, HGRN2Model
+from fla.models.lightnet import LightNetConfig, LightNetForCausalLM, LightNetModel
+from fla.models.linear_attn import LinearAttentionConfig, LinearAttentionForCausalLM, LinearAttentionModel
+from fla.models.mamba import MambaConfig, MambaForCausalLM, MambaModel
+from fla.models.mamba2 import Mamba2Config, Mamba2ForCausalLM, Mamba2Model
+from fla.models.nsa import NSAConfig, NSAForCausalLM, NSAModel
+from fla.models.retnet import RetNetConfig, RetNetForCausalLM, RetNetModel
+from fla.models.rwkv6 import RWKV6Config, RWKV6ForCausalLM, RWKV6Model
+from fla.models.rwkv7 import RWKV7Config, RWKV7ForCausalLM, RWKV7Model
+from fla.models.samba import SambaConfig, SambaForCausalLM, SambaModel
+from fla.models.transformer import TransformerConfig, TransformerForCausalLM, TransformerModel
+from fla.models.transformer_with_pruning import TransformerWithPruningConfig, TransformerWithPruningForCausalLM, TransformerWithPruningModel
+
+__all__ = [
+    'ABCConfig', 'ABCForCausalLM', 'ABCModel',
+    'BitNetConfig', 'BitNetForCausalLM', 'BitNetModel',
+    'DeltaNetConfig', 'DeltaNetForCausalLM', 'DeltaNetModel',
+    'ForgettingTransformerConfig', 'ForgettingTransformerForCausalLM', 'ForgettingTransformerModel',
+    'GatedDeltaNetConfig', 'GatedDeltaNetForCausalLM', 'GatedDeltaNetModel',
+    'GLAConfig', 'GLAForCausalLM', 'GLAModel',
+    'GSAConfig', 'GSAForCausalLM', 'GSAModel',
+    'HGRNConfig', 'HGRNForCausalLM', 'HGRNModel',
+    'HGRN2Config', 'HGRN2ForCausalLM', 'HGRN2Model',
+    'LightNetConfig', 'LightNetForCausalLM', 'LightNetModel',
+    'LinearAttentionConfig', 'LinearAttentionForCausalLM', 'LinearAttentionModel',
+    'MambaConfig', 'MambaForCausalLM', 'MambaModel',
+    'Mamba2Config', 'Mamba2ForCausalLM', 'Mamba2Model',
+    'NSAConfig', 'NSAForCausalLM', 'NSAModel',
+    'RetNetConfig', 'RetNetForCausalLM', 'RetNetModel',
+    'RWKV6Config', 'RWKV6ForCausalLM', 'RWKV6Model',
+    'RWKV7Config', 'RWKV7ForCausalLM', 'RWKV7Model',
+    'SambaConfig', 'SambaForCausalLM', 'SambaModel',
+    'TransformerConfig', 'TransformerForCausalLM', 'TransformerModel',
+    'TransformerWithPruningConfig', 'TransformerWithPruningForCausalLM', 'TransformerWithPruningModel',
+    'GatedDeltaProductConfig', 'GatedDeltaProductForCausalLM', 'GatedDeltaProductModel',
+]

fla/models/utils.py

@@ -0,0 +1,147 @@
+# -*- coding: utf-8 -*-
+
+from __future__ import annotations
+
+from typing import Any, Dict, List, Optional, Tuple
+
+import torch
+import transformers
+
+
+class Cache(transformers.cache_utils.Cache):
+    """
+    A cache used for storing hidden states produced by flash linear attention models.
+
+    It stores the states of each layer as the tensor of shape `[batch_size, key_dim, value_dim]`.
+    """
+
+    is_compileable = True
+
+    def __init__(
+        self,
+        seen_tokens: int = 0
+    ) -> Cache:
+        super().__init__()
+
+        self.states: List[Dict[str, Any]] = []
+
+        self._seen_tokens = seen_tokens  # Used in `generate` to keep tally of how many tokens the cache has seen
+
+    def __getitem__(self, layer_idx: int) -> Dict[str, Any]:
+        if layer_idx < len(self):
+            return self.states[layer_idx]
+        else:
+            raise KeyError(f"Cache only has {len(self)} layers, attempted to access layer with index {layer_idx}")
+
+    def __iter__(self):
+        for state in self.states:
+            yield state
+
+    def __len__(self):
+        return len(self.states)
+
+    def update(
+        self,
+        recurrent_state: torch.Tensor = None,
+        attn_state: Tuple[torch.Tensor, torch.Tensor] = None,
+        conv_state: Tuple[torch.Tensor] = None,
+        ffn_state: torch.Tensor = None,
+        layer_idx: int = 0,
+        offset: Optional[int] = 1,
+        cache_kwargs: Optional[Dict[str, Any]] = None,
+    ) -> Dict[str, Any]:
+        """
+        Updates the cache with the new `recurrent_state`/`attn_state`/`conv_state` for the layer `layer_idx`.
+
+        Args:
+            recurrent_state (`torch.Tensor`, `optional`):
+                The new recurrent state to cache.
+            attn_state (`Tuple[torch.Tensor, torch.Tensor]`, `optional`):
+                The new attention key/value states to cache.
+            conv_state (`Tuple[torch.Tensor]`, `optional`):
+                The new convolution state to cache.
+            layer_idx (`int`, defaults to 0):
+                The index of the layer to cache the states for.
+            offset (`int`, `optional`, defaults to 1):
+                The number of new tokens being processed.
+            cache_kwargs (`Dict[str, Any]`, `optional`):
+                Additional arguments for the cache subclass.
+
+        Return:
+            Dictionary of the updated state.
+        """
+
+        # Update the number of seen tokens
+        if layer_idx == 0:
+            self._seen_tokens += offset
+
+        if attn_state is not None:
+            input_size = attn_state[0].shape[-2]
+            window_size = cache_kwargs.get('window_size', None)
+            if not isinstance(attn_state, Tuple) or len(attn_state) != 2:
+                raise ValueError("`attn_state` must be a tuple of two tensors for key/value states")
+        if len(self.states) <= layer_idx:
+            if attn_state is not None:
+                if window_size is not None and input_size > window_size:
+                    attn_state = (attn_state[0][..., -window_size:, :].contiguous(),
+                                  attn_state[1][..., -window_size:, :].contiguous())
+            state = dict(
+                recurrent_state=recurrent_state,
+                attn_state=attn_state,
+                conv_state=conv_state,
+                ffn_state=ffn_state
+            )
+            self.states.append(state)
+        else:
+            state = self.states[layer_idx]
+            if recurrent_state is not None:
+                state['recurrent_state'] = recurrent_state
+            if attn_state is not None:
+                key_state, value_state = state['attn_state']
+                if window_size is not None and key_state.shape[-2] == window_size:
+                    # DO NOT allocate new memory if the cache is full
+                    # roll the key/value states to the left by `input_size`
+                    key_state = key_state.roll(-input_size, -2)
+                    value_state = value_state.roll(-input_size, -2)
+                    # replace the last `input_size` tokens with the new key/value states
+                    key_state[..., -input_size:, :] = attn_state[0]
+                    value_state[..., -input_size:, :] = attn_state[1]
+                    attn_state = (key_state, value_state)
+                else:
+                    attn_state = (torch.cat([key_state, attn_state[0]], -2),
+                                  torch.cat([value_state, attn_state[1]], -2),)
+                state['attn_state'] = attn_state
+            if conv_state is not None:
+                state['conv_state'] = conv_state
+            if ffn_state is not None:
+                state['ffn_state'] = ffn_state
+
+        return state
+
+    def get_seq_length(self, layer_idx: Optional[int] = 0) -> int:
+        """Returns the sequence length of the cached states. A layer index can be optionally passed."""
+        if len(self.states) <= layer_idx:
+            return 0
+        return self._seen_tokens
+
+    def get_max_length(self) -> Optional[int]:
+        """Returns the maximum sequence length of the cached states. Cache does not have a maximum length."""
+        return None
+
+    def to_legacy_cache(self) -> Tuple:
+        return tuple(self.states)
+
+    @classmethod
+    @torch.compiler.disable
+    def from_legacy_cache(
+        cls,
+        past_key_values: Optional[Tuple] = None,
+        seen_tokens: int = 0
+    ) -> Cache:
+        """Converts a cache in the legacy cache format into an equivalent `Cache`."""
+
+        cache = cls(seen_tokens)
+        if isinstance(past_key_values, list):
+            for layer_idx in range(len(past_key_values)):
+                cache.states.append(past_key_values[layer_idx])
+        return cache

fla/modules/activations.py

@@ -0,0 +1,471 @@
+# -*- coding: utf-8 -*-
+# Copyright (c) 2023-2025, Tri Dao, Yu Zhang, Songlin Yang.
+
+import torch
+import torch.nn.functional as F
+import triton
+import triton.language as tl
+
+from fla.ops.utils.op import exp, log
+from fla.utils import autocast_custom_bwd, autocast_custom_fwd, get_multiprocessor_count, input_guard
+
+sigmoid_fwd_codestring = """
+template <typename T> T sigmoid_fwd(T x) {
+    return 1.0f / (1.0f + ::exp(-float(x)));
+}
+"""
+sigmoid_bwd_codestring = """
+template <typename T> T sigmoid_bwd(T x, T g) {
+    float x_sigmoid = 1.0f / (1.0f + ::exp(-float(x)));
+    return float(g) * x_sigmoid * (1.0f - x_sigmoid);
+}
+"""
+
+sigmoid_fwd_jit_fn = torch.cuda.jiterator._create_jit_fn(sigmoid_fwd_codestring)
+sigmoid_bwd_jit_fn = torch.cuda.jiterator._create_jit_fn(sigmoid_bwd_codestring)
+
+
+@torch.compiler.disable
+def sigmoid_fwd(x):
+    return sigmoid_fwd_jit_fn(x)
+
+
+@torch.compiler.disable
+def sigmoid_bwd(x, g):
+    return sigmoid_bwd_jit_fn(x, g)
+
+
+class SigmoidFunction(torch.autograd.Function):
+
+    @staticmethod
+    def forward(ctx, x):
+        ctx.save_for_backward(x)
+        return sigmoid_fwd(x)
+
+    @staticmethod
+    def backward(ctx, dout):
+        x, = ctx.saved_tensors
+        return sigmoid_bwd(x, dout)
+
+
+sigmoid = SigmoidFunction.apply
+
+
+@triton.autotune(
+    configs=[
+        triton.Config({}, num_warps=num_warps)
+        for num_warps in [1, 2, 4, 8, 16, 32]
+    ],
+    key=['D']
+)
+@triton.jit
+def logsigmoid_fwd_kernel(
+    x,
+    y,
+    temperature,
+    T: tl.constexpr,
+    D: tl.constexpr,
+    B: tl.constexpr
+):
+    i = tl.program_id(0)
+    o_i = i * B + tl.arange(0, B)
+    m_i = o_i < T
+
+    b_x = tl.load(x + o_i, mask=m_i, other=0.).to(tl.float32)
+    b_m = tl.minimum(0., b_x)
+    b_z = 1. + exp(-tl.abs(b_x))
+    b_y = (b_m - log(b_z)) / temperature
+    tl.store(y + o_i, b_y.to(y.dtype.element_ty), mask=m_i)
+
+
+@triton.autotune(
+    configs=[
+        triton.Config({}, num_warps=num_warps)
+        for num_warps in [1, 2, 4, 8, 16, 32]
+    ],
+    key=['D']
+)
+@triton.jit
+def logsigmoid_bwd_kernel(
+    x,
+    dx,
+    dy,
+    temperature,
+    T: tl.constexpr,
+    D: tl.constexpr,
+    B: tl.constexpr
+):
+    i = tl.program_id(0)
+    o_i = i * B + tl.arange(0, B)
+    m_i = o_i < T
+
+    b_x = tl.load(x + o_i, mask=m_i, other=0.).to(tl.float32)
+    b_dy = tl.load(dy + o_i, mask=m_i, other=0.).to(tl.float32)
+    b_dx = b_dy * (1. - tl.sigmoid(b_x)) / temperature
+    tl.store(dx + o_i, b_dx.to(dx.dtype.element_ty), mask=m_i)
+
+
+def logsigmoid_fwd(x: torch.Tensor, temperature: float = 1.) -> torch.Tensor:
+    T, D = x.numel(), x.shape[-1]
+    B = triton.next_power_of_2(triton.cdiv(T, get_multiprocessor_count(x.device.index)))
+    y = torch.empty_like(x)
+    logsigmoid_fwd_kernel[(triton.cdiv(T, B),)](
+        x=x,
+        y=y,
+        temperature=temperature,
+        T=T,
+        D=D,
+        B=B
+    )
+    return y
+
+
+def logsigmoid_bwd(x: torch.Tensor, dy: torch.Tensor, temperature: float = 1.) -> torch.Tensor:
+    T, D = x.numel(), x.shape[-1]
+    B = triton.next_power_of_2(triton.cdiv(T, get_multiprocessor_count(x.device.index)))
+    dx = torch.empty_like(x)
+    logsigmoid_bwd_kernel[(triton.cdiv(T, B),)](
+        x=x,
+        dx=dx,
+        dy=dy,
+        temperature=temperature,
+        T=T,
+        D=D,
+        B=B
+    )
+    return dx
+
+
+class LogSigmoidFunction(torch.autograd.Function):
+
+    @staticmethod
+    @input_guard
+    def forward(ctx, x, temperature):
+        ctx.save_for_backward(x,)
+        ctx.temperature = temperature
+        return logsigmoid_fwd(x, temperature)
+
+    @staticmethod
+    @input_guard
+    def backward(ctx, dy):
+        x, = ctx.saved_tensors
+        return logsigmoid_bwd(x, dy, ctx.temperature), None
+
+
+def logsigmoid(x: torch.Tensor, temperature: float = 1.) -> torch.Tensor:
+    return LogSigmoidFunction.apply(x, temperature)
+
+
+swish_fwd_codestring = """
+template <typename T> T swish_fwd(T x) {
+    float x_sigmoid = 1.0f / (1.0f + ::exp(-float(x)));
+    return float(x) * x_sigmoid;
+}
+"""
+swish_bwd_codestring = """
+template <typename T> T swish_bwd(T x, T g) {
+    float x_sigmoid = 1.0f / (1.0f + ::exp(-float(x)));
+    return float(g) * x_sigmoid * (1.0f - float(x) * x_sigmoid + float(x));
+}
+"""
+
+swish_fwd_jit_fn = torch.cuda.jiterator._create_jit_fn(swish_fwd_codestring)
+swish_bwd_jit_fn = torch.cuda.jiterator._create_jit_fn(swish_bwd_codestring)
+
+
+@torch.compiler.disable
+def swish_fwd(x):
+    return swish_fwd_jit_fn(x)
+
+
+@torch.compiler.disable
+def swish_bwd(x, g):
+    return swish_bwd_jit_fn(x, g)
+
+
+class SwishFunction(torch.autograd.Function):
+
+    @staticmethod
+    def forward(ctx, x):
+        ctx.save_for_backward(x)
+        return swish_fwd(x)
+
+    @staticmethod
+    def backward(ctx, dout):
+        x, = ctx.saved_tensors
+        return swish_bwd(x, dout)
+
+
+swish = SwishFunction.apply
+
+# 1/sqrt(2*pi)-> 0.3989423
+# 1/sqrt(2)   -> 0.70710678
+# sqrt(2/pi)  -> 0.79788456
+
+
+# this function is tanh approximation of gelu
+# actual gelu is:
+# x * 0.5 * (1.0 + torch.erf(x * 0.70710678))
+@torch.compile
+def bias_gelu(y, bias):
+    x = bias + y
+    return (x * 0.5 * (1.0 + torch.tanh(0.79788456 * x * (1 + 0.044715 * x * x)))).to(dtype=y.dtype)
+
+
+# gradient of tanh approximation of gelu
+# gradient of actual gelu is:
+# 0.5 * (1. + torch.erf(x * 0.70710678)) + 0.3989423 * x * torch.exp(-0.5 * x * x)
+@torch.compile
+def bias_gelu_bwd(g, y, bias):
+    """Assume that y has shape (B, D) and bias has shape (D)"""
+    x = bias + y
+    tanh_out = torch.tanh(0.79788456 * x * (1 + 0.044715 * x * x))
+    # sqrt(2/pi) * 3 * 0.044715 -> 0.1070322243
+    ff = 0.5 * x * ((1 - tanh_out * tanh_out) * (0.79788456 + 0.1070322243 * x * x)) + 0.5 * (
+        1 + tanh_out
+    )
+    grad_y = ff * g
+    return grad_y.to(dtype=y.dtype), grad_y.sum(dim=(0), dtype=bias.dtype)
+
+
+class GeLUFunction(torch.autograd.Function):
+
+    @staticmethod
+    # bias is an optional argument
+    def forward(ctx, input, bias):
+        ctx.save_for_backward(input, bias)
+        return bias_gelu(input, bias)
+
+    @staticmethod
+    def backward(ctx, grad_output):
+        input, bias = ctx.saved_tensors
+        tmp = bias_gelu_bwd(grad_output, input, bias)
+        return tmp, tmp
+
+
+bias_gelu_impl = GeLUFunction.apply
+
+
+# this function is tanh approximation of gelu
+# actual gelu is:
+# x * 0.5 * (1.0 + torch.erf(x * 0.70710678))
+@torch.compile
+def gelu_fwd(x):
+    return (x * 0.5 * (1.0 + torch.tanh(0.79788456 * x * (1 + 0.044715 * x * x)))).to(dtype=x.dtype)
+
+
+# gradient of tanh approximation of gelu
+# gradient of actual gelu is:
+# 0.5 * (1. + torch.erf(x * 0.70710678)) + 0.3989423 * x * torch.exp(-0.5 * x * x)
+@torch.compile
+def gelu_bwd(g, x):
+    tanh_out = torch.tanh(0.79788456 * x * (1 + 0.044715 * x * x))
+    # sqrt(2/pi) * 3 * 0.044715 -> 0.1070322243
+    ff = 0.5 * x * ((1 - tanh_out * tanh_out) * (0.79788456 + 0.1070322243 * x * x)) + 0.5 * (
+        1 + tanh_out
+    )
+    return (ff * g).to(dtype=x.dtype)
+
+
+class FastGeLUFunction(torch.autograd.Function):
+    @staticmethod
+    # bias is an optional argument
+    def forward(ctx, input):
+        ctx.save_for_backward(input)
+        return gelu_fwd(input)
+
+    @staticmethod
+    def backward(ctx, grad_output):
+        (input,) = ctx.saved_tensors
+        tmp = gelu_bwd(grad_output, input)
+        return tmp
+
+
+fast_gelu_impl = FastGeLUFunction.apply
+
+
+@torch.compile
+def relu_bwd(g, x):
+    return torch.where(x >= 0, g, 0.0).to(dtype=x.dtype)
+
+
+@torch.compile
+def sqrelu_fwd(x):
+    r = F.relu(x.float())
+    return (r * r).to(dtype=x.dtype)
+
+
+@torch.compile
+def sqrelu_bwd(g, x):
+    return (2.0 * g * F.relu(x.float())).to(dtype=x.dtype)
+
+
+class SquaredReLUFunction(torch.autograd.Function):
+
+    @staticmethod
+    def forward(ctx, input):
+        ctx.save_for_backward(input)
+        return sqrelu_fwd(input)
+
+    @staticmethod
+    def backward(ctx, grad_output):
+        input, = ctx.saved_tensors
+        return sqrelu_bwd(grad_output, input)
+
+
+sqrelu = SquaredReLUFunction.apply
+
+
+swiglu_fwd_codestring = """
+template <typename T> T swiglu_fwd(T x, T y) {
+    return float(x) * float(y) / (1.0f + ::exp(-float(x)));
+}
+"""
+swiglu_bwd_codestring = """
+template <typename T> T swiglu_bwd(T x, T y, T g, T& dx, T& dy) {
+    float x_sigmoid = 1.0f / (1.0f + ::exp(-float(x)));
+    dx = x_sigmoid * (1 + float(x) * (1.0f - x_sigmoid)) * float(g) * float(y);
+    dy = float(x) * x_sigmoid * float(g);
+}
+"""
+
+swiglu_fwdbwd_codestring = """
+template <typename T> T swiglu_fwdbwd(T x, T y, T g, T& dx, T& dy, T& z) {
+    float x_sigmoid = 1.0f / (1.0f + ::exp(-float(x)));
+    float x_swish = float(x) * x_sigmoid;
+    dx = x_sigmoid * (1 + float(x) * (1.0f - x_sigmoid)) * float(g) * float(y);
+    dy = x_swish * float(g);
+    z = x_swish * float(y);
+}
+"""
+
+
+swiglu_fwd_jit_fn = torch.cuda.jiterator._create_jit_fn(swiglu_fwd_codestring)
+swiglu_bwd_jit_fn = torch.cuda.jiterator._create_multi_output_jit_fn(swiglu_bwd_codestring, num_outputs=2)
+swiglu_fwdbwd_jit_fn = torch.cuda.jiterator._create_multi_output_jit_fn(swiglu_fwdbwd_codestring, num_outputs=3)
+
+
+@torch.compiler.disable
+def swiglu_fwd(x, y):
+    return swiglu_fwd_jit_fn(x, y)
+
+
+@torch.compiler.disable
+def swiglu_bwd(x, y, g):
+    return swiglu_bwd_jit_fn(x, y, g)
+
+
+@torch.compiler.disable
+def swiglu_fwdbwd(x, y, g):
+    return swiglu_fwdbwd_jit_fn(x, y, g)
+
+
+@torch.compile
+def swiglu_fwd_torch(x, y):
+    return (F.silu(x.float()) * y).to(x.dtype)
+
+
+@torch.compile
+def swiglu_bwd_torch(x, y, g):
+    dtype = x.dtype
+    x, y, g = x.float(), y.float(), g.float()
+    x_sigmoid = x.sigmoid()
+    x_swish = x * x_sigmoid
+    dx = x_sigmoid * (1 + x * (1.0 - x_sigmoid)) * g * y
+    dy = x_swish * g
+    return dx.to(dtype), dy.to(dtype)
+
+
+@torch.compile
+def swiglu_fwdbwd_torch(x, y, g):
+    dtype = x.dtype
+    x, y, g = x.float(), y.float(), g.float()
+    x_sigmoid = x.sigmoid()
+    x_swish = x * x_sigmoid
+    dx = x_sigmoid * (1 + x * (1.0 - x_sigmoid)) * g * y
+    dy = x_swish * g
+    z = x_swish * y
+    return dx.to(dtype), dy.to(dtype), z.to(dtype)
+
+
+class SwiGLUFunction(torch.autograd.Function):
+    r"""
+    Swish-Gated Linear Unit (SwiGLU) function.
+
+    .. math::
+        \text{SwiGLU}(x, y) = swish(x) * y = \frac{x}{1 + \exp(-x)} * y
+    """
+
+    @staticmethod
+    def forward(ctx, x, y):
+        ctx.save_for_backward(x, y)
+        if torch.compiler.is_compiling() or isinstance(x, torch.distributed.tensor.DTensor):
+            return swiglu_fwd_torch(x, y)
+        else:
+            return swiglu_fwd(x, y)
+
+    @staticmethod
+    def backward(ctx, dout):
+        x, y = ctx.saved_tensors
+        if torch.compiler.is_compiling() or isinstance(x, torch.distributed.tensor.DTensor):
+            return swiglu_bwd_torch(x, y, dout)
+        else:
+            return swiglu_bwd(x, y, dout)
+
+
+class SwiGLULinearFunction(torch.autograd.Function):
+    r"""
+    Swish-Gated Linear Unit (SwiGLU) function followed by a linear transformation.
+
+    .. math::
+        \text{SwiGLULinear}(x, y, W, b) = (swish(x) * y) W + b
+
+    This simple wrap discards the intermediate results of SwiGLU(x, y) to save memory.
+    """
+
+    @staticmethod
+    @autocast_custom_fwd
+    def forward(ctx, x, y, weight, bias):
+        with torch.no_grad():
+            if torch.compiler.is_compiling() or isinstance(x, torch.distributed.tensor.DTensor):
+                z = swiglu_fwd_torch(x, y)
+            else:
+                z = swiglu_fwd(x, y)
+        out = F.linear(z, weight, bias)
+        # We don't store z, will be recomputed in the backward pass to save memory
+        ctx.save_for_backward(x, y, weight)
+        ctx.linear_bias_is_none = bias is None
+        return out
+
+    @staticmethod
+    @autocast_custom_bwd
+    def backward(ctx, dout, *args):
+        x, y, weight = ctx.saved_tensors
+        dout = dout.reshape(-1, dout.shape[-1])
+        dz = F.linear(dout, weight.t()).view_as(x)
+        with torch.no_grad():
+            if torch.compiler.is_compiling() or isinstance(x, torch.distributed.tensor.DTensor):
+                dx, dy, z = swiglu_fwdbwd_torch(x, y, dz)
+            else:
+                dx, dy, z = swiglu_fwdbwd(x, y, dz)
+        dlinear_weight = torch.einsum("bo,bi->oi", dout, z.reshape(-1, z.shape[-1]))
+        dlinear_bias = None if ctx.linear_bias_is_none else dout.sum(0)
+        return dx, dy, dlinear_weight, dlinear_bias
+
+
+swiglu = SwiGLUFunction.apply
+
+
+swiglu_linear = SwiGLULinearFunction.apply
+
+
+ACT2FN = {
+    'relu': F.relu,
+    'sigmoid': sigmoid,
+    'logsigmoid': logsigmoid,
+    'silu': swish,
+    'swish': swish,
+    'sqrelu': sqrelu,
+    'gelu': fast_gelu_impl,
+    'bias_gelu': bias_gelu_impl,
+}

fla/modules/fused_cross_entropy.py

@@ -0,0 +1,419 @@
+# -*- coding: utf-8 -*-
+
+# Copyright (c) 2023, Tri Dao.
+
+from typing import Any, Tuple
+
+import torch
+import torch.nn as nn
+import triton
+import triton.language as tl
+
+from fla.ops.utils.op import exp, log
+from fla.utils import input_guard
+
+# `all_gather_into_tensor` and `reduce_scatter_tensor` are new placeholders for
+# `_all_gather_base` and `_reduce_scatter_base`. They require the most recent
+# version of PyTorch. The following 2 lines are for backward compatibility with
+# older PyTorch.
+if "all_gather_into_tensor" not in dir(torch.distributed):
+    torch.distributed.all_gather_into_tensor = torch.distributed._all_gather_base
+
+
+@triton.heuristics({
+    "HAS_SMOOTHING": lambda args: args["label_smoothing"] > 0.0,
+})
+@triton.jit
+def cross_entropy_fwd_kernel(
+    loss_ptr,  # data ptrs
+    lse_ptr,
+    z_loss_ptr,
+    logits_ptr,
+    labels_ptr,
+    label_smoothing,
+    logit_scale,
+    lse_square_scale,
+    ignore_index,
+    total_classes,
+    class_start_idx,  # Useful for tensor parallel when each rank only has a subset of classes
+    n_cols,  # shapes
+    n_rows,
+    logits_row_stride,  # strides
+    BLOCK_SIZE: tl.constexpr,
+    HAS_SMOOTHING: tl.constexpr,
+    # if SPLIT (e.g. tensor parallel), don't include the LSE in the loss since it's not the final LSE
+    SPLIT: tl.constexpr,
+):
+    row_idx = tl.program_id(0)
+    col_block_idx = tl.program_id(1)
+    logits_ptr = logits_ptr + row_idx * logits_row_stride.to(tl.int64)
+    col_offsets = col_block_idx * BLOCK_SIZE + tl.arange(0, BLOCK_SIZE)
+    label_idx = tl.load(labels_ptr + row_idx)
+    logits = tl.load(logits_ptr + col_offsets, mask=col_offsets < n_cols, other=-float("inf"))
+    logits = logits.to(tl.float32) * logit_scale
+    max_logits = tl.max(logits, 0)
+    if HAS_SMOOTHING:
+        sum_logits = tl.sum(tl.where(col_offsets < n_cols, logits, 0.0), 0)
+    lse = log(tl.sum(exp(logits - max_logits), 0)) + max_logits
+    tl.store(lse_ptr + col_block_idx * n_rows + row_idx, lse)
+    if label_idx == ignore_index:
+        loss = 0.0
+        z_loss = 0.0
+    else:
+        label_idx -= class_start_idx
+        if label_idx >= col_block_idx * BLOCK_SIZE and label_idx < min(
+            n_cols, (col_block_idx + 1) * BLOCK_SIZE
+        ):
+            logits_label = tl.load(logits_ptr + label_idx) * logit_scale
+            if HAS_SMOOTHING:
+                loss = (
+                    (lse if not SPLIT else 0.0)
+                    - label_smoothing * sum_logits / total_classes
+                    - (1 - label_smoothing) * logits_label
+                )
+            else:
+                loss = (lse if not SPLIT else 0.0) - logits_label
+        else:
+            # If label is out of bounds, we set the CE loss to 0.0. But we still want the label_smoothing loss
+            if HAS_SMOOTHING:
+                loss = label_smoothing * ((lse if not SPLIT else 0.0) - sum_logits / total_classes)
+            else:
+                loss = 0.0
+        if not SPLIT:
+            z_loss = lse_square_scale * lse * lse
+            loss += z_loss
+        else:
+            z_loss = 0.0
+    tl.store(loss_ptr + col_block_idx * n_rows + row_idx, loss)
+    if not SPLIT:
+        tl.store(z_loss_ptr + col_block_idx * n_rows + row_idx, z_loss)
+
+
+@triton.heuristics({
+    "HAS_SMOOTHING": lambda args: args["label_smoothing"] > 0.0,
+})
+@triton.jit
+def cross_entropy_bwd_kernel(
+    dlogits_ptr,  # data ptrs
+    dloss_ptr,
+    logits_ptr,
+    lse_ptr,
+    labels_ptr,
+    label_smoothing,
+    logit_scale,
+    lse_square_scale,
+    ignore_index,
+    total_classes,
+    class_start_idx,  # Useful for tensor parallel when each rank only has a subset of classes
+    n_cols,  # shapes
+    logits_row_stride,  # strides
+    dlogits_row_stride,
+    dloss_row_stride,
+    BLOCK_SIZE: tl.constexpr,
+    HAS_SMOOTHING: tl.constexpr,
+):
+    row_idx = tl.program_id(0)
+    col_block_idx = tl.program_id(1)
+    logits_ptr = logits_ptr + row_idx * logits_row_stride.to(tl.int64)
+    dlogits_ptr = dlogits_ptr + row_idx * dlogits_row_stride.to(tl.int64)
+    col_offsets = col_block_idx * BLOCK_SIZE + tl.arange(0, BLOCK_SIZE)
+    label_idx = tl.load(labels_ptr + row_idx)
+    if label_idx != ignore_index:
+        dloss = tl.load(dloss_ptr + row_idx * dloss_row_stride)
+    else:
+        dloss = 0.0
+    logits = tl.load(logits_ptr + col_offsets, mask=col_offsets < n_cols, other=-float("inf")).to(
+        tl.float32
+    ) * logit_scale
+    lse = tl.load(lse_ptr + row_idx)
+    probs = exp(logits - lse)
+    probs += 2.0 * lse_square_scale * lse * probs
+    label_idx -= class_start_idx
+    if HAS_SMOOTHING:
+        smooth_negative = label_smoothing / total_classes
+        probs = tl.where(col_offsets == label_idx, probs - (1 - label_smoothing), probs) - smooth_negative
+    else:
+        probs = tl.where(col_offsets == label_idx, probs - 1.0, probs)
+    tl.store(dlogits_ptr + col_offsets, (dloss * logit_scale) * probs, mask=col_offsets < n_cols)
+
+
+def fused_cross_entropy_forward(
+    logits: torch.Tensor,
+    target: torch.Tensor,
+    label_smoothing: float = 0.0,
+    logit_scale: float = 1.0,
+    lse_square_scale: float = 0.0,
+    ignore_index: int = -100,
+    process_group=None,
+):
+    n_rows, n_cols = logits.shape
+    assert target.shape == (n_rows,)
+    world_size = 1 if process_group is None else torch.distributed.get_world_size(process_group)
+    total_classes = world_size * n_cols
+    rank = 0 if process_group is None else torch.distributed.get_rank(process_group)
+    class_start_idx = rank * n_cols
+
+    if logits.stride(-1) != 1:
+        logits = logits.contiguous()
+    # Set these similar to https://github.com/openai/triton/blob/main/python/tutorials/02-fused-softmax.py
+    MAX_BLOCK_SIZE = 64 * 1024
+    BLOCK_SIZE = min(triton.next_power_of_2(n_cols), MAX_BLOCK_SIZE)
+    num_warps = (
+        4
+        if BLOCK_SIZE < 2048
+        else (8 if BLOCK_SIZE < 8192 else (16 if BLOCK_SIZE < 128 * 1024 else 32))
+    )
+    # We may split the lse computation across multiple blocks, then do a reduction
+    # lse(local_lse) to get the final LSE. This is faster for large n_cols (e.g., > 64k)
+    # where having just one thread block processing more than 64k elements is slow.
+    split = world_size > 1 or n_cols > MAX_BLOCK_SIZE
+    n_splits = (n_cols + BLOCK_SIZE - 1) // BLOCK_SIZE
+    loss_shape = (n_splits, n_rows) if n_splits > 1 else (n_rows,)
+    losses = torch.empty(*loss_shape, dtype=torch.float, device=logits.device)
+    lse = torch.empty(*loss_shape, dtype=torch.float, device=logits.device)
+    z_losses = torch.empty(*loss_shape, dtype=torch.float, device=logits.device)
+
+    cross_entropy_fwd_kernel[(n_rows, n_splits)](
+        losses,  # data ptrs
+        lse,
+        z_losses,
+        logits,
+        target,
+        label_smoothing,
+        logit_scale,
+        lse_square_scale,
+        ignore_index,
+        total_classes,
+        class_start_idx,
+        n_cols,  # shapes
+        n_rows,
+        logits.stride(0),  # strides
+        BLOCK_SIZE=BLOCK_SIZE,  # constants
+        num_warps=num_warps,
+        SPLIT=split
+    )
+
+    if split:
+        # If there's no label_smoothing, if target are in the vocab of this partition, losses contains
+        # - predicted logit, and 0 otherwise.
+        # If there's label_smoothing=0.1, for target in the vocab of this partition, losses contains
+        # -0.9 * predicted logit - 0.1 * sum logit / total_classes.
+        # For target not in the vocab of this partition, losses contains
+        # -0.1 * sum logit / total_classes.
+        if n_splits > 1:
+            lse = torch.logsumexp(lse, dim=0)
+            losses = losses.sum(dim=0)
+        if world_size > 1:
+            lse_allgather = torch.empty(world_size, n_rows, dtype=lse.dtype, device=lse.device)
+            torch.distributed.all_gather_into_tensor(lse_allgather, lse, group=process_group)
+            handle_losses = torch.distributed.all_reduce(
+                losses, op=torch.distributed.ReduceOp.SUM, group=process_group, async_op=True
+            )
+            lse = torch.logsumexp(lse_allgather, dim=0)
+            handle_losses.wait()
+        # After the allreduce, if there's no label_smoothing, the total losses are - predicted_logit,
+        # we just have to add the (global) lse.
+        # If there's label_smoothing=0.1, the total losses are
+        # -0.9 * predicted_logit - 0.1 * sum logit / total_classes.
+        # Again, we just have to add the (global) lse.
+        losses += lse
+        if lse_square_scale != 0.0:
+            z_losses = lse_square_scale * lse.square()
+            z_losses.masked_fill_(target == ignore_index, 0.0)
+            losses += z_losses
+        else:
+            z_losses = torch.zeros_like(losses)
+        losses.masked_fill_(target == ignore_index, 0.0)
+
+    return losses, z_losses, lse, total_classes, class_start_idx
+
+
+class CrossEntropyLossFunction(torch.autograd.Function):
+
+    @staticmethod
+    @input_guard
+    def forward(
+        ctx,
+        logits,
+        target,
+        label_smoothing=0.0,
+        logit_scale=1.0,
+        lse_square_scale=0.0,
+        ignore_index=-100,
+        inplace_backward=False,
+        process_group=None,
+    ):
+        losses, z_losses, lse, total_classes, class_start_idx = fused_cross_entropy_forward(
+            logits,
+            target,
+            label_smoothing,
+            logit_scale,
+            lse_square_scale,
+            ignore_index,
+            process_group,
+        )
+        ctx.save_for_backward(logits, lse, target)
+        ctx.mark_non_differentiable(z_losses)
+        ctx.label_smoothing = label_smoothing
+        ctx.logit_scale = logit_scale
+        ctx.lse_square_scale = lse_square_scale
+        ctx.ignore_index = ignore_index
+        ctx.total_classes = total_classes
+        ctx.class_start_idx = class_start_idx
+        ctx.inplace_backward = inplace_backward
+
+        return losses, z_losses
+
+    @staticmethod
+    @input_guard
+    def backward(ctx, grad_losses, grad_z_losses):
+        del grad_z_losses  # z_losses are only for logging.
+
+        logits, lse, target = ctx.saved_tensors
+        dlogits = logits if ctx.inplace_backward else torch.empty_like(logits)
+        n_rows, n_cols = logits.shape
+        BLOCK_SIZE = min(triton.next_power_of_2(n_cols), 4 * 1024)
+        num_warps = 4 if BLOCK_SIZE < 2048 else (8 if BLOCK_SIZE < 8192 else 16)
+        def grid(META): return (n_rows, triton.cdiv(n_cols, META["BLOCK_SIZE"]))  # noqa
+        cross_entropy_bwd_kernel[grid](
+            dlogits,  # data ptrs
+            grad_losses,
+            logits,
+            lse,
+            target,
+            ctx.label_smoothing,
+            ctx.logit_scale,
+            ctx.lse_square_scale,
+            ctx.ignore_index,
+            ctx.total_classes,
+            ctx.class_start_idx,
+            n_cols,  # shapes
+            logits.stride(0),  # strides
+            dlogits.stride(0),
+            grad_losses.stride(0),
+            BLOCK_SIZE=BLOCK_SIZE,  # constants
+            num_warps=num_warps,
+        )
+        return dlogits, None, None, None, None, None, None, None, None
+
+
+def cross_entropy_loss(
+    logits: torch.Tensor,
+    target: torch.Tensor,
+    label_smoothing: float = 0.0,
+    logit_scale: float = 1.0,
+    lse_square_scale: float = 0.0,
+    ignore_index=-100,
+    inplace_backward: bool = False,
+    process_group=None,
+) -> Tuple[torch.Tensor, torch.Tensor]:
+    """
+    Arguments:
+        logits: [batch, vocab_size]
+        target: [batch,]
+        label_smoothing: float
+        logit_scale: float.
+            Multiply logits by this scale before calculating the loss.
+        lse_square_scale: float.
+            If > 0, we add lse_square_scale * lse(logits) ^ 2 to the loss.
+            This is also referred to as "z-loss".
+        ignore_index: int.
+            If target == ignore_index, the loss is set to 0.0.
+        inplace_backward: bool.
+            If True, we do the backward pass in-place by modifying the logits.
+            This saves memory.
+        process_group:
+            if not None, we're doing Tensor Parallel: each process is responsible for
+            one part of the vocab. The loss will be aggregated across processes.
+    Returns:
+        losses: [batch,], float
+        z_losses: [batch,], float
+    """
+    return CrossEntropyLossFunction.apply(
+        logits,
+        target,
+        label_smoothing,
+        logit_scale,
+        lse_square_scale,
+        ignore_index,
+        inplace_backward,
+        process_group,
+    )
+
+
+class FusedCrossEntropyLoss(nn.Module):
+    def __init__(
+        self,
+        ignore_index: int = -100,
+        reduction: str = "mean",
+        label_smoothing: float = 0.0,
+        logit_scale: float = 1.0,
+        lse_square_scale: float = 0.0,
+        inplace_backward: bool = False,
+        process_group: Any = None,
+        return_z_loss: bool = False,
+    ):
+        """
+        Arguments:
+            ignore_index: int. If target == ignore_index, the loss is set to 0.0.
+            label_smoothing: float
+            lse_square_scale: float. If > 0, we add lse_square_scale * lse(logits) ^ 2 to the loss.
+                This is also referred to as "z-loss".
+            inplace_backward: bool. If True, we do the backward pass in-place by modifying the logits.
+                This saves memory.
+            process_group: if not None, we're doing Tensor Parallel: each process is responsible for
+                one part of the vocab. The loss will be aggregated across processes.
+            return_z_loss: bool. If True, we return the component of the loss contributed by
+                the lse_square_scale value. This value is only for logging and does not support
+                backprop.
+        """
+        super().__init__()
+        if reduction not in ["mean", "none", "sum"]:
+            raise NotImplementedError("Only support reduction = 'mean' or 'none' or 'sum'")
+        self.ignore_index = ignore_index
+        self.reduction = reduction
+        self.label_smoothing = label_smoothing
+        self.logit_scale = logit_scale
+        self.lse_square_scale = lse_square_scale
+        self.inplace_backward = inplace_backward
+        self.process_group = process_group
+        self.return_z_loss = return_z_loss
+
+    def forward(self, input, target):
+        """
+        Arguments:
+            input: (batch, vocab_size)
+            target: (batch,)
+        Returns:
+            losses: (batch,) if reduction is 'none', else (1,), dtype float
+            z_loss: (batch,) if reduction is 'none', else (1,), dtype float (if self.return_z_loss)
+        """
+        assert input.is_cuda and target.is_cuda, "Only support CUDA tensors"
+        loss, z_loss = cross_entropy_loss(
+            input,
+            target,
+            label_smoothing=self.label_smoothing,
+            logit_scale=self.logit_scale,
+            lse_square_scale=self.lse_square_scale,
+            ignore_index=self.ignore_index,
+            inplace_backward=self.inplace_backward,
+            process_group=self.process_group,
+        )
+        if self.reduction == "mean":
+            loss = loss.sum() / (target != self.ignore_index).sum()
+        elif self.reduction == "sum":
+            loss = loss.sum()
+        else:
+            loss = loss
+
+        if not self.return_z_loss:
+            return loss
+
+        if self.reduction == "mean":
+            z_loss = z_loss.sum() / (target != self.ignore_index).sum()
+        elif self.reduction == "sum":
+            z_loss = z_loss.sum()
+        else:
+            z_loss = z_loss
+
+        return loss, z_loss

fla/modules/fused_norm_gate.py

@@ -0,0 +1,995 @@
+# -*- coding: utf-8 -*-
+# Copyright (c) 2023-2025, Songlin Yang, Yu Zhang
+
+from __future__ import annotations
+
+import math
+from typing import Optional
+
+import torch
+import torch.nn as nn
+import torch.nn.functional as F
+import triton
+import triton.language as tl
+
+from fla.utils import get_multiprocessor_count, input_guard
+
+
+@triton.autotune(
+    configs=[
+        triton.Config({}, num_warps=num_warps, num_stages=num_stages)
+        for num_warps in [1, 2, 4, 8, 16, 32]
+        for num_stages in [2, 3, 4]
+    ],
+    key=['N', 'HAS_RESIDUAL', 'STORE_RESIDUAL_OUT', 'IS_RMS_NORM', 'HAS_BIAS'],
+)
+@triton.jit
+def layer_norm_gated_fwd_kernel(
+    X,  # pointer to the input
+    G,  # pointer to the gate
+    Y,  # pointer to the output
+    W,  # pointer to the weights
+    B,  # pointer to the biases
+    RESIDUAL,  # pointer to the residual
+    RESIDUAL_OUT,  # pointer to the residual
+    Mean,  # pointer to the mean
+    Rstd,  # pointer to the 1/std
+    N,  # number of columns in X
+    eps,  # epsilon to avoid division by zero
+    ACTIVATION: tl.constexpr,
+    IS_RMS_NORM: tl.constexpr,
+    BLOCK_N: tl.constexpr,
+    HAS_RESIDUAL: tl.constexpr,
+    STORE_RESIDUAL_OUT: tl.constexpr,
+    HAS_WEIGHT: tl.constexpr,
+    HAS_BIAS: tl.constexpr
+):
+    # Map the program id to the row of X and Y it should compute.
+    row = tl.program_id(0)
+    X += row * N
+    Y += row * N
+    G += row * N
+    if HAS_RESIDUAL:
+        RESIDUAL += row * N
+    if STORE_RESIDUAL_OUT:
+        RESIDUAL_OUT += row * N
+    # Compute mean and variance
+    cols = tl.arange(0, BLOCK_N)
+    x = tl.load(X + cols, mask=cols < N, other=0.0).to(tl.float32)
+    if HAS_RESIDUAL:
+        residual = tl.load(RESIDUAL + cols, mask=cols < N, other=0.0).to(tl.float32)
+        x += residual
+    if STORE_RESIDUAL_OUT:
+        tl.store(RESIDUAL_OUT + cols, x, mask=cols < N)
+    if not IS_RMS_NORM:
+        mean = tl.sum(x, axis=0) / N
+        tl.store(Mean + row, mean)
+        xbar = tl.where(cols < N, x - mean, 0.0)
+        var = tl.sum(xbar * xbar, axis=0) / N
+    else:
+        xbar = tl.where(cols < N, x, 0.0)
+        var = tl.sum(xbar * xbar, axis=0) / N
+    rstd = 1 / tl.sqrt(var + eps)
+    tl.store(Rstd + row, rstd)
+    # Normalize and apply linear transformation
+    mask = cols < N
+    if HAS_WEIGHT:
+        w = tl.load(W + cols, mask=mask).to(tl.float32)
+    if HAS_BIAS:
+        b = tl.load(B + cols, mask=mask).to(tl.float32)
+    x_hat = (x - mean) * rstd if not IS_RMS_NORM else x * rstd
+    y = x_hat * w if HAS_WEIGHT else x_hat
+    if HAS_BIAS:
+        y = y + b
+
+    # Swish output gate
+    g = tl.load(G + cols, mask=cols < N, other=0.0).to(tl.float32)
+    if ACTIVATION == 'swish':
+        y = y * g * tl.sigmoid(g)
+    elif ACTIVATION == 'silu':
+        y = y * g * tl.sigmoid(g)
+    elif ACTIVATION == 'sigmoid':
+        y = y * tl.sigmoid(g)
+
+    # Write output
+    tl.store(Y + cols, y, mask=mask)
+
+
+def layer_norm_gated_fwd(
+    x: torch.Tensor,
+    g: torch.Tensor,
+    weight: torch.Tensor,
+    bias: torch.Tensor,
+    activation: str = 'swish',
+    eps: float = 1e-5,
+    residual: torch.Tensor = None,
+    out_dtype: torch.dtype = None,
+    residual_dtype: torch.dtype = None,
+    is_rms_norm: bool = False
+):
+    if residual is not None:
+        residual_dtype = residual.dtype
+    M, N = x.shape
+    if residual is not None:
+        assert residual.shape == (M, N)
+    if weight is not None:
+        assert weight.shape == (N,)
+    if bias is not None:
+        assert bias.shape == (N,)
+    # allocate output
+    y = torch.empty_like(x, dtype=x.dtype if out_dtype is None else out_dtype)
+    if residual is not None or (residual_dtype is not None and residual_dtype != x.dtype):
+        residual_out = torch.empty(M, N, device=x.device, dtype=residual_dtype)
+    else:
+        residual_out = None
+    mean = torch.empty((M,), dtype=torch.float, device=x.device) if not is_rms_norm else None
+    rstd = torch.empty((M,), dtype=torch.float, device=x.device)
+    # Less than 64KB per feature: enqueue fused kernel
+    MAX_FUSED_SIZE = 65536 // x.element_size()
+    BLOCK_N = min(MAX_FUSED_SIZE, triton.next_power_of_2(N))
+    if N > BLOCK_N:
+        raise RuntimeError("This layer norm doesn't support feature dim >= 64KB.")
+    # heuristics for number of warps
+
+    layer_norm_gated_fwd_kernel[(M,)](
+        x,
+        g,
+        y,
+        weight,
+        bias,
+        residual,
+        residual_out,
+        mean,
+        rstd,
+        N,
+        eps,
+        ACTIVATION=activation,
+        IS_RMS_NORM=is_rms_norm,
+        BLOCK_N=BLOCK_N,
+        HAS_RESIDUAL=residual is not None,
+        STORE_RESIDUAL_OUT=residual_out is not None,
+        HAS_WEIGHT=weight is not None,
+        HAS_BIAS=bias is not None,
+    )
+    # residual_out is None if residual is None and residual_dtype == input_dtype
+    return y, mean, rstd, residual_out if residual_out is not None else x
+
+
+@triton.heuristics({
+    'RECOMPUTE_OUTPUT': lambda args: args["Y"] is not None
+})
+@triton.autotune(
+    configs=[
+        triton.Config({}, num_warps=num_warps, num_stages=num_stages)
+        for num_warps in [1, 2, 4, 8, 16, 32]
+        for num_stages in [2, 3, 4]
+    ],
+    key=['N', 'HAS_DRESIDUAL', 'STORE_DRESIDUAL', 'IS_RMS_NORM', 'HAS_BIAS'],
+)
+@triton.jit
+def layer_norm_gated_bwd_kernel(
+    X,  # pointer to the input
+    G,  # pointer to the gate
+    W,  # pointer to the weights
+    B,  # pointer to the biases
+    Y,  # pointer to the output to be recomputed
+    DY,  # pointer to the output gradient
+    DX,  # pointer to the input gradient
+    DG,  # pointer to the gate gradient
+    DW,  # pointer to the partial sum of weights gradient
+    DB,  # pointer to the partial sum of biases gradient
+    DRESIDUAL,
+    DRESIDUAL_IN,
+    Mean,  # pointer to the mean
+    Rstd,  # pointer to the 1/std
+    M,  # number of rows in X
+    N,  # number of columns in X
+    eps,  # epsilon to avoid division by zero
+    rows_per_program,
+    ACTIVATION: tl.constexpr,
+    IS_RMS_NORM: tl.constexpr,
+    BLOCK_N: tl.constexpr,
+    HAS_DRESIDUAL: tl.constexpr,
+    STORE_DRESIDUAL: tl.constexpr,
+    HAS_WEIGHT: tl.constexpr,
+    HAS_BIAS: tl.constexpr,
+    RECOMPUTE_OUTPUT: tl.constexpr,
+):
+    # Map the program id to the elements of X, DX, and DY it should compute.
+    row_block_id = tl.program_id(0)
+    row_start = row_block_id * rows_per_program
+    cols = tl.arange(0, BLOCK_N)
+    mask = cols < N
+    X += row_start * N
+    G += row_start * N
+    if HAS_DRESIDUAL:
+        DRESIDUAL += row_start * N
+    if STORE_DRESIDUAL:
+        DRESIDUAL_IN += row_start * N
+    DY += row_start * N
+    DX += row_start * N
+    DG += row_start * N
+    if RECOMPUTE_OUTPUT:
+        Y += row_start * N
+    if HAS_WEIGHT:
+        w = tl.load(W + cols, mask=mask).to(tl.float32)
+        dw = tl.zeros((BLOCK_N,), dtype=tl.float32)
+    if HAS_BIAS:
+        b = tl.load(B + cols, mask=mask, other=0.0).to(tl.float32)
+    if HAS_BIAS:
+        db = tl.zeros((BLOCK_N,), dtype=tl.float32)
+
+    row_end = min((row_block_id + 1) * rows_per_program, M)
+    for row in range(row_start, row_end):
+        # Load data to SRAM
+        x = tl.load(X + cols, mask=mask, other=0).to(tl.float32)
+        g = tl.load(G + cols, mask=mask, other=0).to(tl.float32)
+        dy = tl.load(DY + cols, mask=mask, other=0).to(tl.float32)
+
+        if not IS_RMS_NORM:
+            mean = tl.load(Mean + row)
+        rstd = tl.load(Rstd + row)
+        # Compute dx
+        xhat = (x - mean) * rstd if not IS_RMS_NORM else x * rstd
+        xhat = tl.where(mask, xhat, 0.0)
+
+        y = xhat * w if HAS_WEIGHT else xhat
+        if HAS_BIAS:
+            y = y + b
+        if RECOMPUTE_OUTPUT:
+            tl.store(Y + cols, y, mask=mask)
+
+        sigmoid_g = tl.sigmoid(g)
+        if ACTIVATION == 'swish':
+            dg = dy * y * (sigmoid_g + g * sigmoid_g * (1 - sigmoid_g))
+            dy = dy * g * sigmoid_g
+        elif ACTIVATION == 'silu':
+            dg = dy * y * (sigmoid_g + g * sigmoid_g * (1 - sigmoid_g))
+            dy = dy * g * sigmoid_g
+        elif ACTIVATION == 'sigmoid':
+            dg = dy * y * sigmoid_g * (1 - sigmoid_g)
+            dy = dy * sigmoid_g
+        wdy = dy
+        if HAS_WEIGHT:
+            wdy = dy * w
+            dw += dy * xhat
+        if HAS_BIAS:
+            db += dy
+        if not IS_RMS_NORM:
+            c1 = tl.sum(xhat * wdy, axis=0) / N
+            c2 = tl.sum(wdy, axis=0) / N
+            dx = (wdy - (xhat * c1 + c2)) * rstd
+        else:
+            c1 = tl.sum(xhat * wdy, axis=0) / N
+            dx = (wdy - xhat * c1) * rstd
+        if HAS_DRESIDUAL:
+            dres = tl.load(DRESIDUAL + cols, mask=mask, other=0).to(tl.float32)
+            dx += dres
+        # Write dx
+        if STORE_DRESIDUAL:
+            tl.store(DRESIDUAL_IN + cols, dx, mask=mask)
+        tl.store(DX + cols, dx, mask=mask)
+        tl.store(DG + cols, dg, mask=mask)
+
+        X += N
+        G += N
+        if HAS_DRESIDUAL:
+            DRESIDUAL += N
+        if STORE_DRESIDUAL:
+            DRESIDUAL_IN += N
+        if RECOMPUTE_OUTPUT:
+            Y += N
+        DY += N
+        DX += N
+        DG += N
+    if HAS_WEIGHT:
+        tl.store(DW + row_block_id * N + cols, dw, mask=mask)
+    if HAS_BIAS:
+        tl.store(DB + row_block_id * N + cols, db, mask=mask)
+
+
+def layer_norm_gated_bwd(
+    dy: torch.Tensor,
+    x: torch.Tensor,
+    g: torch.Tensor,
+    weight: torch.Tensor,
+    bias: torch.Tensor,
+    activation: str = 'swish',
+    eps: float = 1e-5,
+    mean: torch.Tensor = None,
+    rstd: torch.Tensor = None,
+    dresidual: torch.Tensor = None,
+    has_residual: bool = False,
+    is_rms_norm: bool = False,
+    x_dtype: torch.dtype = None,
+    recompute_output: bool = False,
+):
+    M, N = x.shape
+    assert dy.shape == (M, N)
+    if dresidual is not None:
+        assert dresidual.shape == (M, N)
+    if weight is not None:
+        assert weight.shape == (N,)
+    if bias is not None:
+        assert bias.shape == (N,)
+    # allocate output
+    dx = torch.empty_like(x) if x_dtype is None else torch.empty(M, N, dtype=x_dtype, device=x.device)
+    dg = torch.empty_like(g) if x_dtype is None else torch.empty(M, N, dtype=x_dtype, device=x.device)
+    dresidual_in = torch.empty_like(x) if has_residual and dx.dtype != x.dtype else None
+    y = torch.empty(M, N, dtype=dy.dtype, device=dy.device) if recompute_output else None
+
+    # Less than 64KB per feature: enqueue fused kernel
+    MAX_FUSED_SIZE = 65536 // x.element_size()
+    BLOCK_N = min(MAX_FUSED_SIZE, triton.next_power_of_2(N))
+    if N > BLOCK_N:
+        raise RuntimeError("This layer norm doesn't support feature dim >= 64KB.")
+    sm_count = get_multiprocessor_count(x.device.index)
+    dw = torch.empty((sm_count, N), dtype=torch.float, device=weight.device) if weight is not None else None
+    db = torch.empty((sm_count, N), dtype=torch.float, device=bias.device) if bias is not None else None
+    rows_per_program = math.ceil(M / sm_count)
+    grid = (sm_count,)
+    layer_norm_gated_bwd_kernel[grid](
+        x,
+        g,
+        weight,
+        bias,
+        y,
+        dy,
+        dx,
+        dg,
+        dw,
+        db,
+        dresidual,
+        dresidual_in,
+        mean,
+        rstd,
+        M,
+        N,
+        eps,
+        rows_per_program,
+        ACTIVATION=activation,
+        IS_RMS_NORM=is_rms_norm,
+        BLOCK_N=BLOCK_N,
+        HAS_DRESIDUAL=dresidual is not None,
+        STORE_DRESIDUAL=dresidual_in is not None,
+        HAS_WEIGHT=weight is not None,
+        HAS_BIAS=bias is not None,
+    )
+    dw = dw.sum(0).to(weight.dtype) if weight is not None else None
+    db = db.sum(0).to(bias.dtype) if bias is not None else None
+    # Don't need to compute dresidual_in separately in this case
+    if has_residual and dx.dtype == x.dtype:
+        dresidual_in = dx
+    return (dx, dg, dw, db, dresidual_in) if not recompute_output else (dx, dg, dw, db, dresidual_in, y)
+
+
+class LayerNormGatedFunction(torch.autograd.Function):
+
+    @staticmethod
+    @input_guard
+    def forward(
+        ctx,
+        x: torch.Tensor,
+        g: torch.Tensor,
+        weight: torch.Tensor,
+        bias: torch.Tensor,
+        activation: str,
+        residual: Optional[torch.Tensor] = None,
+        eps: float = 1e-6,
+        prenorm: bool = False,
+        residual_in_fp32: bool = False,
+        is_rms_norm: bool = False,
+    ):
+        x_shape_og = x.shape
+        g_shape_og = g.shape
+        # reshape input data into 2D tensor
+        x = x.reshape(-1, x.shape[-1])
+        g = g.reshape(-1, g.shape[-1])
+        if residual is not None:
+            assert residual.shape == x_shape_og
+            residual = residual.reshape(-1, residual.shape[-1])
+        residual_dtype = (
+            residual.dtype
+            if residual is not None
+            else (torch.float if residual_in_fp32 else None)
+        )
+        y, mean, rstd, residual_out = layer_norm_gated_fwd(
+            x=x,
+            g=g,
+            weight=weight,
+            bias=bias,
+            activation=activation,
+            eps=eps,
+            residual=residual,
+            residual_dtype=residual_dtype,
+            is_rms_norm=is_rms_norm
+        )
+        ctx.save_for_backward(residual_out, g, weight, bias, mean, rstd)
+        ctx.x_shape_og = x_shape_og
+        ctx.g_shape_og = g_shape_og
+        ctx.activation = activation
+        ctx.eps = eps
+        ctx.is_rms_norm = is_rms_norm
+        ctx.has_residual = residual is not None
+        ctx.prenorm = prenorm
+        ctx.x_dtype = x.dtype
+        y = y.reshape(x_shape_og)
+        return y if not prenorm else (y, residual_out.reshape(x_shape_og))
+
+    @staticmethod
+    @input_guard
+    def backward(ctx, dy, *args):
+        x, g, weight, bias, mean, rstd = ctx.saved_tensors
+        dy = dy.reshape(-1, dy.shape[-1])
+        assert dy.shape == x.shape
+        if ctx.prenorm:
+            dresidual = args[0]
+            dresidual = dresidual.reshape(-1, dresidual.shape[-1])
+            assert dresidual.shape == x.shape
+        else:
+            dresidual = None
+        dx, dg, dw, db, dresidual_in = layer_norm_gated_bwd(
+            dy=dy,
+            x=x,
+            g=g,
+            weight=weight,
+            bias=bias,
+            activation=ctx.activation,
+            eps=ctx.eps,
+            mean=mean,
+            rstd=rstd,
+            dresidual=dresidual,
+            has_residual=ctx.has_residual,
+            is_rms_norm=ctx.is_rms_norm,
+            x_dtype=ctx.x_dtype,
+        )
+        return (
+            dx.reshape(ctx.x_shape_og),
+            dg.reshape(ctx.g_shape_og),
+            dw,
+            db,
+            None,
+            dresidual_in.reshape(ctx.x_shape_og) if ctx.has_residual else None,
+            None,
+            None,
+            None,
+            None,
+        )
+
+
+class LayerNormGatedLinearFunction(torch.autograd.Function):
+
+    @staticmethod
+    @input_guard
+    def forward(
+        ctx,
+        x: torch.Tensor,
+        g: torch.Tensor,
+        norm_weight: torch.Tensor,
+        norm_bias: torch.Tensor,
+        linear_weight: torch.Tensor,
+        linear_bias: torch.Tensor,
+        residual: Optional[torch.Tensor] = None,
+        eps: float = 1e-6,
+        prenorm: bool = False,
+        residual_in_fp32: bool = False,
+        is_rms_norm: bool = False,
+    ):
+        x_shape_og = x.shape
+        g_shape_og = g.shape
+        # reshape input data into 2D tensor
+        x = x.reshape(-1, x.shape[-1])
+        g = g.reshape(-1, g.shape[-1])
+        if residual is not None:
+            assert residual.shape == x_shape_og
+            residual = residual.reshape(-1, residual.shape[-1])
+        residual_dtype = (
+            residual.dtype
+            if residual is not None
+            else (torch.float if residual_in_fp32 else None)
+        )
+        y, mean, rstd, residual_out = layer_norm_gated_fwd(
+            x=x,
+            g=g,
+            weight=norm_weight,
+            bias=norm_bias,
+            eps=eps,
+            residual=residual,
+            residual_dtype=residual_dtype,
+            is_rms_norm=is_rms_norm
+        )
+        y = y.reshape(x_shape_og)
+        dtype = torch.get_autocast_gpu_dtype() if torch.is_autocast_enabled() else y.dtype
+        linear_weight = linear_weight.to(dtype)
+        linear_bias = linear_bias.to(dtype) if linear_bias is not None else None
+        out = F.linear(y.to(linear_weight.dtype), linear_weight, linear_bias)
+        # We don't store y, will be recomputed in the backward pass to save memory
+        ctx.save_for_backward(residual_out, g, norm_weight, norm_bias, linear_weight, mean, rstd)
+        ctx.x_shape_og = x_shape_og
+        ctx.g_shape_og = g_shape_og
+        ctx.eps = eps
+        ctx.is_rms_norm = is_rms_norm
+        ctx.has_residual = residual is not None
+        ctx.prenorm = prenorm
+        ctx.x_dtype = x.dtype
+        ctx.linear_bias_is_none = linear_bias is None
+        return out if not prenorm else (out, residual_out.reshape(x_shape_og))
+
+    @staticmethod
+    @input_guard
+    def backward(ctx, dout, *args):
+        x, g, norm_weight, norm_bias, linear_weight, mean, rstd = ctx.saved_tensors
+        dout = dout.reshape(-1, dout.shape[-1])
+        dy = F.linear(dout, linear_weight.t())
+        dlinear_bias = None if ctx.linear_bias_is_none else dout.sum(0)
+        assert dy.shape == x.shape
+        if ctx.prenorm:
+            dresidual = args[0]
+            dresidual = dresidual.reshape(-1, dresidual.shape[-1])
+            assert dresidual.shape == x.shape
+        else:
+            dresidual = None
+        dx, dg, dnorm_weight, dnorm_bias, dresidual_in, y = layer_norm_gated_bwd(
+            dy=dy,
+            x=x,
+            g=g,
+            norm_weight=norm_weight,
+            norm_bias=norm_bias,
+            eps=ctx.eps,
+            mean=mean,
+            rstd=rstd,
+            dresidual=dresidual,
+            has_residual=ctx.has_residual,
+            is_rms_norm=ctx.is_rms_norm,
+            x_dtype=ctx.x_dtype,
+            recompute_output=True,
+        )
+        dlinear_weight = torch.einsum("bo,bi->oi", dout, y)
+        return (
+            dx.reshape(ctx.x_shape_og),
+            dg.reshape(ctx.g_shape_og),
+            dnorm_weight,
+            dnorm_bias,
+            dlinear_weight,
+            dlinear_bias,
+            dresidual_in.reshape(ctx.x_shape_og) if ctx.has_residual else None,
+            None,
+            None,
+            None,
+            None,
+        )
+
+
+def layer_norm_gated(
+    x: torch.Tensor,
+    g: torch.Tensor,
+    weight: torch.Tensor,
+    bias: torch.Tensor,
+    activation: str = 'swish',
+    residual: Optional[torch.Tensor] = None,
+    prenorm: bool = False,
+    residual_in_fp32: bool = False,
+    eps: float = 1e-6
+):
+    return LayerNormGatedFunction.apply(
+        x,
+        g,
+        weight,
+        bias,
+        activation,
+        residual,
+        eps,
+        prenorm,
+        residual_in_fp32,
+        False
+    )
+
+
+def rms_norm_gated(
+    x: torch.Tensor,
+    g: torch.Tensor,
+    weight: torch.Tensor,
+    bias: torch.Tensor,
+    activation: str = 'swish',
+    residual: Optional[torch.Tensor] = None,
+    prenorm: bool = False,
+    residual_in_fp32: bool = False,
+    eps: float = 1e-6
+):
+    return LayerNormGatedFunction.apply(
+        x,
+        g,
+        weight,
+        bias,
+        activation,
+        residual,
+        eps,
+        prenorm,
+        residual_in_fp32,
+        True
+    )
+
+
+def layer_norm_swish_gate_linear(
+    x: torch.Tensor,
+    g: torch.Tensor,
+    norm_weight: torch.Tensor,
+    norm_bias: torch.Tensor,
+    linear_weight: torch.Tensor,
+    linear_bias: torch.Tensor,
+    residual: Optional[torch.Tensor] = None,
+    prenorm: bool = False,
+    residual_in_fp32: bool = False,
+    eps: float = 1e-6
+):
+    return LayerNormGatedLinearFunction.apply(
+        x,
+        g,
+        norm_weight,
+        norm_bias,
+        linear_weight,
+        linear_bias,
+        residual,
+        eps,
+        prenorm,
+        residual_in_fp32,
+        False
+    )
+
+
+def rms_norm_swish_gate_linear(
+    x,
+    g: torch.Tensor,
+    norm_weight: torch.Tensor,
+    norm_bias: torch.Tensor,
+    linear_weight: torch.Tensor,
+    linear_bias: torch.Tensor,
+    residual: Optional[torch.Tensor] = None,
+    prenorm: bool = False,
+    residual_in_fp32: bool = False,
+    eps: float = 1e-6
+):
+    return LayerNormGatedLinearFunction.apply(
+        x,
+        g,
+        norm_weight,
+        norm_bias,
+        linear_weight,
+        linear_bias,
+        residual,
+        eps,
+        prenorm,
+        residual_in_fp32,
+        True
+    )
+
+
+class FusedLayerNormGated(nn.Module):
+
+    def __init__(
+        self,
+        hidden_size: int,
+        elementwise_affine: bool = True,
+        bias: bool = False,
+        activation: str = 'swish',
+        eps: float = 1e-5,
+        device: Optional[torch.device] = None,
+        dtype: Optional[torch.dtype] = None,
+    ) -> FusedLayerNormGated:
+        factory_kwargs = {"device": device, "dtype": dtype}
+        super().__init__()
+
+        self.hidden_size = hidden_size
+        self.elementwise_affine = elementwise_affine
+        self.eps = eps
+        self.activation = activation
+
+        if self.activation not in ['swish', 'silu', 'sigmoid']:
+            raise ValueError(f"Unsupported activation: {self.activation}")
+
+        self.register_parameter("weight", None)
+        self.register_parameter("bias", None)
+        if elementwise_affine:
+            self.weight = nn.Parameter(torch.empty(hidden_size, **factory_kwargs))
+            if bias:
+                self.bias = nn.Parameter(torch.empty(hidden_size, **factory_kwargs))
+
+        self.reset_parameters()
+
+    def reset_parameters(self):
+        if self.elementwise_affine:
+            nn.init.ones_(self.weight)
+            if self.bias is not None:
+                nn.init.zeros_(self.bias)
+
+    def __repr__(self) -> str:
+        s = f"{self.__class__.__name__}({self.hidden_size}"
+        if not self.elementwise_affine:
+            s += f", elementwise_affine={self.elementwise_affine}"
+        s += f", eps={self.eps}"
+        s += f", activation={self.activation}"
+        s += ")"
+        return s
+
+    def forward(
+        self,
+        x: torch.Tensor,
+        g: torch.Tensor,
+        residual: Optional[torch.Tensor] = None,
+        prenorm: bool = False,
+        residual_in_fp32: bool = False
+    ) -> torch.Tensor:
+        return layer_norm_gated(
+            x,
+            g,
+            self.weight,
+            self.bias,
+            self.activation,
+            residual=residual,
+            eps=self.eps,
+            prenorm=prenorm,
+            residual_in_fp32=residual_in_fp32
+        )
+
+
+class FusedRMSNormGated(nn.Module):
+
+    def __init__(
+        self,
+        hidden_size: int,
+        elementwise_affine: bool = True,
+        eps: float = 1e-5,
+        activation: str = 'swish',
+        device: Optional[torch.device] = None,
+        dtype: Optional[torch.dtype] = None,
+    ) -> FusedRMSNormGated:
+        factory_kwargs = {"device": device, "dtype": dtype}
+        super().__init__()
+
+        self.hidden_size = hidden_size
+        self.elementwise_affine = elementwise_affine
+        self.eps = eps
+        self.activation = activation
+
+        if self.activation not in ['swish', 'silu', 'sigmoid']:
+            raise ValueError(f"Unsupported activation: {self.activation}")
+
+        if elementwise_affine:
+            self.weight = nn.Parameter(torch.empty(hidden_size, **factory_kwargs))
+        else:
+            self.register_parameter("weight", None)
+        self.register_parameter("bias", None)
+
+        self.reset_parameters()
+
+    def reset_parameters(self):
+        if self.elementwise_affine:
+            nn.init.ones_(self.weight)
+
+    def __repr__(self) -> str:
+        s = f"{self.__class__.__name__}({self.hidden_size}"
+        if not self.elementwise_affine:
+            s += f", elementwise_affine={self.elementwise_affine}"
+        s += f", eps={self.eps}"
+        s += f", activation={self.activation}"
+        s += ")"
+        return s
+
+    def forward(
+        self,
+        x: torch.Tensor,
+        g: torch.Tensor,
+        residual: Optional[torch.Tensor] = None,
+        prenorm: bool = False,
+        residual_in_fp32: bool = False
+    ) -> torch.Tensor:
+        return rms_norm_gated(
+            x,
+            g,
+            self.weight,
+            self.bias,
+            self.activation,
+            residual=residual,
+            eps=self.eps,
+            prenorm=prenorm,
+            residual_in_fp32=residual_in_fp32
+        )
+
+
+class FusedLayerNormSwishGate(FusedLayerNormGated):
+
+    def __init__(
+        self,
+        hidden_size: int,
+        elementwise_affine: bool = True,
+        bias: bool = False,
+        eps: float = 1e-5,
+        device: Optional[torch.device] = None,
+        dtype: Optional[torch.dtype] = None,
+    ) -> FusedLayerNormSwishGate:
+        super().__init__(
+            hidden_size=hidden_size,
+            elementwise_affine=elementwise_affine,
+            bias=bias,
+            eps=eps,
+            device=device,
+            dtype=dtype
+        )
+
+
+class FusedRMSNormSwishGate(FusedRMSNormGated):
+
+    def __init__(
+        self,
+        hidden_size: int,
+        elementwise_affine: bool = True,
+        eps: float = 1e-5,
+        device: Optional[torch.device] = None,
+        dtype: Optional[torch.dtype] = None,
+    ) -> FusedRMSNormSwishGate:
+        super().__init__(
+            hidden_size=hidden_size,
+            elementwise_affine=elementwise_affine,
+            eps=eps,
+            device=device,
+            dtype=dtype
+        )
+
+
+class FusedLayerNormGatedLinear(nn.Module):
+
+    def __init__(
+        self,
+        hidden_size: int,
+        elementwise_affine: bool = True,
+        eps: float = 1e-5,
+        device: Optional[torch.device] = None,
+        dtype: Optional[torch.dtype] = None,
+    ) -> FusedLayerNormGatedLinear:
+        factory_kwargs = {"device": device, "dtype": dtype}
+        super().__init__()
+
+        self.hidden_size = hidden_size
+        self.elementwise_affine = elementwise_affine
+        self.eps = eps
+
+        if elementwise_affine:
+            self.weight = nn.Parameter(torch.empty(hidden_size, **factory_kwargs))
+        else:
+            self.register_parameter("weight", None)
+        self.register_parameter("bias", None)
+
+        self.reset_parameters()
+
+    def reset_parameters(self):
+        if self.elementwise_affine:
+            nn.init.ones_(self.weight)
+
+    def __repr__(self) -> str:
+        s = f"{self.__class__.__name__}({self.hidden_size}"
+        if not self.elementwise_affine:
+            s += f", elementwise_affine={self.elementwise_affine}"
+        s += f", eps={self.eps}"
+        s += ")"
+        return s
+
+    def forward(
+        self,
+        x: torch.Tensor,
+        g: torch.Tensor,
+        weight: Optional[torch.Tensor] = None,
+        bias: Optional[torch.Tensor] = None,
+        residual: Optional[torch.Tensor] = None,
+        prenorm: bool = False,
+        residual_in_fp32: bool = False
+    ) -> torch.Tensor:
+        return layer_norm_swish_gate_linear(
+            x,
+            g,
+            self.weight,
+            self.bias,
+            weight,
+            bias,
+            residual=residual,
+            eps=self.eps,
+            prenorm=prenorm,
+            residual_in_fp32=residual_in_fp32
+        )
+
+
+class FusedLayerNormSwishGateLinear(FusedLayerNormGatedLinear):
+
+    def __init__(
+        self,
+        hidden_size: int,
+        elementwise_affine: bool = True,
+        eps: float = 1e-5,
+        device: Optional[torch.device] = None,
+        dtype: Optional[torch.dtype] = None,
+    ) -> FusedLayerNormSwishGateLinear:
+        super().__init__(
+            hidden_size=hidden_size,
+            elementwise_affine=elementwise_affine,
+            eps=eps,
+            device=device,
+            dtype=dtype
+        )
+
+
+class FusedRMSNormGatedLinear(nn.Module):
+
+    def __init__(
+        self,
+        hidden_size,
+        elementwise_affine: bool = True,
+        eps: float = 1e-5,
+        device: Optional[torch.device] = None,
+        dtype: Optional[torch.dtype] = None,
+    ) -> FusedRMSNormGatedLinear:
+        factory_kwargs = {"device": device, "dtype": dtype}
+        super().__init__()
+
+        self.hidden_size = hidden_size
+        self.elementwise_affine = elementwise_affine
+        self.eps = eps
+
+        self.register_parameter("weight", None)
+        self.register_parameter("bias", None)
+        if elementwise_affine:
+            self.weight = nn.Parameter(torch.empty(hidden_size, **factory_kwargs))
+
+        self.reset_parameters()
+
+    def reset_parameters(self):
+        if self.elementwise_affine:
+            nn.init.ones_(self.weight)
+
+    def __repr__(self) -> str:
+        s = f"{self.__class__.__name__}({self.hidden_size}"
+        if not self.elementwise_affine:
+            s += f", elementwise_affine={self.elementwise_affine}"
+        s += f", eps={self.eps}"
+        s += ")"
+        return s
+
+    def forward(
+        self,
+        x: torch.Tensor,
+        g: torch.Tensor,
+        weight: Optional[torch.Tensor] = None,
+        bias: Optional[torch.Tensor] = None,
+        residual: Optional[torch.Tensor] = None,
+        prenorm: bool = False,
+        residual_in_fp32: bool = False
+    ) -> torch.Tensor:
+        return rms_norm_swish_gate_linear(
+            x,
+            g,
+            self.weight,
+            self.bias,
+            weight,
+            bias,
+            residual=residual,
+            eps=self.eps,
+            prenorm=prenorm,
+            residual_in_fp32=residual_in_fp32
+        )
+
+
+class FusedRMSNormSwishGateLinear(FusedRMSNormGatedLinear):
+
+    def __init__(
+        self,
+        hidden_size: int,
+        elementwise_affine: bool = True,
+        eps: float = 1e-5,
+        device: Optional[torch.device] = None,
+        dtype: Optional[torch.dtype] = None,
+    ) -> FusedRMSNormSwishGateLinear:
+        super().__init__(
+            hidden_size=hidden_size,
+            elementwise_affine=elementwise_affine,
+            eps=eps,
+            device=device,
+            dtype=dtype
+        )

fla/modules/grpo.py

@@ -0,0 +1,396 @@
+# -*- coding: utf-8 -*-
+
+# https://github.com/huggingface/trl/blob/main/trl/trainer/grpo_trainer.py
+"""
+# Get the per-token log probabilities for the completions for the model and the reference model
+    def _get_per_token_logps(self, model, input_ids, attention_mask, logits_to_keep):
+        # We add 1 to `logits_to_keep` because the last logits of the sequence is later excluded
+        logits = model(input_ids=input_ids, attention_mask=attention_mask, logits_to_keep=logits_to_keep + 1).logits
+        logits = logits[:, :-1, :]  # (B, L-1, V), exclude the last logit: it corresponds to the next token pred
+
+        input_ids = input_ids[:, -logits_to_keep:]
+        # For transformers<=4.48, logits_to_keep argument isn't supported, so here we drop logits ourselves.
+        # See https://github.com/huggingface/trl/issues/2770
+        logits = logits[:, -logits_to_keep:]
+        return selective_log_softmax(logits, input_ids)  #  compute logprobs for the input tokens
+
+    def compute_loss(self, model, inputs, return_outputs=False, num_items_in_batch=None):
+        if return_outputs:
+            raise ValueError("The GRPOTrainer does not support returning outputs")
+        # Compute the per-token log probabilities for the model
+
+        prompt_ids, prompt_mask = inputs["prompt_ids"], inputs["prompt_mask"]
+        completion_ids, completion_mask = inputs["completion_ids"], inputs["completion_mask"]
+        input_ids = torch.cat([prompt_ids, completion_ids], dim=1)
+        attention_mask = torch.cat([prompt_mask, completion_mask], dim=1)
+        logits_to_keep = completion_ids.size(1)  # we only need to compute the logits for the completion tokens
+
+        per_token_logps = self._get_per_token_logps(model, input_ids, attention_mask, logits_to_keep)
+
+        # Compute the KL divergence between the model and the reference model
+        ref_per_token_logps = inputs["ref_per_token_logps"]
+        per_token_kl = torch.exp(ref_per_token_logps - per_token_logps) - (ref_per_token_logps - per_token_logps) - 1
+
+        # x - x.detach() allows for preserving gradients from x
+        advantages = inputs["advantages"]
+        per_token_loss = torch.exp(per_token_logps - per_token_logps.detach()) * advantages.unsqueeze(1)
+        per_token_loss = -(per_token_loss - self.beta * per_token_kl)
+        loss = ((per_token_loss * completion_mask).sum(dim=1) / completion_mask.sum(dim=1)).mean()
+
+        # Log the metrics
+        completion_length = self.accelerator.gather_for_metrics(completion_mask.sum(1)).float().mean().item()
+        self._metrics["completion_length"].append(completion_length)
+
+        mean_kl = ((per_token_kl * completion_mask).sum(dim=1) / completion_mask.sum(dim=1)).mean()
+        self._metrics["kl"].append(self.accelerator.gather_for_metrics(mean_kl).mean().item())
+
+        return loss
+"""
+
+
+import torch
+import triton
+import triton.language as tl
+
+from fla.ops.utils.op import exp, log
+from fla.utils import input_guard
+
+
+@triton.autotune(
+    [triton.Config({'BLOCK_SIZE': BLOCK_SIZE},  num_warps=NUM_WARPS, num_stages=NUM_STAGES)
+     for BLOCK_SIZE in [1024, 2048, 4096, 8192]
+     for NUM_WARPS in [8, 16, 32]
+     for NUM_STAGES in [1, 2, 4]
+     ], key=['B', 'N']
+)
+@triton.jit
+def grpo_fwd_kernel(
+    logits_ptr,
+    ref_logp_ptr,
+    input_ids_ptr,
+    advantages_ptr,
+    completion_mask_ptr,
+    loss_ptr,
+    lse_ptr,
+    beta,
+    save_kl: tl.constexpr,
+    B,
+    M,
+    N,
+    L,
+    start_idx,
+    BLOCK_SIZE: tl.constexpr
+):
+    row_idx = tl.program_id(0)
+
+    off_b = row_idx // L
+    N = tl.cast(N, tl.int64)
+
+    loss_ptr += row_idx
+
+    completion_mask_ptr += row_idx
+    not_skip = tl.load(completion_mask_ptr).to(tl.int1)
+    if not_skip == 1:
+        ref_logp_ptr += row_idx
+        lse_ptr += row_idx
+        advantages_ptr += off_b
+        logits_ptr += N * (row_idx + off_b)
+        input_ids_ptr += row_idx + (off_b+1) * start_idx
+        base_cols = tl.arange(0, BLOCK_SIZE)
+
+        m_i = -float("inf")
+        l_i = 0.0
+        for start_n in tl.range(0, N, BLOCK_SIZE):
+            cols = start_n + base_cols
+            mask = cols < N
+            logits = tl.load(logits_ptr+cols, mask=mask, other=-float('inf')).to(tl.float32)
+            m_ij = tl.max(logits)
+            new_m_i = tl.maximum(m_i, m_ij)
+            l_i = l_i * exp(m_i - new_m_i) + tl.sum(exp(logits - new_m_i))
+            m_i = new_m_i
+        lse = log(l_i) + m_i
+
+        idx = tl.load(input_ids_ptr)
+        x = tl.load(logits_ptr+idx).to(tl.float32)
+        advantage = tl.load(advantages_ptr).to(tl.float32)
+        ref_logp = tl.load(ref_logp_ptr)
+        logp = x - lse
+        diff = ref_logp - logp
+        kl = exp(diff) - diff - 1
+        loss = kl * beta - advantage
+
+        tl.store(loss_ptr, loss.to(loss_ptr.dtype.element_ty))
+        tl.store(lse_ptr, lse.to(lse_ptr.dtype.element_ty))
+        if save_kl:
+            tl.store(loss_ptr+M, kl.to(loss_ptr.dtype.element_ty))
+    else:
+        # store 0
+        tl.store(loss_ptr, 0.0)
+        if save_kl:
+            tl.store(loss_ptr+M, 0.0)
+
+
+@triton.autotune(
+    [triton.Config({'BLOCK_SIZE': BLOCK_SIZE},  num_warps=NUM_WARPS, num_stages=NUM_STAGES)
+     for BLOCK_SIZE in [1024, 2048, 4096, 8192]
+     for NUM_WARPS in [8, 16, 32]
+     for NUM_STAGES in [1, 2, 4]
+     ], key=['B', 'N']
+)
+@triton.jit
+def grpo_bwd_kernel(
+    dloss_ptr,
+    dlogits_ptr,
+    logits_ptr,
+    ref_logp_ptr,
+    input_ids_ptr,
+    advantages_ptr,
+    completion_mask_ptr,
+    lse_ptr,
+    beta,
+    B,
+    N,
+    L,
+    start_idx,
+    BLOCK_SIZE: tl.constexpr
+):
+
+    row_idx = tl.program_id(0)  # B*L
+    off_b = row_idx // L
+
+    N = tl.cast(N, tl.int64)
+
+    dlogits_ptr += N * (row_idx + off_b)
+    base_cols = tl.arange(0, BLOCK_SIZE)
+    completion_mask_ptr += row_idx
+    not_skip = tl.load(completion_mask_ptr).to(tl.int1)
+
+    if not_skip == 1:
+        lse_ptr += row_idx
+        dloss_ptr += row_idx
+        advantages_ptr += off_b
+        ref_logp_ptr += row_idx
+        logits_ptr += N * (row_idx + off_b)
+        input_ids_ptr += row_idx + (off_b+1) * start_idx
+        dloss = tl.load(dloss_ptr).to(tl.float32)
+        lse = tl.load(lse_ptr).to(tl.float32)
+        idx = tl.load(input_ids_ptr)
+        x = tl.load(logits_ptr+idx).to(tl.float32)
+        advantage = tl.load(advantages_ptr).to(tl.float32)
+        ref_logp = tl.load(ref_logp_ptr)
+        logp = x - lse
+
+        dlogp = (beta * (-1.0 * exp(ref_logp - logp) + 1)
+                 - advantage) * dloss
+
+        for start_n in tl.range(0, N, BLOCK_SIZE):
+            cols = start_n + base_cols
+            mask = cols < N
+            logits = tl.load(logits_ptr+cols, mask=mask, other=-float('inf')).to(tl.float32)
+            probs = exp(logits - lse)
+            dlogits = tl.where(cols == idx, 1-probs, -probs) * dlogp
+
+            tl.store(dlogits_ptr+cols, dlogits.to(dlogits_ptr.dtype.element_ty), mask=mask)
+    else:
+        dlogits = tl.zeros((BLOCK_SIZE,), dtype=tl.float32)
+        for start_n in tl.range(0, N, BLOCK_SIZE):
+            cols = start_n + base_cols
+            mask = cols < N
+
+            tl.store(dlogits_ptr+cols, dlogits.to(dlogits_ptr.dtype.element_ty), mask=mask)
+
+
+class GrpoLoss(torch.autograd.Function):
+
+    @input_guard
+    @staticmethod
+    def forward(ctx, logits, ref_logp, input_ids, advantages, beta, completion_mask, save_kl):
+        ctx.input_shape = logits.shape
+        B, L_ADD_1, N = ctx.input_shape
+        L = L_ADD_1 - 1
+        M = B * L
+        input_ids_start_index = input_ids.size(1) - L
+
+        if not save_kl:
+            loss = torch.empty(B, L, device=logits.device, dtype=torch.float32)
+        else:
+            loss = torch.empty(B*2, L, device=logits.device, dtype=torch.float32)
+
+        lse = torch.empty(B, L, device=logits.device, dtype=torch.float32)
+
+        if completion_mask is None:
+            completion_mask = torch.ones(B, L, device=logits.device, dtype=torch.int32)
+        else:
+            loss[:B].masked_fill_(completion_mask.logical_not(), 0.0)
+
+        grpo_fwd_kernel[(M,)](
+            logits_ptr=logits,
+            ref_logp_ptr=ref_logp,
+            input_ids_ptr=input_ids,
+            advantages_ptr=advantages,
+            completion_mask_ptr=completion_mask,
+            loss_ptr=loss,
+            lse_ptr=lse,
+            beta=beta,
+            save_kl=save_kl,
+            B=B, M=M, N=N, L=L,
+            start_idx=input_ids_start_index,
+        )
+        ctx.beta = beta
+        ctx.save_for_backward(lse, logits, input_ids, advantages, completion_mask)
+        ctx.ref_logp = ref_logp
+        return loss
+
+    @input_guard
+    @staticmethod
+    def backward(ctx, dloss):
+        # The grad of logits comes from two parts, the reward part and the kl part
+        lse, logits, input_ids, advantages, completion_mask = ctx.saved_tensors
+        B, L_ADD_1, N = ctx.input_shape
+        L = L_ADD_1 - 1
+        M = B * L
+
+        input_ids_start_index = input_ids.size(1) - L
+
+        dlogits = torch.empty_like(logits)  # B, L_ADD_1, N
+
+        grpo_bwd_kernel[(M,)](
+            dloss_ptr=dloss,
+            dlogits_ptr=dlogits,
+            logits_ptr=logits,
+            ref_logp_ptr=ctx.ref_logp,
+            input_ids_ptr=input_ids,
+            advantages_ptr=advantages,
+            completion_mask_ptr=completion_mask,
+            lse_ptr=lse,
+            beta=ctx.beta,
+            B=B, N=N, L=L,
+            start_idx=input_ids_start_index,
+        )
+        # The last token in the completion is not used in the loss computation
+        # and therefore its gradient should be set to 0
+        dlogits[:, -1, :].fill_(0.0)
+        return dlogits.view(*ctx.input_shape), None, None, None, None, None, None
+
+
+def fused_grpo_loss(logits, ref_logp, input_ids, advantages, beta=0.1, completion_mask=None, save_kl=False) -> torch.Tensor:
+    '''
+    compute grpo loss, save memory(no addition usage) and fast speed(6X for A800)
+
+    Args:
+        logtits: Tensor, [B, L+1, vocab_size], the origin output of model, it's not logits[:, :-1]
+        ref_logp: Tensor, [B, L], the origin output of model, it's not ref_logits[:, :-1]
+        input_ids: Tensor, [B, K+L], it's prompt_completion_id, it contains the prompt ids and output ids
+        advantages: Tensor, [B], the advantages of each prompt
+        beta: float, the weight of kl loss
+        completion_mask: Tensor, loss mask
+        save_kl: bool, if true will save kl
+
+    Retutn:
+        loss: Tensor, [B, L], the loss of grpo, it contains the advantage part and kl part
+
+    NOTE: logits(ref_logits) is computed by these steps
+        logits_to_keep = completion_ids.size(1)
+
+        def get_per_token_logits(model, input_ids, attention_mask, logits_to_keep):
+            # We add 1 to `logits_to_keep` because the last logits of the sequence is later excluded
+            logits = model(
+                input_ids=input_ids, attention_mask=attention_mask, logits_to_keep=logits_to_keep + 1
+            ).logits
+            return logits
+
+        logits = get_per_token_logits(model, prompt_completion_ids, attention_mask, logits_to_keep)
+    '''
+    out = GrpoLoss.apply(logits, ref_logp, input_ids, advantages, beta, completion_mask, save_kl)
+    if not save_kl:
+        return out
+    else:
+        return out.chunk(2, axis=0)
+
+
+def grpo_loss_torch(logits, ref_logp, input_ids, advantages, beta=0.1, completion_mask=None, save_kl=False):
+    def get_log_probs(logits, input_ids):
+        per_token_logps = []
+        for logits_row, input_ids_row in zip(logits, input_ids[:, -logits.size(1):]):
+            log_probs = logits_row.log_softmax(dim=-1)
+            token_log_prob = torch.gather(log_probs, dim=1, index=input_ids_row.unsqueeze(1)).squeeze(1)
+            per_token_logps.append(token_log_prob)
+        return torch.stack(per_token_logps)
+
+    logits = logits[:, :-1]
+    per_token_logps = get_log_probs(logits, input_ids)
+    ref_per_token_logps = ref_logp
+    per_token_kl = torch.exp(ref_per_token_logps - per_token_logps) - (ref_per_token_logps - per_token_logps) - 1
+
+    per_token_loss = torch.exp(per_token_logps - per_token_logps.detach()) * advantages.unsqueeze(1)
+    per_token_loss = -(per_token_loss - beta * per_token_kl)
+    if completion_mask is not None:
+        per_token_loss *= completion_mask
+        if save_kl:
+            per_token_kl *= completion_mask
+    return per_token_loss if not save_kl else (per_token_loss, per_token_kl)
+
+
+@torch.compile(fullgraph=True)
+def grpo_loss_with_old_logps(
+    logps: torch.Tensor,
+    ref_logps: torch.Tensor,
+    old_logps: torch.Tensor,
+    pad_mask: torch.Tensor,
+    logits_to_keep: int,
+    rewards: torch.Tensor,
+    beta: float = 0.2,
+    epsilon: float = 0.2
+):
+    """
+    Compute the GRPO (Group Relative Policy Optimization) loss.
+
+    Args:
+        logps (torch.Tensor): [Batch, Token_length] Log probabilities of the current policy.
+        ref_logps (torch.Tensor):[Batch, Token_length]  Log probabilities of the reference policy.
+        old_logps (torch.Tensor): [Batch, Token_length] Log probabilities of the old policy.
+        completion_ids (torch.Tensor): [Batch, Token_length] Completion token IDs (bool).
+        pad_token_id: Pad token ID.
+        logits_to_keep (int): Number of logits to keep for masking.
+        rewards (torch.Tensor): [Batch] Rewards for each generation.
+        beta (float) = 0.2: A hyperparameter for weighting the KL divergence term.
+        epsilon (float) = 0.2: An float hyperparameter for clipping the importance weights.
+
+    Returns:
+        torch.Tensor: The computed GRPO loss.
+    """
+    B = logps.shape[0]
+    assert B > 1, "Batch * Num generations should be greater than 1"
+
+    rewards_shaped = rewards.view(-1, B)  # B,num_generations
+    advantages = (rewards_shaped - rewards_shaped.mean(dim=1, keepdim=True)) / \
+        (rewards_shaped.std(dim=1, keepdim=True) + 1e-8)
+    advantages = advantages.view(-1)  # B*num_generations
+    # Calculate the per - token KL divergence
+    per_token_kl = torch.exp(ref_logps - logps) - (ref_logps - logps) - 1
+
+    # Calculate the ratio of probabilities (importance weights)
+    # Importance weights are calculated as exp(log_pi_theta - log_pi_theta_old)
+    importance_weights = torch.exp(logps - old_logps)
+
+    # Clip the importance weights to the range [1 - epsilon, 1 + epsilon]
+    importance_weights_clipped = torch.clamp(importance_weights, 1 - epsilon, 1 + epsilon)
+
+    # Create a completion mask. It checks which positions are valid based on logits_to_keep
+    completion_mask = torch.arange(logits_to_keep, device=logps.device)[None, :] >= 0
+
+    # Combine the completion mask and padding mask
+    completion_mask = completion_mask & pad_mask  # Ensure matching shape
+
+    # Add an extra dimension to advantages to match the shape for element - wise multiplication
+    advantages = advantages.unsqueeze(1)
+
+    # Calculate the per - token loss. It takes the minimum of the unclipped and clipped importance weights
+    # and subtracts the KL divergence term weighted by beta, then multiplies by the completion mask
+    token_loss = -(torch.min(advantages * importance_weights, advantages *
+                   importance_weights_clipped) - beta * per_token_kl) * completion_mask
+
+    # Calculate the final loss by summing the token losses and normalizing by the number of valid tokens
+    loss = -token_loss.sum() / completion_mask.sum()
+
+    return loss

fla/modules/l2norm.py

@@ -0,0 +1,176 @@
+# -*- coding: utf-8 -*-
+# Copyright (c) 2023-2025, Songlin Yang, Yu Zhang
+
+from typing import Optional
+
+import torch
+import triton
+import triton.language as tl
+
+from fla.utils import input_guard
+
+
+@triton.autotune(
+    configs=[
+        triton.Config({}, num_warps=num_warps)
+        for num_warps in [1, 2, 4, 8, 16, 32]
+    ],
+    key=['N']
+)
+@triton.jit
+def l2norm_fwd_kernel(
+    X,
+    Y,
+    N,
+    eps,
+    BLOCK_N: tl.constexpr,
+):
+    i_m = tl.program_id(0)
+    X += i_m * N
+    Y += i_m * N
+    # Compute mean and variance
+    cols = tl.arange(0, BLOCK_N)
+    mask = cols < N
+    x = tl.load(X + cols, mask=mask, other=0.0).to(tl.float32)
+    xbar = tl.where(mask, x, 0.0)
+    var = tl.sum(xbar * xbar, axis=0)
+    rstd = 1 / tl.sqrt(var + eps)
+    # tl.store(Rstd + i_m, rstd)
+    # Normalize and apply linear transformation
+    y = x * rstd
+    # Write output
+    tl.store(Y + cols, y, mask=mask)
+
+
+@triton.autotune(
+    configs=[
+        triton.Config({}, num_warps=num_warps)
+        for num_warps in [1, 2, 4, 8, 16, 32]
+    ],
+    key=['N']
+)
+@triton.jit
+def l2norm_bwd_kernel(
+    X,
+    DY,
+    DX,
+    N,
+    eps,
+    BLOCK_N: tl.constexpr,
+):
+    i_m = tl.program_id(0)
+    X += i_m * N
+    DX += i_m * N
+    DY += i_m * N
+
+    # Y += i_m * stride_y_row
+    cols = tl.arange(0, BLOCK_N)
+    mask = cols < N
+    x = tl.load(X + cols, mask=mask, other=0.0).to(tl.float32)
+    x = tl.where(mask, x, 0.0)
+    var = tl.sum(x * x)
+    rstd = 1 / tl.sqrt(var + eps)
+    # tl.store(Rstd + i_m, rstd)
+    # Normalize and apply linear transformation
+    # y = x * rstd
+    dy = tl.load(DY + cols, mask=mask, other=0.0).to(tl.float32)
+    dy = tl.where(mask, dy, 0.0)
+    dx = dy * rstd - tl.sum(dy * x) * (1 / (var+eps)) * rstd * x
+    tl.store(DX + cols, dx, mask=mask)
+
+
+def l2norm_fwd(
+    x: torch.Tensor,
+    eps: float = 1e-6,
+    output_dtype: Optional[torch.dtype] = None
+):
+    x_shape_og = x.shape
+    x = x.reshape(-1, x.shape[-1])
+    # allocate output
+    if output_dtype is None:
+        y = torch.empty_like(x)
+    else:
+        y = torch.empty_like(x, dtype=output_dtype)
+    assert y.stride(-1) == 1
+    N = x.shape[-1]
+    M = x.shape[0]
+    # rstd = torch.empty((M,), dtype=torch.float32, device=x.device)
+    # Less than 64KB per feature: enqueue fused kernel
+    MAX_FUSED_SIZE = 65536 // x.element_size()
+    BLOCK_N = min(MAX_FUSED_SIZE, triton.next_power_of_2(N))
+    if N > BLOCK_N:
+        raise RuntimeError("This layer norm doesn't support feature dim >= 64KB.")
+    # heuristics for number of warps
+    l2norm_fwd_kernel[(M,)](
+        x,
+        y,
+        N,
+        eps,
+        BLOCK_N,
+    )
+    return y.reshape(x_shape_og)
+
+
+def l2norm_bwd(
+    x: torch.Tensor,
+    dy: torch.Tensor,
+    eps: float = 1e-5
+):
+    x_shape_og = x.shape
+    x = x.reshape(-1, dy.shape[-1])
+    dy = dy.reshape(-1, dy.shape[-1])
+    if dy.stride(-1) != 1:
+        dy = dy.contiguous()
+    assert dy.shape == x.shape
+    # allocate output
+    dx = torch.empty_like(x)
+    M = x.shape[0]
+    N = x.shape[-1]
+    # rstd = torch.empty((M,), dtype=torch.float32, device=x.device)
+    # Less than 64KB per feature: enqueue fused kernel
+    MAX_FUSED_SIZE = 65536 // x.element_size()
+    BLOCK_N = min(MAX_FUSED_SIZE, triton.next_power_of_2(N))
+    if N > BLOCK_N:
+        raise RuntimeError("This layer norm doesn't support feature dim >= 64KB.")
+    # heuristics for number of warps
+    l2norm_bwd_kernel[(M,)](
+        x,
+        dy,
+        dx,
+        N,
+        eps,
+        BLOCK_N,
+    )
+    return dx.reshape(x_shape_og)
+
+
+class L2NormFunction(torch.autograd.Function):
+
+    @staticmethod
+    @input_guard
+    def forward(
+        ctx,
+        x,
+        eps=1e-6,
+        output_dtype=None
+    ):
+        y = l2norm_fwd(x, eps, output_dtype)
+        ctx.eps = eps
+        ctx.x_dtype = x.dtype
+        ctx.save_for_backward(x)
+        return y
+
+    @staticmethod
+    @input_guard
+    def backward(ctx, dy):
+        x, = ctx.saved_tensors
+        dx = l2norm_bwd(x, dy, ctx.eps)
+        return dx, None, None
+
+
+def l2_norm(
+    x: torch.Tensor,
+    eps: float = 1e-6,
+    output_dtype: Optional[torch.dtype] = None
+) -> torch.Tensor:
+    return L2NormFunction.apply(x, eps, output_dtype)

fla/modules/layernorm_gated.py

@@ -0,0 +1,528 @@
+# Copyright (c) 2024, Tri Dao.
+# Based on the Triton LayerNorm tutorial: https://triton-lang.org/main/getting-started/tutorials/05-layer-norm.html
+# For the backward pass, we keep weight_grad and bias_grad in registers and accumulate.
+# This backward pass is faster for dimensions up to 8k, but after that it's much slower due to register spilling.
+# The models we train have hidden dim up to 8k anyway (e.g. Llama 70B), so this is fine.
+
+import math
+from typing import Optional
+
+import torch
+import torch.nn as nn
+import torch.nn.functional as F
+import triton
+import triton.language as tl
+from einops import rearrange
+
+from fla.utils import get_multiprocessor_count, input_guard
+
+
+def rms_norm_ref(x, weight, bias, z=None, eps=1e-6, group_size=None, norm_before_gate=True, upcast=True):
+    dtype = x.dtype
+    weight = weight.float()
+    bias = bias.float() if bias is not None else None
+    if upcast:
+        x = x.float()
+        z = z.float() if z is not None else z
+    if z is not None and not norm_before_gate:
+        x = x * F.silu(z)
+    if group_size is None:
+        rstd = 1 / torch.sqrt((x.square()).mean(dim=-1, keepdim=True) + eps)
+        out = (x * rstd * weight) + bias if bias is not None else (x * rstd * weight)
+    else:
+        x_group = rearrange(x, "... (g d) -> ... g d", d=group_size)
+        rstd = 1 / torch.sqrt((x_group.square()).mean(dim=-1, keepdim=True) + eps)
+        out = rearrange(x_group * rstd, "... g d -> ... (g d)") * weight
+        if bias is not None:
+            out = out + bias
+    if z is not None and norm_before_gate:
+        out *= F.silu(z)
+    return out.to(dtype)
+
+
+@triton.heuristics({
+    "HAS_BIAS": lambda args: args["B"] is not None,
+    "HAS_Z": lambda args: args["Z"] is not None,
+})
+@triton.jit
+def layer_norm_fwd_kernel(
+    X,  # pointer to the input
+    Y,  # pointer to the output
+    W,  # pointer to the weights
+    B,  # pointer to the biases
+    Z,  # pointer to the other branch
+    Mean,  # pointer to the mean
+    Rstd,  # pointer to the 1/std
+    stride_x_row,  # how much to increase the pointer when moving by 1 row
+    stride_y_row,
+    stride_z_row,
+    M,  # number of rows in X
+    N,  # number of columns in X
+    eps,  # epsilon to avoid division by zero
+    BLOCK_N: tl.constexpr,
+    HAS_BIAS: tl.constexpr,
+    HAS_Z: tl.constexpr,
+    NORM_BEFORE_GATE: tl.constexpr,
+    IS_RMS_NORM: tl.constexpr,
+):
+    # Map the program id to the row of X and Y it should compute.
+    row = tl.program_id(0)
+    group = tl.program_id(1)
+    X += row * stride_x_row + group * N
+    Y += row * stride_y_row + group * N
+    if HAS_Z:
+        Z += row * stride_z_row + group * N
+    if not IS_RMS_NORM:
+        Mean += group * M
+    Rstd += group * M
+    W += group * N
+    if HAS_BIAS:
+        B += group * N
+    # Compute mean and variance
+    cols = tl.arange(0, BLOCK_N)
+    x = tl.load(X + cols, mask=cols < N, other=0.).to(tl.float32)
+    if HAS_Z and not NORM_BEFORE_GATE:
+        z = tl.load(Z + cols, mask=cols < N).to(tl.float32)
+        x *= z * tl.sigmoid(z)
+    if not IS_RMS_NORM:
+        mean = tl.sum(x, axis=0) / N
+        tl.store(Mean + row, mean)
+        xbar = tl.where(cols < N, x - mean, 0.)
+        var = tl.sum(xbar * xbar, axis=0) / N
+    else:
+        xbar = tl.where(cols < N, x, 0.)
+        var = tl.sum(xbar * xbar, axis=0) / N
+    rstd = 1 / tl.sqrt(var + eps)
+    tl.store(Rstd + row, rstd)
+    # Normalize and apply linear transformation
+    mask = cols < N
+    w = tl.load(W + cols, mask=mask).to(tl.float32)
+    if HAS_BIAS:
+        b = tl.load(B + cols, mask=mask).to(tl.float32)
+    x_hat = (x - mean) * rstd if not IS_RMS_NORM else x * rstd
+    y = x_hat * w + b if HAS_BIAS else x_hat * w
+    if HAS_Z and NORM_BEFORE_GATE:
+        z = tl.load(Z + cols, mask=mask).to(tl.float32)
+        y *= z * tl.sigmoid(z)
+    # Write output
+    tl.store(Y + cols, y, mask=mask)
+
+
+def layer_norm_fwd(
+    x: torch.Tensor,
+    weight: torch.Tensor,
+    bias: torch.Tensor,
+    eps: float,
+    z: torch.Tensor = None,
+    out: torch.Tensor = None,
+    group_size: int = None,
+    norm_before_gate: bool = True,
+    is_rms_norm: bool = False,
+):
+    M, N = x.shape
+    if group_size is None:
+        group_size = N
+    assert N % group_size == 0
+    ngroups = N // group_size
+    assert x.stride(-1) == 1
+    if z is not None:
+        assert z.stride(-1) == 1
+        assert z.shape == (M, N)
+    assert weight.shape == (N,)
+    assert weight.stride(-1) == 1
+    if bias is not None:
+        assert bias.stride(-1) == 1
+        assert bias.shape == (N,)
+    # allocate output
+    if out is not None:
+        assert out.shape == x.shape
+    else:
+        out = torch.empty_like(x)
+    assert out.stride(-1) == 1
+    mean = torch.empty((ngroups * M, ), dtype=torch.float32, device=x.device) if not is_rms_norm else None
+    rstd = torch.empty((ngroups * M, ), dtype=torch.float32, device=x.device)
+    # Less than 64KB per feature: enqueue fused kernel
+    MAX_FUSED_SIZE = 65536 // x.element_size()
+    BLOCK_N = min(MAX_FUSED_SIZE, triton.next_power_of_2(group_size))
+    if group_size > BLOCK_N:
+        raise RuntimeError("This layer norm doesn't support feature dim >= 64KB.")
+    # heuristics for number of warps
+    num_warps = min(max(BLOCK_N // 256, 1), 8)
+    grid = (M, ngroups)
+    layer_norm_fwd_kernel[grid](
+        x,
+        out,
+        weight,
+        bias,
+        z,
+        mean,
+        rstd,
+        x.stride(0),
+        out.stride(0),
+        z.stride(0) if z is not None else 0,
+        M,
+        group_size,
+        eps,
+        BLOCK_N=BLOCK_N,
+        NORM_BEFORE_GATE=norm_before_gate,
+        IS_RMS_NORM=is_rms_norm,
+        num_warps=num_warps
+    )
+    return out, mean, rstd
+
+
+@triton.heuristics({
+    "HAS_BIAS": lambda args: args["B"] is not None,
+    "HAS_Z": lambda args: args["Z"] is not None,
+    "RECOMPUTE_OUTPUT": lambda args: args["Y"] is not None,
+})
+@triton.jit
+def layer_norm_bwd_kernel(
+    X,   # pointer to the input
+    W,   # pointer to the weights
+    B,   # pointer to the biases
+    Z,   # pointer to the other branch
+    Y,   # pointer to the output to be recomputed
+    DY,  # pointer to the output gradient
+    DX,  # pointer to the input gradient
+    DW,  # pointer to the partial sum of weights gradient
+    DB,  # pointer to the partial sum of biases gradient
+    DZ,  # pointer to the other branch
+    Mean,   # pointer to the mean
+    Rstd,   # pointer to the 1/std
+    stride_x_row,  # how much to increase the pointer when moving by 1 row
+    stride_z_row,
+    stride_y_row,
+    stride_dy_row,
+    stride_dx_row,
+    stride_dz_row,
+    stride_dw_row,
+    stride_db_row,
+    M,  # number of rows in X
+    N,  # number of columns in X
+    eps,  # epsilon to avoid division by zero
+    rows_per_program,
+    NORM_BEFORE_GATE: tl.constexpr,
+    IS_RMS_NORM: tl.constexpr,
+    HAS_BIAS: tl.constexpr,
+    HAS_Z: tl.constexpr,
+    RECOMPUTE_OUTPUT: tl.constexpr,
+    BLOCK_N: tl.constexpr,
+):
+    # Map the program id to the elements of X, DX, and DY it should compute.
+    row_block_id = tl.program_id(0)
+    group = tl.program_id(1)
+    row_start = row_block_id * rows_per_program
+    cols = tl.arange(0, BLOCK_N)
+    mask = cols < N
+    X += row_start * stride_x_row + group * N
+    if HAS_Z:
+        Z += row_start * stride_z_row + group * N
+        DZ += row_start * stride_dz_row + group * N
+    DY += row_start * stride_dy_row + group * N
+    DX += row_start * stride_dx_row + group * N
+    if RECOMPUTE_OUTPUT:
+        Y += row_start * stride_y_row + group * N
+    if not IS_RMS_NORM:
+        Mean += group * M
+    Rstd += group * M
+    W += group * N
+    w = tl.load(W + cols, mask=mask).to(tl.float32)
+    if (RECOMPUTE_OUTPUT or HAS_Z) and HAS_BIAS:
+        B += group * N
+        b = tl.load(B + cols, mask=mask, other=0.).to(tl.float32)
+    dw = tl.zeros((BLOCK_N,), dtype=tl.float32)
+    if HAS_BIAS:
+        db = tl.zeros((BLOCK_N,), dtype=tl.float32)
+    row_end = min((row_block_id + 1) * rows_per_program, M)
+    for row in range(row_start, row_end):
+        # Load data to SRAM
+        x = tl.load(X + cols, mask=mask, other=0).to(tl.float32)
+        dy = tl.load(DY + cols, mask=mask, other=0).to(tl.float32)
+        if not IS_RMS_NORM:
+            mean = tl.load(Mean + row)
+        if HAS_Z and not NORM_BEFORE_GATE:
+            z = tl.load(Z + cols, mask=mask, other=0.).to(tl.float32)
+            x_og = x
+            x = x_og * z * tl.sigmoid(z)
+        rstd = tl.load(Rstd + row)
+        # Compute dx
+        xhat = (x - mean) * rstd if not IS_RMS_NORM else x * rstd
+        xhat = tl.where(mask, xhat, 0.)
+        if HAS_Z and NORM_BEFORE_GATE:
+            z = tl.load(Z + cols, mask=mask, other=0.).to(tl.float32)
+            z_sigmoid = tl.sigmoid(z)
+            y = xhat * w + b if HAS_BIAS else xhat * w
+            if RECOMPUTE_OUTPUT:
+                tl.store(Y + cols, y * z * z_sigmoid, mask=mask)
+            dz = dy * y * z_sigmoid * (1 + z * (1 - z_sigmoid))
+            tl.store(DZ + cols, dz, mask=mask)
+            dy *= z * z_sigmoid
+        else:
+            if RECOMPUTE_OUTPUT:
+                y = xhat * w + b if HAS_BIAS else xhat * w
+                tl.store(Y + cols, y, mask=mask)
+        wdy = w * dy
+        c1 = tl.sum(xhat * wdy, axis=0) / N
+        if not IS_RMS_NORM:
+            c2 = tl.sum(wdy, axis=0) / N
+            dx = (wdy - (xhat * c1 + c2)) * rstd
+        else:
+            dx = (wdy - xhat * c1) * rstd
+        dw += dy * xhat
+        if HAS_BIAS:
+            db += dy
+        if HAS_Z and not NORM_BEFORE_GATE:
+            z_sigmoid = tl.sigmoid(z)
+            dz = dx * x_og * z_sigmoid * (1 + z * (1 - z_sigmoid))
+            tl.store(DZ + cols, dz, mask=mask)
+            dx *= z * z_sigmoid
+        # Write dx
+        tl.store(DX + cols, dx, mask=mask)
+
+        X += stride_x_row
+        if HAS_Z:
+            Z += stride_z_row
+            DZ += stride_dz_row
+        if RECOMPUTE_OUTPUT:
+            Y += stride_y_row
+        DY += stride_dy_row
+        DX += stride_dx_row
+    tl.store(DW + row_block_id * stride_dw_row + group * N + cols, dw, mask=mask)
+    if HAS_BIAS:
+        tl.store(DB + row_block_id * stride_db_row + group * N + cols, db, mask=mask)
+
+
+def layer_norm_bwd(
+    dy: torch.Tensor,
+    x: torch.Tensor,
+    weight: torch.Tensor,
+    bias: torch.Tensor,
+    eps: float,
+    mean: torch.Tensor,
+    rstd: torch.Tensor,
+    z: torch.Tensor = None,
+    group_size: int = None,
+    norm_before_gate: bool = True,
+    is_rms_norm: bool = False,
+    recompute_output: bool = False,
+    dz: torch.Tensor = None,
+    out: torch.Tensor = None,
+):
+    M, N = x.shape
+    if group_size is None:
+        group_size = N
+    assert N % group_size == 0
+    ngroups = N // group_size
+    assert x.stride(-1) == 1
+    assert dy.stride(-1) == 1
+    assert dy.shape == (M, N)
+    if z is not None:
+        assert z.stride(-1) == 1
+        assert z.shape == (M, N)
+    assert weight.shape == (N,)
+    assert weight.stride(-1) == 1
+    if bias is not None:
+        assert bias.stride(-1) == 1
+        assert bias.shape == (N,)
+    # allocate output
+    dx = torch.empty_like(x)
+    if dz is not None:
+        assert z is not None
+        assert dz.shape == z.shape
+        assert dz.stride(-1) == 1
+    else:
+        dz = torch.empty_like(z) if z is not None else None
+    if recompute_output:
+        if out is None:
+            out = torch.empty_like(x)
+        assert out.shape == x.shape
+
+    # Less than 64KB per feature: enqueue fused kernel
+    MAX_FUSED_SIZE = 65536 // x.element_size()
+    BLOCK_N = min(MAX_FUSED_SIZE, triton.next_power_of_2(group_size))
+    if group_size > BLOCK_N:
+        raise RuntimeError("This layer norm doesn't support feature dim >= 64KB.")
+    # heuristics for number of warps
+    num_warps = min(max(BLOCK_N // 256, 1), 8)
+    sm_count = get_multiprocessor_count(x.device.index)
+    # If group size is small (e.g., 64), we're only using 1 warp. So having just 108 programs
+    # would limit the occupancy.
+    nrow_groups = math.ceil(sm_count * math.ceil(4 / num_warps) / ngroups)
+    _dw = torch.empty((nrow_groups, N), dtype=torch.float32, device=weight.device)
+    _db = torch.empty((nrow_groups, N), dtype=torch.float32, device=bias.device) if bias is not None else None
+    rows_per_program = math.ceil(M / nrow_groups)
+    grid = (nrow_groups, ngroups)
+    layer_norm_bwd_kernel[grid](
+        x,
+        weight,
+        bias,
+        z,
+        out if recompute_output else None,
+        dy,
+        dx,
+        _dw,
+        _db,
+        dz,
+        mean,
+        rstd,
+        x.stride(0),
+        z.stride(0) if z is not None else 0,
+        0 if not recompute_output else out.stride(0),
+        dy.stride(0),
+        dx.stride(0),
+        dz.stride(0) if dz is not None else 0,
+        _dw.stride(0),
+        _db.stride(0) if _db is not None else 0,
+        M, group_size, eps,
+        rows_per_program,
+        BLOCK_N=BLOCK_N,
+        NORM_BEFORE_GATE=norm_before_gate,
+        IS_RMS_NORM=is_rms_norm,
+        num_warps=num_warps
+    )
+    dw = _dw.sum(0).to(weight.dtype)
+    db = _db.sum(0).to(bias.dtype) if bias is not None else None
+    return (dx, dw, db, dz) if not recompute_output else (dx, dw, db, dz, out)
+
+
+class LayerNormFn(torch.autograd.Function):
+
+    @input_guard
+    @staticmethod
+    def forward(ctx, x, weight, bias, z=None, eps=1e-6, group_size=None, norm_before_gate=True,
+                is_rms_norm=False):
+        """If z is not None, we do norm(x) * silu(z) if norm_before_gate, else norm(x * silu(z))
+        """
+
+        x_shape_og = x.shape
+        # reshape input data into 2D tensor
+        x = x.reshape(-1, x.shape[-1])
+        if x.stride(-1) != 1:
+            x = x.contiguous()
+        if z is not None:
+            assert z.shape == x_shape_og
+            z = z.reshape(-1, z.shape[-1])
+            if z.stride(-1) != 1:
+                z = z.contiguous()
+        weight = weight.contiguous()
+        if bias is not None:
+            bias = bias.contiguous()
+        y, mean, rstd = layer_norm_fwd(
+            x,
+            weight,
+            bias,
+            eps,
+            z=z,
+            group_size=group_size,
+            norm_before_gate=norm_before_gate,
+            is_rms_norm=is_rms_norm,
+        )
+        ctx.save_for_backward(x, weight, bias, mean, rstd, z)
+        ctx.x_shape_og = x_shape_og
+        ctx.eps = eps
+        ctx.group_size = group_size
+        ctx.norm_before_gate = norm_before_gate
+        ctx.is_rms_norm = is_rms_norm
+        return y.reshape(x_shape_og)
+
+    @input_guard
+    @staticmethod
+    def backward(ctx, dy):
+        x, weight, bias, mean, rstd, z = ctx.saved_tensors
+        dy = dy.reshape(-1, dy.shape[-1])
+        if dy.stride(-1) != 1:
+            dy = dy.contiguous()
+        assert dy.shape == x.shape
+        dx, dw, db, dz = layer_norm_bwd(
+            dy,
+            x,
+            weight,
+            bias,
+            ctx.eps,
+            mean,
+            rstd,
+            z,
+            ctx.group_size,
+            ctx.norm_before_gate,
+            ctx.is_rms_norm
+        )
+        dx = dx.reshape(ctx.x_shape_og)
+        dz = dz.reshape(ctx.x_shape_og) if dz is not None else None
+        return dx, dw, db, dz, None, None, None, None
+
+
+def layernorm_fn(x, weight, bias, z=None, eps=1e-6, group_size=None, norm_before_gate=True, is_rms_norm=False):
+    return LayerNormFn.apply(x, weight, bias, z, eps, group_size, norm_before_gate, is_rms_norm)
+
+
+def rmsnorm_fn(x, weight, bias, z=None, eps=1e-6, group_size=None, norm_before_gate=True):
+    return LayerNormFn.apply(x, weight, bias, z, eps, group_size, norm_before_gate, True)
+
+
+class LayerNormGated(nn.Module):
+
+    def __init__(
+        self,
+        hidden_size,
+        eps: float = 1e-5,
+        group_size: Optional[int] = None,
+        norm_before_gate: bool = True,
+        device: Optional[torch.device] = None,
+        dtype: Optional[torch.dtype] = None,
+    ):
+        """If group_size is not None, we do GroupNorm with each group having group_size elements.
+        group_size=None is equivalent to group_size=hidden_size (i.e. there's only 1 group).
+        """
+
+        factory_kwargs = {"device": device, "dtype": dtype}
+        super().__init__()
+        self.eps = eps
+        self.weight = nn.Parameter(torch.empty(hidden_size, **factory_kwargs))
+        self.bias = nn.Parameter(torch.empty(hidden_size, **factory_kwargs))
+        self.group_size = group_size
+        self.norm_before_gate = norm_before_gate
+        self.reset_parameters()
+
+    def reset_parameters(self):
+        torch.nn.init.ones_(self.weight)
+        torch.nn.init.zeros_(self.bias)
+
+    def forward(self, x, z=None):
+        """If z is not None, we do norm(x) * silu(z) if norm_before_gate, else norm(x * silu(z))
+        """
+        return layernorm_fn(x, self.weight, self.bias, z=z, group_size=self.group_size, eps=self.eps,
+                            norm_before_gate=self.norm_before_gate)
+
+
+class RMSNormGated(nn.Module):
+
+    def __init__(
+        self,
+        hidden_size,
+        eps: float = 1e-5,
+        group_size: Optional[int] = None,
+        norm_before_gate: bool = False,
+        device: Optional[torch.device] = None,
+        dtype: Optional[torch.dtype] = None,
+    ):
+        """If group_size is not None, we do GroupNorm with each group having group_size elements.
+        group_size=None is equivalent to group_size=hidden_size (i.e. there's only 1 group).
+        """
+        factory_kwargs = {"device": device, "dtype": dtype}
+        super().__init__()
+        self.eps = eps
+        self.weight = nn.Parameter(torch.empty(hidden_size, **factory_kwargs))
+        self.register_parameter("bias", None)
+        self.group_size = group_size
+        self.norm_before_gate = norm_before_gate
+        self.reset_parameters()
+
+    def reset_parameters(self):
+        torch.nn.init.ones_(self.weight)
+
+    def forward(self, x, z=None):
+        """If z is not None, we do norm(x) * silu(z) if norm_before_gate, else norm(x * silu(z))
+        """
+        return rmsnorm_fn(x, self.weight, self.bias, z=z, eps=self.eps, group_size=self.group_size,
+                          norm_before_gate=self.norm_before_gate)

fla/modules/mlp.py

@@ -0,0 +1,127 @@
+# -*- coding: utf-8 -*-
+# Copyright (c) 2023-2025, Songlin Yang, Yu Zhang
+
+from __future__ import annotations
+
+from functools import partial
+from typing import TYPE_CHECKING, Any, Optional
+
+import torch
+import torch.nn as nn
+from torch.distributed import DeviceMesh
+from torch.distributed.tensor import DTensor, Placement, Replicate, Shard, distribute_module
+from torch.distributed.tensor.parallel import ParallelStyle
+
+from fla.modules.activations import swiglu, swiglu_linear
+
+if TYPE_CHECKING:
+    from transformers.processing_utils import Unpack
+
+
+class GatedMLP(nn.Module):
+
+    def __init__(
+        self,
+        hidden_size: int,
+        hidden_ratio: Optional[int] = None,
+        intermediate_size: Optional[int] = None,
+        hidden_act: str = 'swish',
+        fuse_swiglu: bool = True
+    ) -> GatedMLP:
+        super().__init__()
+
+        self.hidden_size = hidden_size
+        # the final number of params is `hidden_ratio * hidden_size^2`
+        # `intermediate_size` is chosen to be a multiple of 256 closest to `2/3 * hidden_size * hidden_ratio`
+        if hidden_ratio is None:
+            hidden_ratio = 4
+        if intermediate_size is None:
+            intermediate_size = int(hidden_size * hidden_ratio * 2 / 3)
+            intermediate_size = 256 * ((intermediate_size + 256 - 1) // 256)
+        self.hidden_ratio = hidden_ratio
+        self.intermediate_size = intermediate_size
+        self.hidden_act = hidden_act
+        self.fuse_swiglu = fuse_swiglu
+
+        if hidden_act != 'swish':
+            raise ValueError(f'Unsupported hidden_act: {hidden_act}')
+
+        self.gate_proj = nn.Linear(self.hidden_size, self.intermediate_size, bias=False)
+        self.up_proj = nn.Linear(self.hidden_size, self.intermediate_size, bias=False)
+        self.down_proj = nn.Linear(self.intermediate_size, self.hidden_size, bias=False)
+        if self.fuse_swiglu:
+            self.swiglu_linear = SwiGLULinear()
+
+    def forward(
+        self,
+        x: torch.Tensor,
+        **kwargs: Unpack[Any]
+    ) -> torch.Tensor:
+        gate, y = self.gate_proj(x), self.up_proj(x)
+        if self.fuse_swiglu:
+            return self.swiglu_linear(gate, y, self.down_proj.weight, self.down_proj.bias)
+        else:
+            return self.down_proj(swiglu(gate, y))
+
+
+class SwiGLULinear(nn.Module):
+
+    def forward(self, x, y, weight, bias):
+        return swiglu_linear(x, y, weight, bias)
+
+
+class SwiGLULinearParallel(ParallelStyle):
+    def __init__(
+        self,
+        *,
+        input_layouts: Optional[Placement] = None,
+        output_layouts: Optional[Placement] = None,
+        use_local_output: bool = True,
+    ):
+        super().__init__()
+        self.input_layouts = (input_layouts or Shard(-1),)
+        self.output_layouts = (output_layouts or Replicate(),)
+        self.desired_input_layouts = (Shard(-1),)
+        self.use_local_output = use_local_output
+
+    @staticmethod
+    def _prepare_input_fn(
+        input_layouts, desired_input_layouts, mod, inputs, device_mesh
+    ):
+        x, y, weight, bias = inputs
+        if not isinstance(x, DTensor):
+            x = DTensor.from_local(x, device_mesh, input_layouts, run_check=False)
+        if x.placements != desired_input_layouts:
+            x = x.redistribute(placements=desired_input_layouts, async_op=True)
+
+        if not isinstance(y, DTensor):
+            y = DTensor.from_local(y, device_mesh, input_layouts, run_check=False)
+        if y.placements != desired_input_layouts:
+            y = y.redistribute(placements=desired_input_layouts, async_op=True)
+
+        if not isinstance(weight, DTensor):
+            weight = DTensor.from_local(weight, device_mesh, (Shard(1),))
+
+        if bias is not None and not isinstance(bias, DTensor):
+            bias = DTensor.from_local(bias, device_mesh, (Replicate(),))
+
+        return x, y, weight, bias
+
+    @staticmethod
+    def _prepare_output_fn(output_layouts, use_local_output, mod, outputs, device_mesh):
+        # Rowwise sharding produces partial output, depending on output layouts:
+        # 1. to replicate -> allreduce
+        # 2. to shard -> reduce_scatter
+        if outputs.placements != output_layouts:
+            outputs = outputs.redistribute(placements=output_layouts, async_op=True)
+        # back to local tensor if use_local_output is True
+        return outputs.to_local() if use_local_output else outputs
+
+    def _apply(self, module: nn.Module, device_mesh: DeviceMesh) -> nn.Module:
+        return distribute_module(
+            module,
+            device_mesh,
+            partition_fn=None,
+            input_fn=partial(self._prepare_input_fn, self.input_layouts, self.desired_input_layouts),
+            output_fn=partial(self._prepare_output_fn, self.output_layouts, self.use_local_output)
+        )

fla/ops/attn/__init__.py

@@ -0,0 +1,17 @@
+# -*- coding: utf-8 -*-
+
+from .parallel import parallel_attn
+from .parallel_rectified import parallel_rectified_attn
+from .parallel_softpick import parallel_softpick_attn
+from .naive import naive_attn
+from .naive_rectified import naive_rectified_attn
+from .naive_softpick import naive_softpick_attn
+
+__all__ = [
+    'parallel_attn',
+    'parallel_rectified_attn',
+    'parallel_softpick_attn',
+    'naive_attn',
+    'naive_rectified_attn',
+    'naive_softpick_attn',
+]

fla/ops/attn/naive_softpick.py

@@ -0,0 +1,39 @@
+import torch
+import torch.nn.functional as F
+from typing import Optional
+from einops import rearrange
+
+def softpick(x, dim=-1, eps=1e-8):
+    # softpick function: relu(exp(x)-1) / sum(abs(exp(x)-1))
+    # numerically stable version
+    x_m = torch.max(x, dim=dim, keepdim=True).values
+    x_m_e_m = torch.exp(-x_m)
+    x_e_1 = torch.exp(x - x_m) - x_m_e_m
+    r_x_e_1 = F.relu(x_e_1)
+    a_x_e_1 = torch.where(x.isfinite(), torch.abs(x_e_1), 0)
+    return r_x_e_1 / (torch.sum(a_x_e_1, dim=dim, keepdim=True) + eps) # epsilon is only useful if all inputs are EXACTLY 0. we might not even need it
+
+def naive_softpick_attn(
+    q: torch.Tensor,
+    k: torch.Tensor,
+    v: torch.Tensor,
+    scale: Optional[float] = None,
+    cu_seqlens: Optional[torch.LongTensor] = None,
+    head_first: bool = False
+) -> torch.Tensor:
+    head_dim = q.shape[-1]
+    if scale is None:
+        scale = 1.0 / (head_dim ** 0.5)
+    if not head_first:
+        q, k, v = map(lambda x: rearrange(x, 'b t h d -> b h t d'), (q, k, v))
+    q_len = q.shape[-2]
+    k_len = k.shape[-2]
+    mask = torch.tril(torch.ones(k_len, k_len, device=q.device))
+    wei = torch.matmul(q, k.transpose(2, 3)) # shape: (batch_size, num_heads, q_len, k_len)
+    wei = wei * scale
+    wei = wei.masked_fill(mask[k_len-q_len:k_len, :k_len] == 0, float('-inf'))
+    wei = softpick(wei.float(), dim=-1).to(q.dtype)
+    o = torch.matmul(wei, v) # shape: (batch_size, num_heads, q_len, head_dim)
+    if not head_first:
+        o = rearrange(o, 'b h t d -> b t h d')
+    return o, wei

fla/ops/based/__init__.py

@@ -0,0 +1,9 @@
+# -*- coding: utf-8 -*-
+
+from .fused_chunk import fused_chunk_based
+from .parallel import parallel_based
+
+__all__ = [
+    'fused_chunk_based',
+    'parallel_based'
+]

fla/ops/common/__init__.py

@@ -0,0 +1 @@
+# -*- coding: utf-8 -*-

fla/ops/common/chunk_delta_h.py

@@ -0,0 +1,399 @@
+# -*- coding: utf-8 -*-
+# Copyright (c) 2023-2025, Songlin Yang, Yu Zhang
+
+from typing import Optional, Tuple
+
+import torch
+import triton
+import triton.language as tl
+
+from fla.ops.common.utils import prepare_chunk_offsets
+from fla.ops.utils.op import exp
+from fla.utils import check_shared_mem, is_nvidia_hopper, use_cuda_graph
+
+NUM_WARPS = [2, 4] if is_nvidia_hopper else [2, 4, 8, 16]
+
+
+@triton.heuristics({
+    'USE_G': lambda args: args['g'] is not None,
+    'USE_INITIAL_STATE': lambda args: args['h0'] is not None,
+    'STORE_FINAL_STATE': lambda args: args['ht'] is not None,
+    'USE_OFFSETS': lambda args: args['offsets'] is not None,
+})
+@triton.autotune(
+    configs=[
+        triton.Config({}, num_warps=num_warps, num_stages=num_stages)
+        for num_warps in NUM_WARPS
+        for num_stages in [2, 3, 4]
+    ],
+    key=['H', 'K', 'V', 'BT', 'BK', 'BV', 'USE_G'],
+    use_cuda_graph=use_cuda_graph,
+)
+@triton.jit(do_not_specialize=['T'])
+def chunk_gated_delta_rule_fwd_kernel_h(
+    k,
+    v,
+    d,
+    v_new,
+    g,
+    h,
+    h0,
+    ht,
+    offsets,
+    chunk_offsets,
+    T,
+    H: tl.constexpr,
+    K: tl.constexpr,
+    V: tl.constexpr,
+    BT: tl.constexpr,
+    BC: tl.constexpr,
+    BK: tl.constexpr,
+    BV: tl.constexpr,
+    NT: tl.constexpr,
+    USE_G: tl.constexpr,
+    USE_INITIAL_STATE: tl.constexpr,
+    STORE_FINAL_STATE: tl.constexpr,
+    USE_OFFSETS: tl.constexpr,
+    HEAD_FIRST: tl.constexpr,
+):
+    i_k, i_v, i_nh = tl.program_id(0), tl.program_id(1), tl.program_id(2)
+    i_n, i_h = i_nh // H, i_nh % H
+    if USE_OFFSETS:
+        bos, eos = tl.load(offsets + i_n).to(tl.int32), tl.load(offsets + i_n + 1).to(tl.int32)
+        T = eos - bos
+        NT = tl.cdiv(T, BT)
+        boh = tl.load(chunk_offsets + i_n).to(tl.int32)
+    else:
+        bos, eos = i_n * T, i_n * T + T
+        NT = tl.cdiv(T, BT)
+        boh = i_n * NT
+
+    # [BK, BV]
+    b_h = tl.zeros([BK, BV], dtype=tl.float32)
+    if USE_INITIAL_STATE:
+        p_h0 = tl.make_block_ptr(h0 + i_nh * K*V, (K, V), (V, 1), (i_k * BK, i_v * BV), (BK, BV), (1, 0))
+        b_h = tl.load(p_h0, boundary_check=(0, 1)).to(tl.float32)
+
+    for i_t in range(NT):
+        if HEAD_FIRST:
+            p_h = tl.make_block_ptr(h + (i_nh * NT + i_t) * K*V, (K, V), (V, 1), (i_k * BK, i_v * BV), (BK, BV), (1, 0))
+        else:
+            p_h = tl.make_block_ptr(h + ((boh + i_t) * H + i_h) * K*V, (K, V), (V, 1), (i_k * BK, i_v * BV), (BK, BV), (1, 0))
+        tl.store(p_h, b_h.to(p_h.dtype.element_ty), boundary_check=(0, 1))
+        b_hc = tl.zeros([BK, BV], dtype=tl.float32)
+        if USE_G:
+            last_idx = min((i_t + 1) * BT, T) - 1
+            if HEAD_FIRST:
+                b_g_last = tl.load(g + i_nh * T + last_idx)
+            else:
+                b_g_last = tl.load(g + bos * H + last_idx * H + i_h)
+        else:
+            b_g_last = None
+            last_idx = None
+        # since we need to make all DK in the SRAM. we face serve SRAM memory burden. By subchunking we allievate such burden
+        for i_c in range(tl.cdiv(min(BT, T - i_t * BT), BC)):
+            if HEAD_FIRST:
+                p_k = tl.make_block_ptr(k + i_nh * T*K, (K, T), (1, K), (i_k * BK, i_t * BT + i_c * BC), (BK, BC), (0, 1))
+                p_d = tl.make_block_ptr(d + i_nh * T*K, (T, K), (K, 1), (i_t * BT + i_c * BC, i_k * BK), (BC, BK), (1, 0))
+                p_v = tl.make_block_ptr(v + i_nh * T*V, (T, V), (V, 1), (i_t * BT + i_c * BC, i_v * BV), (BC, BV), (1, 0))
+                p_v_new = tl.make_block_ptr(v_new+i_nh*T*V, (T, V), (V, 1), (i_t * BT + i_c * BC, i_v * BV), (BC, BV), (1, 0))
+                p_g = tl.make_block_ptr(g + i_nh * T, (T,), (1,), (i_t * BT + i_c * BC,), (BC,), (0,)) if USE_G else None
+            else:
+                p_k = tl.make_block_ptr(k+(bos*H+i_h)*K, (K, T), (1, H*K), (i_k * BK, i_t * BT + i_c * BC), (BK, BC), (0, 1))
+                p_d = tl.make_block_ptr(d+(bos*H+i_h)*K, (T, K), (H*K, 1), (i_t * BT + i_c * BC, i_k * BK), (BC, BK), (1, 0))
+                p_v = tl.make_block_ptr(v+(bos*H+i_h)*V, (T, V), (H*V, 1), (i_t * BT + i_c * BC, i_v * BV), (BC, BV), (1, 0))
+                p_v_new = tl.make_block_ptr(v_new+(bos*H+i_h)*V, (T, V), (H*V, 1), (i_t*BT+i_c*BC, i_v * BV), (BC, BV), (1, 0))
+                p_g = tl.make_block_ptr(g+bos*H+i_h, (T,), (H,), (i_t*BT+i_c*BC, ), (BC,), (0,)) if USE_G else None
+            b_g = tl.load(p_g, boundary_check=(0, )) if USE_G else None
+            # [BK, BC]
+            b_k = tl.load(p_k, boundary_check=(0, 1))
+            b_k = (b_k * exp(b_g_last - b_g)[None, :]).to(b_k.dtype) if USE_G else b_k
+            # [BC, BK]
+            b_d = tl.load(p_d, boundary_check=(0, 1))
+            b_d = (b_d * exp(b_g)[:, None]).to(b_d.dtype) if USE_G else b_d
+            # [BC, BV]
+            b_v = tl.load(p_v, boundary_check=(0, 1))
+            b_v2 = b_v - tl.dot(b_d, b_h.to(b_d.dtype))
+            # [BK, BV]
+            tl.store(p_v_new, b_v2.to(p_v_new.dtype.element_ty), boundary_check=(0, 1))
+            b_hc += tl.dot(b_k, b_v2.to(b_k.dtype), allow_tf32=False)
+        b_h *= exp(b_g_last) if USE_G else 1
+        b_h += b_hc
+
+    if STORE_FINAL_STATE:
+        p_ht = tl.make_block_ptr(ht + i_nh * K*V, (K, V), (V, 1), (i_k * BK, i_v * BV), (BK, BV), (1, 0))
+        tl.store(p_ht, b_h.to(p_ht.dtype.element_ty), boundary_check=(0, 1))
+
+
+@triton.heuristics({
+    'USE_G': lambda args: args['g'] is not None,
+    'USE_INITIAL_STATE': lambda args: args['dh0'] is not None,
+    'USE_FINAL_STATE_GRADIENT': lambda args: args['dht'] is not None,
+    'USE_OFFSETS': lambda args: args['offsets'] is not None,
+})
+@triton.autotune(
+    configs=[
+        triton.Config({}, num_warps=num_warps, num_stages=num_stages)
+        for num_warps in NUM_WARPS
+        for num_stages in [2, 3, 4]
+    ],
+    key=['BT', 'BK', 'BV', 'USE_G'],
+    use_cuda_graph=use_cuda_graph,
+)
+@triton.jit(do_not_specialize=['T'])
+def chunk_gated_delta_rule_bwd_kernel_dhu(
+    q,
+    k,
+    d,
+    g,
+    dht,
+    dh0,
+    do,
+    dh,
+    dv,
+    dv2,
+    offsets,
+    chunk_offsets,
+    scale,
+    T,
+    H: tl.constexpr,
+    K: tl.constexpr,
+    V: tl.constexpr,
+    BT: tl.constexpr,
+    BC: tl.constexpr,
+    BK: tl.constexpr,
+    BV: tl.constexpr,
+    USE_G: tl.constexpr,
+    USE_INITIAL_STATE: tl.constexpr,
+    USE_FINAL_STATE_GRADIENT: tl.constexpr,
+    USE_OFFSETS: tl.constexpr,
+    HEAD_FIRST: tl.constexpr
+):
+    i_k, i_v, i_nh = tl.program_id(0), tl.program_id(1), tl.program_id(2)
+    i_n, i_h = i_nh // H, i_nh % H
+    if USE_OFFSETS:
+        bos, eos = tl.load(offsets + i_n).to(tl.int32), tl.load(offsets + i_n + 1).to(tl.int32)
+        T = eos - bos
+        NT = tl.cdiv(T, BT)
+        boh = tl.load(chunk_offsets + i_n).to(tl.int32)
+    else:
+        bos, eos = i_n * T, i_n * T + T
+        NT = tl.cdiv(T, BT)
+        boh = i_n * NT
+
+    # [BK, BV]
+    b_dh = tl.zeros([BK, BV], dtype=tl.float32)
+    if USE_FINAL_STATE_GRADIENT:
+        p_dht = tl.make_block_ptr(dht + i_nh * K*V, (K, V), (V, 1), (i_k * BK, i_v * BV), (BK, BV), (1, 0))
+        b_dh += tl.load(p_dht, boundary_check=(0, 1))
+
+    for i_t in range(NT - 1, -1, -1):
+        if HEAD_FIRST:
+            p_dh = tl.make_block_ptr(dh + (i_nh * NT + i_t) * K*V, (K, V), (V, 1), (i_k * BK, i_v * BV), (BK, BV), (1, 0))
+        else:
+            p_dh = tl.make_block_ptr(dh + ((boh+i_t) * H + i_h) * K*V, (K, V), (V, 1), (i_k * BK, i_v * BV), (BK, BV), (1, 0))
+        tl.store(p_dh, b_dh.to(p_dh.dtype.element_ty), boundary_check=(0, 1))
+        b_dh_tmp = tl.zeros([BK, BV], dtype=tl.float32)
+        if USE_G:
+            last_idx = min((i_t + 1) * BT, T) - 1
+            if HEAD_FIRST:
+                bg_last = tl.load(g + i_nh * T + last_idx)
+            else:
+                bg_last = tl.load(g + (bos + last_idx) * H + i_h)
+        else:
+            bg_last = None
+            last_idx = None
+        for i_c in range(tl.cdiv(BT, BC) - 1, -1, -1):
+            if HEAD_FIRST:
+                p_q = tl.make_block_ptr(q + i_nh * T*K, (K, T), (1, K), (i_k * BK, i_t * BT + i_c * BC), (BK, BC), (0, 1))
+                p_k = tl.make_block_ptr(k + i_nh * T*K, (T, K), (K, 1), (i_t * BT + i_c * BC, i_k * BK), (BC, BK), (1, 0))
+                p_d = tl.make_block_ptr(d + i_nh * T*K, (K, T), (1, K), (i_k * BK, i_t * BT + i_c * BC), (BK, BC), (0, 1))
+                p_dv = tl.make_block_ptr(dv + i_nh * T*V, (T, V), (V, 1), (i_t * BT + i_c * BC, i_v * BV), (BC, BV), (1, 0))
+                p_do = tl.make_block_ptr(do + i_nh * T*V, (T, V), (V, 1), (i_t * BT + i_c * BC, i_v * BV), (BC, BV), (1, 0))
+                p_g = tl.make_block_ptr(g + i_nh * T, (T,), (1,), (i_t * BT + i_c * BC,), (BC,), (0,)) if USE_G else None
+                p_dv2 = tl.make_block_ptr(dv2 + i_nh * T*V, (T, V), (V, 1), (i_t * BT + i_c * BC, i_v * BV), (BC, BV), (1, 0))
+            else:
+                p_q = tl.make_block_ptr(q+(bos*H+i_h)*K, (K, T), (1, H*K), (i_k * BK, i_t * BT + i_c * BC), (BK, BC), (0, 1))
+                p_k = tl.make_block_ptr(k+(bos*H+i_h)*K, (T, K), (H*K, 1), (i_t * BT + i_c * BC, i_k * BK), (BC, BK), (1, 0))
+                p_d = tl.make_block_ptr(d+(bos*H+i_h)*K, (K, T), (1, H*K), (i_k * BK, i_t * BT + i_c * BC), (BK, BC), (0, 1))
+                p_dv = tl.make_block_ptr(dv+(bos*H+i_h)*V, (T, V), (H*V, 1), (i_t*BT + i_c * BC, i_v * BV), (BC, BV), (1, 0))
+                p_do = tl.make_block_ptr(do+(bos*H+i_h)*V, (T, V), (H*V, 1), (i_t*BT + i_c * BC, i_v * BV), (BC, BV), (1, 0))
+                p_g = tl.make_block_ptr(g+bos*H+i_h, (T,), (H,), (i_t*BT + i_c * BC,), (BC,), (0,)) if USE_G else None
+                p_dv2 = tl.make_block_ptr(dv2+(bos*H+i_h)*V, (T, V), (H*V, 1), (i_t*BT + i_c * BC, i_v * BV), (BC, BV), (1, 0))
+            b_g = tl.load(p_g, boundary_check=(0,)) if USE_G else None
+            # [BK, BT]
+            b_q = tl.load(p_q, boundary_check=(0, 1))
+            b_q = (b_q * scale * exp(b_g)[None, :]).to(b_q.dtype) if USE_G else (b_q * scale).to(b_q.dtype)
+            # [BT, BK]
+            b_k = tl.load(p_k, boundary_check=(0, 1))
+            b_d = tl.load(p_d, boundary_check=(0, 1))
+            b_k = (b_k * exp(bg_last - b_g)[:, None]).to(b_k.dtype) if USE_G else b_k
+            b_d = (b_d * exp(b_g)[None, :]).to(b_d.dtype) if USE_G else b_d
+            # [BT, V]
+            b_do = tl.load(p_do, boundary_check=(0, 1))
+            b_dv = tl.load(p_dv, boundary_check=(0, 1))
+            b_dv2 = b_dv + tl.dot(b_k, b_dh.to(b_k.dtype), allow_tf32=False)
+            tl.store(p_dv2, b_dv2.to(p_dv.dtype.element_ty), boundary_check=(0, 1))
+            # [BK, BV]
+            b_dh_tmp += tl.dot(b_q, b_do.to(b_q.dtype), allow_tf32=False)
+            b_dh_tmp -= tl.dot(b_d, b_dv2.to(b_q.dtype), allow_tf32=False)
+        b_dh *= exp(bg_last) if USE_G else 1
+        b_dh += b_dh_tmp
+
+    if USE_INITIAL_STATE:
+        p_dh0 = tl.make_block_ptr(dh0 + i_nh * K*V, (K, V), (V, 1), (i_k * BK, i_v * BV), (BK, BV), (1, 0))
+        tl.store(p_dh0, b_dh.to(p_dh0.dtype.element_ty), boundary_check=(0, 1))
+
+
+def chunk_gated_delta_rule_fwd_h(
+    k: torch.Tensor,
+    w: torch.Tensor,
+    u: torch.Tensor,
+    g: Optional[torch.Tensor] = None,
+    initial_state: Optional[torch.Tensor] = None,
+    output_final_state: bool = False,
+    offsets: Optional[torch.LongTensor] = None,
+    indices: Optional[torch.LongTensor] = None,
+    head_first: bool = True,
+    chunk_size: int = 64
+) -> Tuple[torch.Tensor, torch.Tensor]:
+    if head_first:
+        B, H, T, K, V = *k.shape, u.shape[-1]
+    else:
+        B, T, H, K, V = *k.shape, u.shape[-1]
+    BT = min(chunk_size, max(triton.next_power_of_2(T), 16))
+    # N: the actual number of sequences in the batch with either equal or variable lengths
+    if offsets is None:
+        N, NT, chunk_offsets = B, triton.cdiv(T, BT), None
+    else:
+        N, NT, chunk_offsets = len(offsets) - 1, len(indices), prepare_chunk_offsets(offsets, BT)
+    BK = triton.next_power_of_2(K)
+    assert BK <= 256, "current kernel does not support head dimension larger than 256."
+    # H100 can have larger block size
+    if check_shared_mem('hopper', k.device.index):
+        BV = 64
+        BC = 64 if K <= 128 else 32
+    # A100
+    elif check_shared_mem('ampere', k.device.index):
+        BV = 32
+        BC = 64
+    else:
+        BV = 32
+        BC = 32 if K <= 128 else 16
+    BC = min(BT, BC)
+    NK = triton.cdiv(K, BK)
+    NV = triton.cdiv(V, BV)
+    assert NK == 1, 'NK > 1 is not supported because it involves time-consuming synchronization'
+
+    if head_first:
+        h = k.new_empty(B, H, NT, K, V)
+    else:
+        h = k.new_empty(B, NT, H, K, V)
+    final_state = k.new_empty(N, H, K, V, dtype=torch.float32) if output_final_state else None
+
+    v_new = torch.empty_like(u)
+    grid = (NK, NV, N * H)
+
+    chunk_gated_delta_rule_fwd_kernel_h[grid](
+        k=k,
+        v=u,
+        d=w,
+        v_new=v_new,
+        g=g,
+        h=h,
+        h0=initial_state,
+        ht=final_state,
+        offsets=offsets,
+        chunk_offsets=chunk_offsets,
+        T=T,
+        H=H,
+        K=K,
+        V=V,
+        BT=BT,
+        BC=BC,
+        BK=BK,
+        BV=BV,
+        NT=NT,
+        HEAD_FIRST=head_first
+    )
+    return h, v_new, final_state
+
+
+def chunk_gated_delta_rule_bwd_dhu(
+    q: torch.Tensor,
+    k: torch.Tensor,
+    w: torch.Tensor,
+    g: torch.Tensor,
+    h0: torch.Tensor,
+    dht: Optional[torch.Tensor],
+    do: torch.Tensor,
+    dv: torch.Tensor,
+    scale: float,
+    offsets: Optional[torch.LongTensor] = None,
+    indices: Optional[torch.LongTensor] = None,
+    head_first: bool = True,
+    chunk_size: int = 64
+) -> Tuple[torch.Tensor, torch.Tensor, torch.Tensor]:
+    if head_first:
+        B, H, T, K, V = *q.shape, do.shape[-1]
+    else:
+        B, T, H, K, V = *q.shape, do.shape[-1]
+    BT = min(chunk_size, max(triton.next_power_of_2(T), 16))
+    # N: the actual number of sequences in the batch with either equal or variable lengths
+    if offsets is None:
+        N, NT, chunk_offsets = B, triton.cdiv(T, BT), None
+    else:
+        N, NT, chunk_offsets = len(offsets) - 1, len(indices), prepare_chunk_offsets(offsets, BT)
+
+    BK = triton.next_power_of_2(K)
+    assert BK <= 256, "current kernel does not support head dimension being larger than 256."
+
+    # H100
+    if check_shared_mem('hopper', q.device.index):
+        BV = 64
+        BC = 64 if K <= 128 else 32
+    # A100
+    elif check_shared_mem('ampere', q.device.index):
+        BV = 32
+        BC = 64 if K <= 128 else 32
+    else:
+        BV = 32 if K <= 128 else 16
+        BC = 16
+
+    BC = min(BT, BC)
+    NK, NV = triton.cdiv(K, BK), triton.cdiv(V, BV)
+    assert NK == 1, 'NK > 1 is not supported because it involves time-consuming synchronization'
+
+    if head_first:
+        dh = q.new_empty(B, H, NT, K, V)
+    else:
+        dh = q.new_empty(B, NT, H, K, V)
+    dh0 = torch.empty_like(h0, dtype=torch.float32) if h0 is not None else None
+    dv2 = torch.empty_like(dv)
+
+    grid = (NK, NV, N * H)
+    chunk_gated_delta_rule_bwd_kernel_dhu[grid](
+        q=q,
+        k=k,
+        d=w,
+        g=g,
+        dht=dht,
+        dh0=dh0,
+        do=do,
+        dh=dh,
+        dv=dv,
+        dv2=dv2,
+        offsets=offsets,
+        chunk_offsets=chunk_offsets,
+        scale=scale,
+        T=T,
+        H=H,
+        K=K,
+        V=V,
+        BT=BT,
+        BC=BC,
+        BK=BK,
+        BV=BV,
+        HEAD_FIRST=head_first
+    )
+    return dh, dh0, dv2

fla/ops/common/chunk_h.py

@@ -0,0 +1,422 @@
+# -*- coding: utf-8 -*-
+# Copyright (c) 2023-2025, Songlin Yang, Yu Zhang
+
+from typing import Optional, Tuple
+
+import torch
+import triton
+import triton.language as tl
+
+from fla.ops.common.utils import prepare_chunk_offsets
+from fla.ops.utils.op import exp
+from fla.utils import check_shared_mem
+
+BKV_LIST = [32, 64] if check_shared_mem() else [16, 32]
+
+
+@triton.heuristics({
+    'USE_INITIAL_STATE': lambda args: args['h0'] is not None,
+    'STORE_FINAL_STATE': lambda args: args['ht'] is not None,
+    'USE_OFFSETS': lambda args: args['offsets'] is not None
+})
+@triton.autotune(
+    configs=[
+        triton.Config({'BK': BK, 'BV': BV}, num_warps=num_warps, num_stages=num_stages)
+        for BK in BKV_LIST
+        for BV in BKV_LIST
+        for num_warps in [1, 2, 4, 8]
+        for num_stages in [2, 3, 4]
+    ],
+    key=['BT', 'USE_G', 'USE_GK', 'USE_GV']
+)
+@triton.jit(do_not_specialize=['T'])
+def chunk_fwd_kernel_h(
+    k,
+    v,
+    h,
+    g,
+    gk,
+    gv,
+    h0,
+    ht,
+    offsets,
+    split_offsets,
+    T,
+    H: tl.constexpr,
+    K: tl.constexpr,
+    V: tl.constexpr,
+    BT: tl.constexpr,
+    BS: tl.constexpr,
+    BK: tl.constexpr,
+    BV: tl.constexpr,
+    USE_G: tl.constexpr,
+    USE_GK: tl.constexpr,
+    USE_GV: tl.constexpr,
+    USE_INITIAL_STATE: tl.constexpr,
+    STORE_FINAL_STATE: tl.constexpr,
+    USE_OFFSETS: tl.constexpr,
+    HEAD_FIRST: tl.constexpr
+):
+    i_k, i_v, i_nh = tl.program_id(0), tl.program_id(1), tl.program_id(2)
+    i_n, i_h = i_nh // H, i_nh % H
+    if USE_OFFSETS:
+        bos, eos = tl.load(offsets + i_n).to(tl.int32), tl.load(offsets + i_n + 1).to(tl.int32)
+        T = eos - bos
+        NT = tl.cdiv(T, BT)
+        NS = tl.cdiv(T, BS)
+        boh = tl.load(split_offsets + i_n).to(tl.int32)
+    else:
+        bos, eos = i_n * T, i_n * T + T
+        NT = tl.cdiv(T, BT)
+        NS = tl.cdiv(T, BS)
+        boh = i_n * NS
+
+    # [BK, BV]
+    b_h = tl.zeros([BK, BV], dtype=tl.float32)
+    if USE_INITIAL_STATE:
+        p_h0 = tl.make_block_ptr(h0 + i_nh * K*V, (K, V), (V, 1), (i_k * BK, i_v * BV), (BK, BV), (1, 0))
+        b_h = tl.load(p_h0, boundary_check=(0, 1)).to(tl.float32)
+
+    for i_t in range(NT):
+        i_s = i_t // (BS // BT)
+        if HEAD_FIRST:
+            p_k = tl.make_block_ptr(k + i_nh * T*K, (K, T), (1, K), (i_k * BK, i_t * BT), (BK, BT), (0, 1))
+            p_v = tl.make_block_ptr(v + i_nh * T*V, (T, V), (V, 1), (i_t * BT, i_v * BV), (BT, BV), (1, 0))
+
+            o_h = (i_nh * NS + i_s).to(tl.int64) * K*V
+            p_h = tl.make_block_ptr(h + o_h, (K, V), (V, 1), (i_k * BK, i_v * BV), (BK, BV), (1, 0))
+        else:
+            p_k = tl.make_block_ptr(k + (bos*H + i_h) * K, (K, T), (1, H*K), (i_k * BK, i_t * BT), (BK, BT), (0, 1))
+            p_v = tl.make_block_ptr(v + (bos*H + i_h) * V, (T, V), (H*V, 1), (i_t * BT, i_v * BV), (BT, BV), (1, 0))
+
+            o_h = ((boh + i_s) * H + i_h).to(tl.int64) * K*V
+            p_h = tl.make_block_ptr(h + o_h, (K, V), (V, 1), (i_k * BK, i_v * BV), (BK, BV), (1, 0))
+
+        if i_t % (BS // BT) == 0:
+            tl.store(p_h, b_h.to(p_h.dtype.element_ty), boundary_check=(0, 1))
+        # [BK, BT]
+        b_k = tl.load(p_k, boundary_check=(0, 1))
+        # [BT, BV]
+        b_v = tl.load(p_v, boundary_check=(0, 1))
+        last_idx = min((i_t + 1) * BT, T) - 1
+
+        # scalar decay
+        if USE_G:
+            if HEAD_FIRST:
+                b_g_last = tl.load(g + i_nh * T + last_idx)
+                p_g = g + i_nh * T + i_t * BT + tl.arange(0, BT)
+                p_g = tl.max_contiguous(tl.multiple_of(p_g, BT), BT)
+            else:
+                b_g_last = tl.load(g + bos * H + last_idx * H + i_h)
+                p_g = g + bos*H + (i_t * BT + tl.arange(0, BT)) * H + i_h
+            b_h *= exp(b_g_last)
+            b_g = tl.load(p_g, mask=(i_t * BT + tl.arange(0, BT) < T), other=0.)
+            b_v = (b_v * exp(b_g_last - b_g)[:, None]).to(b_v.dtype)
+
+        # vector decay, h = Diag(gk) @ h
+        if USE_GK:
+            if HEAD_FIRST:
+                p_gk = tl.make_block_ptr(gk + i_nh * T*K, (K, T), (1, K), (i_k * BK, i_t * BT), (BK, BT), (0, 1))
+                p_gk_last = gk + i_nh * T*K + last_idx * K + i_k * BK + tl.arange(0, BK)
+                p_gk_last = tl.max_contiguous(tl.multiple_of(p_gk_last, BK), BK)
+            else:
+                p_gk = tl.make_block_ptr(gk + (bos*H + i_h) * K, (K, T), (1, H*K), (i_k * BK, i_t * BT), (BK, BT), (0, 1))
+                p_gk_last = gk + (bos + last_idx) * H*K + i_h * K + i_k * BK + tl.arange(0, BK)
+
+            b_gk_last = tl.load(p_gk_last, mask=(i_k * BK + tl.arange(0, BK) < K), other=0.)
+            b_h *= exp(b_gk_last)[:, None]
+
+            b_gk = tl.load(p_gk, boundary_check=(0, 1))
+            b_k = (b_k * exp(b_gk_last[:, None] - b_gk)).to(b_k.dtype)
+
+        # vector decay, h = h @ Diag(gv)
+        if USE_GV:
+            if HEAD_FIRST:
+                p_gv = tl.make_block_ptr(gv + i_nh * T*V, (T, V), (V, 1), (i_t * BT, i_v * BV), (BT, BV), (1, 0))
+                p_gv_last = gv + i_nh * T*V + last_idx * V + i_v * BV + tl.arange(0, BV)
+                p_gv_last = tl.max_contiguous(tl.multiple_of(p_gv_last, BV), BV)
+            else:
+                p_gv = tl.make_block_ptr(gv + (bos*H + i_h) * V, (T, V), (H*V, 1), (i_t * BT, i_v * BV), (BT, BV), (1, 0))
+                p_gv_last = gv + (bos + last_idx) * H*V + i_h * V + i_v * BV + tl.arange(0, BV)
+
+            b_gv_last = tl.load(p_gv_last, mask=(i_v * BV + tl.arange(0, BV) < V), other=0.)
+            b_h *= exp(b_gv_last)[None, :]
+
+            b_gv = tl.load(p_gv, boundary_check=(0, 1))
+            b_v = (b_v * exp(b_gv_last[None, :] - b_gv)).to(b_v.dtype)
+
+        b_h += tl.dot(b_k, b_v)
+
+    if STORE_FINAL_STATE:
+        p_ht = tl.make_block_ptr(ht + i_nh * K*V, (K, V), (V, 1), (i_k * BK, i_v * BV), (BK, BV), (1, 0))
+        tl.store(p_ht, b_h.to(p_ht.dtype.element_ty), boundary_check=(0, 1))
+
+
+@triton.heuristics({
+    'STORE_INITIAL_STATE_GRADIENT': lambda args: args['dh0'] is not None,
+    'USE_FINAL_STATE_GRADIENT': lambda args: args['dht'] is not None,
+    'USE_OFFSETS': lambda args: args['offsets'] is not None
+})
+@triton.autotune(
+    configs=[
+        triton.Config({'BK': BK, 'BV': BV}, num_warps=num_warps, num_stages=num_stages)
+        for BK in BKV_LIST
+        for BV in BKV_LIST
+        for num_warps in [1, 2, 4, 8]
+        for num_stages in [2, 3, 4]
+    ],
+    key=['BT', 'USE_G', 'USE_GK', 'USE_GV']
+)
+@triton.jit(do_not_specialize=['T'])
+def chunk_bwd_kernel_dh(
+    q,
+    g,
+    gk,
+    gv,
+    do,
+    dh,
+    dht,
+    dh0,
+    offsets,
+    split_offsets,
+    scale,
+    T,
+    HQ: tl.constexpr,
+    H: tl.constexpr,
+    K: tl.constexpr,
+    V: tl.constexpr,
+    BT: tl.constexpr,
+    BS: tl.constexpr,
+    BK: tl.constexpr,
+    BV: tl.constexpr,
+    NG: tl.constexpr,
+    USE_G: tl.constexpr,
+    USE_GK: tl.constexpr,
+    USE_GV: tl.constexpr,
+    STORE_INITIAL_STATE_GRADIENT: tl.constexpr,
+    USE_FINAL_STATE_GRADIENT: tl.constexpr,
+    USE_OFFSETS: tl.constexpr,
+    HEAD_FIRST: tl.constexpr
+):
+    i_k, i_v, i_nh = tl.program_id(0), tl.program_id(1), tl.program_id(2)
+    i_bg = i_nh // NG
+    i_n, i_hq = i_nh // HQ, i_nh % HQ
+    i_h = i_hq // NG
+    if USE_OFFSETS:
+        bos, eos = tl.load(offsets + i_n).to(tl.int32), tl.load(offsets + i_n + 1).to(tl.int32)
+        T = eos - bos
+        NT = tl.cdiv(T, BT)
+        NS = tl.cdiv(T, BS)
+        boh = tl.load(split_offsets + i_n).to(tl.int32)
+    else:
+        bos, eos = i_n * T, i_n * T + T
+        NT = tl.cdiv(T, BT)
+        NS = tl.cdiv(T, BS)
+        boh = i_n * NS
+
+    # [BK, BV]
+    b_dh = tl.zeros([BK, BV], dtype=tl.float32)
+    if USE_FINAL_STATE_GRADIENT:
+        p_dht = tl.make_block_ptr(dht + i_nh * K*V, (K, V), (V, 1), (i_k * BK, i_v * BV), (BK, BV), (1, 0))
+        b_dh += tl.load(p_dht, boundary_check=(0, 1)).to(tl.float32)
+
+    for i_t in range(NT - 1, -1, -1):
+        i_s = i_t // (BS // BT)
+        if HEAD_FIRST:
+            o_dh = (i_nh * NS + i_s).to(tl.int64) * K*V
+            p_dh = tl.make_block_ptr(dh + o_dh, (K, V), (V, 1), (i_k * BK, i_v * BV), (BK, BV), (1, 0))
+        else:
+            o_dh = ((boh + i_s) * H + i_h).to(tl.int64) * K*V
+            p_dh = tl.make_block_ptr(dh + o_dh, (K, V), (V, 1), (i_k * BK, i_v * BV), (BK, BV), (1, 0))
+
+        if i_t % (BS // BT) == 0:
+            tl.store(p_dh, b_dh.to(p_dh.dtype.element_ty), boundary_check=(0, 1))
+        last_idx = min(i_t * BT + BT, T) - 1
+        # [BK, BT]
+        if HEAD_FIRST:
+            p_q = tl.make_block_ptr(q + i_nh * T*K, (K, T), (1, K), (i_k * BK, i_t * BT), (BK, BT), (0, 1))
+            p_do = tl.make_block_ptr(do + i_nh * T*V, (T, V), (V, 1), (i_t * BT, i_v * BV), (BT, BV), (1, 0))
+        else:
+            p_q = tl.make_block_ptr(q + (bos*HQ + i_hq) * K, (K, T), (1, HQ*K), (i_k * BK, i_t * BT), (BK, BT), (0, 1))
+            p_do = tl.make_block_ptr(do + (bos*HQ + i_hq) * V, (T, V), (HQ*V, 1), (i_t * BT, i_v * BV), (BT, BV), (1, 0))
+        b_q = tl.load(p_q, boundary_check=(0, 1))
+        b_q = (b_q * scale).to(b_q.dtype)
+        # [BT, BV]
+        b_do = tl.load(p_do, boundary_check=(0, 1))
+
+        if USE_G:
+            if HEAD_FIRST:
+                p_g = g + i_bg * T + i_t * BT + tl.arange(0, BT)
+                p_g = tl.max_contiguous(tl.multiple_of(p_g, BT), BT)
+                b_g_last = tl.load(g + i_bg * T + last_idx)
+            else:
+                p_g = g + (bos + i_t * BT + tl.arange(0, BT)) * H + i_h
+                b_g_last = tl.load(g + (bos + last_idx) * H + i_h)
+            b_g = tl.load(p_g, mask=(i_t * BT + tl.arange(0, BT) < T), other=0.)
+            b_q = (b_q * exp(b_g)[None, :]).to(b_q.dtype)
+
+            b_dh *= exp(b_g_last)
+
+        if USE_GK:
+            if HEAD_FIRST:
+                p_gk = tl.make_block_ptr(gk + i_bg * T*K, (K, T), (1, K), (i_k * BK, i_t * BT), (BK, BT), (0, 1))
+                p_gk_last = gk + (i_bg * T + last_idx) * K + i_k * BK + tl.arange(0, BK)
+                p_gk_last = tl.max_contiguous(tl.multiple_of(p_gk_last, BK), BK)
+            else:
+                p_gk = tl.make_block_ptr(gk + (bos*H + i_h) * K, (K, T), (1, H*K), (i_k * BK, i_t * BT), (BK, BT), (0, 1))
+                p_gk_last = gk + (bos + last_idx) * H*K + i_h * K + i_k * BK + tl.arange(0, BK)
+
+            b_gk = tl.load(p_gk, boundary_check=(0, 1))
+            b_q = (b_q * exp(b_gk)).to(b_q.dtype)
+            b_gk_last = tl.load(p_gk_last, mask=(i_k * BK + tl.arange(0, BK) < K), other=0.)
+            b_dh *= exp(b_gk_last)[:, None]
+
+        if USE_GV:
+            if HEAD_FIRST:
+                p_gv = tl.make_block_ptr(gv + i_bg * T*V, (T, V), (V, 1), (i_t * BT, i_v * BV), (BT, BV), (1, 0))
+                p_gv_last = gv + (i_bg * T + last_idx) * V + i_v * BV + tl.arange(0, BV)
+                p_gv_last = tl.max_contiguous(tl.multiple_of(p_gv_last, BV), BV)
+            else:
+                p_gv = tl.make_block_ptr(gv + (bos*H + i_h) * V, (T, V), (H*V, 1), (i_t * BT, i_v * BV), (BT, BV), (1, 0))
+                p_gv_last = gv + (bos + last_idx) * H*V + i_h * V + i_v * BV + tl.arange(0, BV)
+
+            b_gv = tl.load(p_gv, boundary_check=(0, 1))
+            b_do = (b_do * exp(b_gv)).to(b_do.dtype)
+
+            b_gv_last = tl.load(p_gv_last, mask=(i_v * BV + tl.arange(0, BV) < V), other=0.)
+            b_dh *= exp(b_gv_last)[None, :]
+
+        b_dh += tl.dot(b_q, b_do)
+
+    if STORE_INITIAL_STATE_GRADIENT:
+        p_dh0 = tl.make_block_ptr(dh0 + i_nh * K*V, (K, V), (V, 1), (i_k * BK, i_v * BV), (BK, BV), (1, 0))
+        tl.store(p_dh0, b_dh.to(p_dh0.dtype.element_ty), boundary_check=(0, 1))
+
+
+def chunk_fwd_h(
+    k: torch.Tensor,
+    v: torch.Tensor,
+    g: torch.Tensor,
+    gk: torch.Tensor,
+    gv: torch.Tensor,
+    h0: torch.Tensor,
+    output_final_state: bool,
+    offsets: Optional[torch.Tensor] = None,
+    head_first: bool = True,
+    chunk_size: int = 64,
+    split_size: Optional[int] = None,
+    states_in_fp32: bool = False
+) -> Tuple[torch.Tensor, torch.Tensor]:
+    if head_first:
+        B, H, T, K, V = *k.shape, v.shape[-1]
+    else:
+        B, T, H, K, V = *k.shape, v.shape[-1]
+    BT = min(chunk_size, max(16, triton.next_power_of_2(T)))
+    BS = BT if split_size is None else min(split_size, max(16, triton.next_power_of_2(T)))
+    assert BS % BT == 0, f"The `split_size` (got {BS}) must be a multiple of `chunk_size` {BT}"
+    # N: the actual number of sequences in the batch with either equal or variable lengths
+    if offsets is None:
+        split_offsets, N, NS = None, B, triton.cdiv(T, BS)
+    else:
+        split_offsets = prepare_chunk_offsets(offsets, BS)
+        N, NS = len(offsets) - 1, split_offsets[-1]
+
+    if head_first:
+        h = k.new_empty(B, H, NS, K, V, dtype=k.dtype if not states_in_fp32 else torch.float)
+    else:
+        h = k.new_empty(B, NS, H, K, V, dtype=k.dtype if not states_in_fp32 else torch.float)
+    ht = k.new_empty(N, H, K, V, dtype=torch.float) if output_final_state else None
+    def grid(meta): return (triton.cdiv(K, meta['BK']), triton.cdiv(V, meta['BV']), N * H)
+    chunk_fwd_kernel_h[grid](
+        k=k,
+        v=v,
+        h=h,
+        g=g,
+        gk=gk,
+        gv=gv,
+        h0=h0,
+        ht=ht,
+        offsets=offsets,
+        split_offsets=split_offsets,
+        T=T,
+        H=H,
+        K=K,
+        V=V,
+        BT=BT,
+        BS=BS,
+        USE_G=g is not None,
+        USE_GK=gk is not None,
+        USE_GV=gv is not None,
+        HEAD_FIRST=head_first
+    )
+    return h, ht
+
+
+def chunk_bwd_dh(
+    q: torch.Tensor,
+    k: torch.Tensor,
+    v: torch.Tensor,
+    g: torch.Tensor,
+    gk: torch.Tensor,
+    gv: torch.Tensor,
+    do: torch.Tensor,
+    h0: torch.Tensor,
+    dht: torch.Tensor,
+    scale: float,
+    offsets: Optional[torch.Tensor] = None,
+    head_first: bool = True,
+    chunk_size: int = 64,
+    split_size: Optional[int] = None,
+    states_in_fp32: bool = False
+) -> Tuple[torch.Tensor, torch.Tensor]:
+    if head_first:
+        B, H, T, K, V = *k.shape, v.shape[-1]
+        HQ = q.shape[1]
+    else:
+        B, T, H, K, V = *k.shape, v.shape[-1]
+        HQ = q.shape[2]
+    BT = min(chunk_size, max(16, triton.next_power_of_2(T)))
+    BS = BT if split_size is None else min(split_size, max(16, triton.next_power_of_2(T)))
+    assert BS % BT == 0, f"The `split_size` (got {BS}) must be a multiple of `chunk_size` {BT}"
+    # N: the actual number of sequences in the batch with either equal or variable lengths
+    # NG: number of groups in GQA
+    if offsets is None:
+        split_offsets, N, NS = None, B, triton.cdiv(T, BS)
+    else:
+        split_offsets = prepare_chunk_offsets(offsets, BS)
+        N, NS = len(offsets) - 1, split_offsets[-1]
+    NG = HQ // H
+
+    if head_first:
+        dh = k.new_empty(B, HQ, NS, K, V, dtype=k.dtype if not states_in_fp32 else torch.float)
+    else:
+        dh = k.new_empty(B, NS, HQ, K, V, dtype=k.dtype if not states_in_fp32 else torch.float)
+    dh0 = torch.empty_like(h0, dtype=torch.float) if h0 is not None else None
+
+    def grid(meta): return (triton.cdiv(K, meta['BK']), triton.cdiv(V, meta['BV']), N * H)
+    chunk_bwd_kernel_dh[grid](
+        q=q,
+        g=g,
+        gk=gk,
+        gv=gv,
+        do=do,
+        dh=dh,
+        dht=dht,
+        dh0=dh0,
+        offsets=offsets,
+        split_offsets=split_offsets,
+        scale=scale,
+        T=T,
+        HQ=HQ,
+        H=H,
+        K=K,
+        V=V,
+        BT=BT,
+        BS=BS,
+        NG=NG,
+        USE_G=g is not None,
+        USE_GK=gk is not None,
+        USE_GV=gv is not None,
+        HEAD_FIRST=head_first
+    )
+    return dh, dh0

fla/ops/common/chunk_h_split.py

@@ -0,0 +1,677 @@
+# -*- coding: utf-8 -*-
+# Copyright (c) 2023-2025, Songlin Yang, Yu Zhang
+
+from typing import Optional, Tuple
+
+import torch
+import triton
+import triton.language as tl
+
+from fla.ops.utils.op import exp
+
+
+@triton.heuristics({
+    'USE_INITIAL_STATE': lambda args: args['h0'] is not None,
+    'STORE_FINAL_STATE': lambda args: args['ht'] is not None,
+    'USE_OFFSETS': lambda args: args['offsets'] is not None
+})
+@triton.autotune(
+    configs=[
+        triton.Config({'BK': BK, 'BV': BV}, num_warps=num_warps, num_stages=num_stages)
+        for BK in [32, 64]
+        for BV in [32, 64]
+        for num_warps in [2, 4, 8]
+        for num_stages in [2, 3]
+    ],
+    key=['BT', 'USE_G', 'USE_GK', 'USE_GV'],
+)
+@triton.jit(do_not_specialize=['T'])
+def chunk_fwd_kernel_h_split(
+    k,
+    v,
+    g,
+    gk,
+    gv,
+    hs,
+    hr,
+    h0,
+    ht,
+    offsets,
+    split_indices,
+    T,
+    S: tl.constexpr,
+    H: tl.constexpr,
+    K: tl.constexpr,
+    V: tl.constexpr,
+    BT: tl.constexpr,
+    BK: tl.constexpr,
+    BV: tl.constexpr,
+    USE_G: tl.constexpr,
+    USE_GK: tl.constexpr,
+    USE_GV: tl.constexpr,
+    USE_INITIAL_STATE: tl.constexpr,
+    STORE_FINAL_STATE: tl.constexpr,
+    USE_OFFSETS: tl.constexpr,
+    HEAD_FIRST: tl.constexpr
+):
+    # handle one split at a time
+    # i_h: head index
+    # i_n: sequence index
+    # i_s: local split index inside a sequence
+    i_k, i_v, i_sh = tl.program_id(0), tl.program_id(1), tl.program_id(2)
+    i_ss, i_h = i_sh // H, i_sh % H
+    if USE_OFFSETS:
+        i_n, i_s = tl.load(split_indices + i_ss * 2).to(tl.int32), tl.load(split_indices + i_ss * 2 + 1).to(tl.int32)
+        bos, eos = tl.load(offsets + i_n).to(tl.int32), tl.load(offsets + i_n + 1).to(tl.int32)
+        T = eos - bos
+        NS = tl.cdiv(T, S)
+    else:
+        NS = tl.cdiv(T, S)
+        i_n, i_s = i_ss // NS, i_ss % NS
+        bos, eos = i_n * T, i_n * T + T
+    i_nh = i_n * H + i_h
+
+    # [BK, BV]
+    b_h = tl.zeros([BK, BV], dtype=tl.float32)
+    # for the first split, we directly store the state as the final result
+    if i_s == 0:
+        if USE_INITIAL_STATE:
+            p_h0 = tl.make_block_ptr(h0 + i_nh * K*V, (K, V), (V, 1), (i_k * BK, i_v * BV), (BK, BV), (1, 0))
+            b_h += tl.load(p_h0, boundary_check=(0, 1)).to(tl.float32)
+        p_hr = tl.make_block_ptr(hr + i_sh * K*V, (K, V), (V, 1), (i_k * BK, i_v * BV), (BK, BV), (1, 0))
+        tl.store(p_hr, b_h.to(p_hr.dtype.element_ty), boundary_check=(0, 1))
+    for i_t in range(tl.cdiv(i_s * S, BT), tl.cdiv(min(i_s * S + S, T), BT)):
+        if HEAD_FIRST:
+            p_k = tl.make_block_ptr(k + i_nh * T*K, (K, T), (1, K), (i_k * BK, i_t * BT), (BK, BT), (0, 1))
+            p_v = tl.make_block_ptr(v + i_nh * T*V, (T, V), (V, 1), (i_t * BT, i_v * BV), (BT, BV), (1, 0))
+        else:
+            p_k = tl.make_block_ptr(k + (bos*H + i_h) * K, (K, T), (1, H*K), (i_k * BK, i_t * BT), (BK, BT), (0, 1))
+            p_v = tl.make_block_ptr(v + (bos*H + i_h) * V, (T, V), (H*V, 1), (i_t * BT, i_v * BV), (BT, BV), (1, 0))
+        # [BK, BT]
+        b_k = tl.load(p_k, boundary_check=(0, 1))
+        # [BT, BV]
+        b_v = tl.load(p_v, boundary_check=(0, 1))
+        last_idx = min(i_t * BT + BT, T) - 1
+
+        # scalar decay
+        if USE_G:
+            if HEAD_FIRST:
+                b_g_last = tl.load(g + i_nh * T + last_idx)
+                p_g = g + i_nh * T + i_t * BT + tl.arange(0, BT)
+                p_g = tl.max_contiguous(tl.multiple_of(p_g, BT), BT)
+            else:
+                b_g_last = tl.load(g + bos * H + last_idx * H + i_h)
+                p_g = g + bos*H + (i_t * BT + tl.arange(0, BT)) * H + i_h
+            b_h *= exp(b_g_last)
+            b_g = tl.load(p_g, mask=(i_t * BT + tl.arange(0, BT) < T), other=0.)
+            b_v = (b_v * exp(b_g_last - b_g)[:, None]).to(b_v.dtype)
+
+        # vector decay, h = Diag(gk) @ h
+        if USE_GK:
+            if HEAD_FIRST:
+                p_gk = tl.make_block_ptr(gk + i_nh * T*K, (K, T), (1, K), (i_k * BK, i_t * BT), (BK, BT), (0, 1))
+                p_gk_last = gk + i_nh * T*K + last_idx * K + i_k * BK + tl.arange(0, BK)
+                p_gk_last = tl.max_contiguous(tl.multiple_of(p_gk_last, BK), BK)
+            else:
+                p_gk = tl.make_block_ptr(gk + (bos*H + i_h) * K, (K, T), (1, H*K), (i_k * BK, i_t * BT), (BK, BT), (0, 1))
+                p_gk_last = gk + (bos + last_idx) * H*K + i_h * K + i_k * BK + tl.arange(0, BK)
+
+            b_gk_last = tl.load(p_gk_last, mask=(i_k * BK + tl.arange(0, BK) < K), other=0.)
+            b_h *= exp(b_gk_last)[:, None]
+
+            b_gk = tl.load(p_gk, boundary_check=(0, 1))
+            b_k = (b_k * exp(b_gk_last[:, None] - b_gk)).to(b_k.dtype)
+
+        # vector decay, h = h @ Diag(gv)
+        if USE_GV:
+            if HEAD_FIRST:
+                p_gv = tl.make_block_ptr(gv + i_nh * T*V, (T, V), (V, 1), (i_t * BT, i_v * BV), (BT, BV), (1, 0))
+                p_gv_last = gv + i_nh * T*V + last_idx * V + i_v * BV + tl.arange(0, BV)
+                p_gv_last = tl.max_contiguous(tl.multiple_of(p_gv_last, BV), BV)
+            else:
+                p_gv = tl.make_block_ptr(gv + (bos*H + i_h) * V, (T, V), (H*V, 1), (i_t * BT, i_v * BV), (BT, BV), (1, 0))
+                p_gv_last = gv + (bos + last_idx) * H*V + i_h * V + i_v * BV + tl.arange(0, BV)
+
+            b_gv_last = tl.load(p_gv_last, mask=(i_v * BV + tl.arange(0, BV) < V), other=0.)
+            b_h *= exp(b_gv_last)[None, :]
+
+            b_gv = tl.load(p_gv, boundary_check=(0, 1))
+            b_v = (b_v * exp(b_gv_last[None, :] - b_gv)).to(b_v.dtype)
+
+        b_h += tl.dot(b_k, b_v)
+
+    # if there are more than one splits, we store the result to (unreduced) hs
+    # otherwise, we store the result to ht as the final state
+    if NS > 1:
+        p_hs = tl.make_block_ptr(hs + i_sh * K*V, (K, V), (V, 1), (i_k * BK, i_v * BV), (BK, BV), (1, 0))
+        tl.store(p_hs, b_h.to(p_hs.dtype.element_ty), boundary_check=(0, 1))
+    elif STORE_FINAL_STATE:
+        p_ht = tl.make_block_ptr(ht + i_nh * K*V, (K, V), (V, 1), (i_k * BK, i_v * BV), (BK, BV), (1, 0))
+        tl.store(p_ht, b_h.to(p_ht.dtype.element_ty), boundary_check=(0, 1))
+
+
+@triton.heuristics({
+    'STORE_FINAL_STATE': lambda args: args['ht'] is not None,
+    'USE_OFFSETS': lambda args: args['offsets'] is not None
+})
+@triton.autotune(
+    configs=[
+        triton.Config({'BK': BK, 'BV': BV}, num_warps=num_warps, num_stages=num_stages)
+        for BK in [32, 64]
+        for BV in [32, 64]
+        for num_warps in [2, 4, 8]
+        for num_stages in [2, 3, 4]
+    ],
+    key=['BT', 'USE_G', 'USE_GK', 'USE_GV'],
+)
+@triton.jit(do_not_specialize=['T'])
+def chunk_fwd_kernel_h_reduction(
+    g,
+    gk,
+    gv,
+    hs,
+    hr,
+    ht,
+    offsets,
+    split_offsets,
+    T,
+    S: tl.constexpr,
+    H: tl.constexpr,
+    K: tl.constexpr,
+    V: tl.constexpr,
+    BT: tl.constexpr,
+    BK: tl.constexpr,
+    BV: tl.constexpr,
+    USE_G: tl.constexpr,
+    USE_GK: tl.constexpr,
+    USE_GV: tl.constexpr,
+    STORE_FINAL_STATE: tl.constexpr,
+    USE_OFFSETS: tl.constexpr,
+    HEAD_FIRST: tl.constexpr
+):
+    i_k, i_v, i_nh = tl.program_id(0), tl.program_id(1), tl.program_id(2)
+    i_n, i_h = i_nh // H, i_nh % H
+    if USE_OFFSETS:
+        bos, eos = tl.load(offsets + i_n).to(tl.int32), tl.load(offsets + i_n + 1).to(tl.int32)
+        T = eos - bos
+        NS = tl.cdiv(T, S)
+        boh = tl.load(split_offsets + i_n).to(tl.int32)
+    else:
+        bos, eos = i_n * T, i_n * T + T
+        NS = tl.cdiv(T, S)
+        boh = i_n * NS
+
+    b_h = tl.zeros([BK, BV], dtype=tl.float32)
+    # skip the first split
+    for i_s in range(1, NS):
+        p_hs = tl.make_block_ptr(hs + ((boh + i_s-1) * H + i_h) * K*V, (K, V), (V, 1), (i_k * BK, i_v * BV), (BK, BV), (1, 0))
+        p_hr = tl.make_block_ptr(hr + ((boh + i_s) * H + i_h) * K*V, (K, V), (V, 1), (i_k * BK, i_v * BV), (BK, BV), (1, 0))
+        b_h += tl.load(p_hs, boundary_check=(0, 1)).to(tl.float32)
+        tl.store(p_hr, b_h.to(p_hr.dtype.element_ty), boundary_check=(0, 1))
+
+        for i_t in range(tl.cdiv(i_s * S, BT), tl.cdiv(min(i_s * S + S, T), BT)):
+            last_idx = min(i_t * BT + BT, T) - 1
+            # scalar decay
+            if USE_G:
+                if HEAD_FIRST:
+                    b_g_last = tl.load(g + i_nh * T + last_idx)
+                else:
+                    b_g_last = tl.load(g + bos * H + last_idx * H + i_h)
+                b_h *= exp(b_g_last)
+
+            # vector decay, h = Diag(gk) @ h
+            if USE_GK:
+                if HEAD_FIRST:
+                    p_gk_last = gk + i_nh * T*K + last_idx * K + i_k * BK + tl.arange(0, BK)
+                    p_gk_last = tl.max_contiguous(tl.multiple_of(p_gk_last, BK), BK)
+                else:
+                    p_gk_last = gk + (bos + last_idx) * H*K + i_h * K + i_k * BK + tl.arange(0, BK)
+
+                b_gk_last = tl.load(p_gk_last, mask=(i_k * BK + tl.arange(0, BK) < K), other=0.)
+                b_h *= exp(b_gk_last)[:, None]
+
+            # vector decay, h = h @ Diag(gv)
+            if USE_GV:
+                if HEAD_FIRST:
+                    p_gv_last = gv + i_nh * T*V + last_idx * V + i_v * BV + tl.arange(0, BV)
+                    p_gv_last = tl.max_contiguous(tl.multiple_of(p_gv_last, BV), BV)
+                else:
+                    p_gv_last = gv + (bos + last_idx) * H*V + i_h * V + i_v * BV + tl.arange(0, BV)
+
+                b_gv_last = tl.load(p_gv_last, mask=(i_v * BV + tl.arange(0, BV) < V), other=0.)
+                b_h *= exp(b_gv_last)[None, :]
+
+    if NS > 1:
+        if STORE_FINAL_STATE:
+            p_hs = tl.make_block_ptr(hs + ((boh + NS-1) * H + i_h)*K*V, (K, V), (V, 1), (i_k * BK, i_v * BV), (BK, BV), (1, 0))
+            p_ht = tl.make_block_ptr(ht + i_nh * K*V, (K, V), (V, 1), (i_k * BK, i_v * BV), (BK, BV), (1, 0))
+            b_h += tl.load(p_hs, boundary_check=(0, 1)).to(tl.float32)
+            tl.store(p_ht, b_h.to(p_ht.dtype.element_ty), boundary_check=(0, 1))
+
+
+@triton.heuristics({
+    'USE_FINAL_STATE_GRADIENT': lambda args: args['dht'] is not None,
+    'STORE_INITIAL_STATE_GRADIENT': lambda args: args['dh0'] is not None,
+    'USE_OFFSETS': lambda args: args['offsets'] is not None
+})
+@triton.autotune(
+    configs=[
+        triton.Config({'BK': BK, 'BV': BV}, num_warps=num_warps, num_stages=num_stages)
+        for BK in [32, 64]
+        for BV in [32, 64]
+        for num_warps in [2, 4, 8]
+        for num_stages in [2, 3]
+    ],
+    key=['BT', 'USE_G', 'USE_GK', 'USE_GV'],
+)
+@triton.jit(do_not_specialize=['T'])
+def chunk_bwd_kernel_dh_split(
+    q,
+    g,
+    gk,
+    gv,
+    do,
+    dht,
+    dhs,
+    dhr,
+    dh0,
+    offsets,
+    split_indices,
+    scale,
+    T,
+    S: tl.constexpr,
+    HQ: tl.constexpr,
+    H: tl.constexpr,
+    K: tl.constexpr,
+    V: tl.constexpr,
+    BT: tl.constexpr,
+    BK: tl.constexpr,
+    BV: tl.constexpr,
+    NG: tl.constexpr,
+    USE_G: tl.constexpr,
+    USE_GK: tl.constexpr,
+    USE_GV: tl.constexpr,
+    USE_FINAL_STATE_GRADIENT: tl.constexpr,
+    STORE_INITIAL_STATE_GRADIENT: tl.constexpr,
+    USE_OFFSETS: tl.constexpr,
+    HEAD_FIRST: tl.constexpr
+):
+    # handle one split at a time
+    # i_h: head index
+    # i_n: sequence index
+    # i_s: local split index inside a sequence
+    i_k, i_v, i_sh = tl.program_id(0), tl.program_id(1), tl.program_id(2)
+    i_ss, i_hq = i_sh // HQ, i_sh % HQ
+    if USE_OFFSETS:
+        i_n, i_s = tl.load(split_indices + i_ss * 2).to(tl.int32), tl.load(split_indices + i_ss * 2 + 1).to(tl.int32)
+        bos, eos = tl.load(offsets + i_n).to(tl.int32), tl.load(offsets + i_n + 1).to(tl.int32)
+        T = eos - bos
+        NS = tl.cdiv(T, S)
+    else:
+        NS = tl.cdiv(T, S)
+        i_n, i_s = i_ss // NS, i_ss % NS
+        bos, eos = i_n * T, i_n * T + T
+    i_nh = i_n * HQ + i_hq
+    i_ng, i_h = i_nh // NG, i_hq // NG
+
+    # [BK, BV]
+    b_dh = tl.zeros([BK, BV], dtype=tl.float32)
+    if i_s == NS - 1:
+        if USE_FINAL_STATE_GRADIENT:
+            p_dht = tl.make_block_ptr(dht + i_nh * K*V, (K, V), (V, 1), (i_k * BK, i_v * BV), (BK, BV), (1, 0))
+            b_dh += tl.load(p_dht, boundary_check=(0, 1)).to(tl.float32)
+        p_dhr = tl.make_block_ptr(dhr + i_sh * K*V, (K, V), (V, 1), (i_k * BK, i_v * BV), (BK, BV), (1, 0))
+        tl.store(p_dhr, b_dh.to(p_dhr.dtype.element_ty), boundary_check=(0, 1))
+
+    for i_t in range(tl.cdiv(min(i_s * S + S, T), BT) - 1, tl.cdiv(i_s * S, BT) - 1, -1):
+        if HEAD_FIRST:
+            p_q = tl.make_block_ptr(q + i_nh * T*K, (K, T), (1, K), (i_k * BK, i_t * BT), (BK, BT), (0, 1))
+            p_do = tl.make_block_ptr(do + i_nh * T*V, (T, V), (V, 1), (i_t * BT, i_v * BV), (BT, BV), (1, 0))
+        else:
+            p_q = tl.make_block_ptr(q + (bos*HQ + i_hq) * K, (K, T), (1, HQ*K), (i_k * BK, i_t * BT), (BK, BT), (0, 1))
+            p_do = tl.make_block_ptr(do + (bos*HQ + i_hq) * V, (T, V), (HQ*V, 1), (i_t * BT, i_v * BV), (BT, BV), (1, 0))
+
+        b_q = tl.load(p_q, boundary_check=(0, 1))
+        b_q = (b_q * scale).to(b_q.dtype)
+        # [BT, BV]
+        b_do = tl.load(p_do, boundary_check=(0, 1))
+
+        last_idx = min(i_t * BT + BT, T) - 1
+        if USE_G:
+            if HEAD_FIRST:
+                p_g = g + i_ng * T + i_t * BT + tl.arange(0, BT)
+                p_g = tl.max_contiguous(tl.multiple_of(p_g, BT), BT)
+                b_g_last = tl.load(g + i_ng * T + last_idx)
+            else:
+                p_g = g + (bos + i_t * BT + tl.arange(0, BT)) * H + i_h
+                b_g_last = tl.load(g + (bos + last_idx) * H + i_h)
+            b_g = tl.load(p_g, mask=(i_t * BT + tl.arange(0, BT) < T), other=0.)
+            b_q = (b_q * exp(b_g)[None, :]).to(b_q.dtype)
+            b_dh *= exp(b_g_last)
+
+        if USE_GK:
+            if HEAD_FIRST:
+                p_gk = tl.make_block_ptr(gk + i_ng * T*K, (K, T), (1, K), (i_k * BK, i_t * BT), (BK, BT), (0, 1))
+                p_gk_last = gk + (i_ng * T + last_idx) * K + i_k * BK + tl.arange(0, BK)
+                p_gk_last = tl.max_contiguous(tl.multiple_of(p_gk_last, BK), BK)
+            else:
+                p_gk = tl.make_block_ptr(gk + (bos*H + i_h) * K, (K, T), (1, H*K), (i_k * BK, i_t * BT), (BK, BT), (0, 1))
+                p_gk_last = gk + (bos + last_idx) * H*K + i_h * K + i_k * BK + tl.arange(0, BK)
+
+            b_gk = tl.load(p_gk, boundary_check=(0, 1))
+            b_q = (b_q * exp(b_gk)).to(b_q.dtype)
+            b_gk_last = tl.load(p_gk_last, mask=(i_k * BK + tl.arange(0, BK) < K), other=0.)
+            b_dh *= exp(b_gk_last)[:, None]
+
+        if USE_GV:
+            if HEAD_FIRST:
+                p_gv = tl.make_block_ptr(gv + i_ng * T*V, (T, V), (V, 1), (i_t * BT, i_v * BV), (BT, BV), (1, 0))
+                p_gv_last = gv + (i_ng * T + last_idx) * V + i_v * BV + tl.arange(0, BV)
+                p_gv_last = tl.max_contiguous(tl.multiple_of(p_gv_last, BV), BV)
+            else:
+                p_gv = tl.make_block_ptr(gv + (bos*H + i_h) * V, (T, V), (H*V, 1), (i_t * BT, i_v * BV), (BT, BV), (1, 0))
+                p_gv_last = gv + (bos + last_idx) * H*V + i_h * V + i_v * BV + tl.arange(0, BV)
+
+            b_gv = tl.load(p_gv, boundary_check=(0, 1))
+            b_do = (b_do * exp(b_gv)).to(b_do.dtype)
+
+            b_gv_last = tl.load(p_gv_last, mask=(i_v * BV + tl.arange(0, BV) < V), other=0.)
+            b_dh *= exp(b_gv_last)[None, :]
+
+        b_dh += tl.dot(b_q, b_do)
+
+    if NS > 1:
+        p_dhs = tl.make_block_ptr(dhs + i_sh * K*V, (K, V), (V, 1), (i_k * BK, i_v * BV), (BK, BV), (1, 0))
+        tl.store(p_dhs, b_dh.to(p_dhs.dtype.element_ty), boundary_check=(0, 1))
+    elif STORE_INITIAL_STATE_GRADIENT:
+        p_dh0 = tl.make_block_ptr(dh0 + i_nh * K*V, (K, V), (V, 1), (i_k * BK, i_v * BV), (BK, BV), (1, 0))
+        tl.store(p_dh0, b_dh.to(p_dh0.dtype.element_ty), boundary_check=(0, 1))
+
+
+@triton.heuristics({
+    'STORE_INITIAL_STATE_GRADIENT': lambda args: args['dh0'] is not None,
+    'USE_OFFSETS': lambda args: args['offsets'] is not None
+})
+@triton.autotune(
+    configs=[
+        triton.Config({'BK': BK, 'BV': BV}, num_warps=num_warps, num_stages=num_stages)
+        for BK in [32, 64]
+        for BV in [32, 64]
+        for num_warps in [2, 4, 8]
+        for num_stages in [2, 3, 4]
+    ],
+    key=['BT', 'USE_G', 'USE_GK', 'USE_GV'],
+)
+@triton.jit(do_not_specialize=['T'])
+def chunk_bwd_kernel_dh_reduction(
+    g,
+    gk,
+    gv,
+    dhs,
+    dhr,
+    dh0,
+    offsets,
+    split_offsets,
+    T,
+    S: tl.constexpr,
+    H: tl.constexpr,
+    HQ: tl.constexpr,
+    K: tl.constexpr,
+    V: tl.constexpr,
+    BT: tl.constexpr,
+    BK: tl.constexpr,
+    BV: tl.constexpr,
+    NG: tl.constexpr,
+    USE_G: tl.constexpr,
+    USE_GK: tl.constexpr,
+    USE_GV: tl.constexpr,
+    STORE_INITIAL_STATE_GRADIENT: tl.constexpr,
+    USE_OFFSETS: tl.constexpr,
+    HEAD_FIRST: tl.constexpr
+):
+    i_k, i_v, i_nh = tl.program_id(0), tl.program_id(1), tl.program_id(2)
+    i_n, i_hq = i_nh // HQ, i_nh % HQ
+    i_ng, i_h = i_nh // NG, i_hq // NG
+    if USE_OFFSETS:
+        bos, eos = tl.load(offsets + i_n).to(tl.int32), tl.load(offsets + i_n + 1).to(tl.int32)
+        T = eos - bos
+        NS = tl.cdiv(T, S)
+        boh = tl.load(split_offsets + i_n).to(tl.int32)
+    else:
+        bos, eos = i_n * T, i_n * T + T
+        NS = tl.cdiv(T, S)
+        boh = i_n * NS
+
+    b_dh = tl.zeros([BK, BV], dtype=tl.float32)
+    for i_s in range(NS - 2, -1, -1):
+        p_dhs = tl.make_block_ptr(dhs + ((boh+i_s+1) * H + i_h) * K*V, (K, V), (V, 1), (i_k * BK, i_v * BV), (BK, BV), (1, 0))
+        p_dhr = tl.make_block_ptr(dhr + ((boh+i_s) * H + i_h) * K*V, (K, V), (V, 1), (i_k * BK, i_v * BV), (BK, BV), (1, 0))
+        b_dh += tl.load(p_dhs, boundary_check=(0, 1)).to(tl.float32)
+        tl.store(p_dhr, b_dh.to(p_dhr.dtype.element_ty), boundary_check=(0, 1))
+
+        for i_t in range(tl.cdiv(min(i_s * S + S, T), BT) - 1, tl.cdiv(i_s * S, BT) - 1, -1):
+            last_idx = min(i_t * BT + BT, T) - 1
+            # scalar decay
+            if USE_G:
+                if HEAD_FIRST:
+                    b_g_last = tl.load(g + i_ng * T + last_idx)
+                else:
+                    b_g_last = tl.load(g + (bos + last_idx) * H + i_h)
+                b_dh *= exp(b_g_last)
+
+            if USE_GK:
+                if HEAD_FIRST:
+                    p_gk_last = gk + (i_ng * T + last_idx) * K + i_k * BK + tl.arange(0, BK)
+                    p_gk_last = tl.max_contiguous(tl.multiple_of(p_gk_last, BK), BK)
+                else:
+                    p_gk_last = gk + (bos + last_idx) * H*K + i_h * K + i_k * BK + tl.arange(0, BK)
+
+                b_gk_last = tl.load(p_gk_last, mask=(i_k * BK + tl.arange(0, BK) < K), other=0.)
+                b_dh *= exp(b_gk_last)[:, None]
+
+            if USE_GV:
+                if HEAD_FIRST:
+                    p_gv_last = gv + (i_ng * T + last_idx) * V + i_v * BV + tl.arange(0, BV)
+                    p_gv_last = tl.max_contiguous(tl.multiple_of(p_gv_last, BV), BV)
+                else:
+                    p_gv_last = gv + (bos + last_idx) * H*V + i_h * V + i_v * BV + tl.arange(0, BV)
+
+                b_gv_last = tl.load(p_gv_last, mask=(i_v * BV + tl.arange(0, BV) < V), other=0.)
+                b_dh *= exp(b_gv_last)[None, :]
+
+    if NS > 1:
+        if STORE_INITIAL_STATE_GRADIENT:
+            p_dhs = tl.make_block_ptr(dhs + (boh * H + i_h)*K*V, (K, V), (V, 1), (i_k * BK, i_v * BV), (BK, BV), (1, 0))
+            p_dh0 = tl.make_block_ptr(dh0 + i_nh * K*V, (K, V), (V, 1), (i_k * BK, i_v * BV), (BK, BV), (1, 0))
+            b_dh += tl.load(p_dhs, boundary_check=(0, 1)).to(tl.float32)
+            tl.store(p_dh0, b_dh.to(p_dh0.dtype.element_ty), boundary_check=(0, 1))
+
+
+def chunk_fwd_h(
+    k: torch.Tensor,
+    v: torch.Tensor,
+    g: torch.Tensor,
+    gk: torch.Tensor,
+    gv: torch.Tensor,
+    h0: torch.Tensor,
+    output_final_state: bool,
+    offsets: Optional[torch.LongTensor] = None,
+    split_offsets: Optional[torch.LongTensor] = None,
+    split_indices: Optional[torch.LongTensor] = None,
+    head_first: bool = True,
+    chunk_size: int = 64,
+    split_size: int = 256,
+    states_in_fp32: bool = True
+) -> Tuple[torch.Tensor, torch.Tensor]:
+    if head_first:
+        B, H, T, K, V = *k.shape, v.shape[-1]
+    else:
+        B, T, H, K, V = *k.shape, v.shape[-1]
+    # B: batch size
+    # N: the actual number of sequences in the batch
+    # H: number of heads
+    # T: sequence length, can be variable across sequences
+    # S: split size, a multiple of chunk size
+    # BT: chunk size
+    S, BT = split_size, chunk_size
+    assert S % BT == 0, f"The `split_size` (got {S}) must be a multiple of `chunk_size` {BT}"
+    if offsets is None:
+        N = B
+        NS = N * triton.cdiv(T, S)
+    else:
+        N = len(offsets) - 1
+        NS = split_offsets[-1]
+
+    # unreduced kv states per split
+    hs = k.new_empty(NS, H, K, V, dtype=torch.float)
+    # reduced states per split
+    hr = k.new_empty(NS, H, K, V, dtype=torch.float if states_in_fp32 else k.dtype)
+    ht = k.new_empty(N, H, K, V, dtype=torch.float) if output_final_state else None
+    # parallelized over splits
+    def grid(meta): return (triton.cdiv(K, meta['BK']), triton.cdiv(V, meta['BV']), NS * H)
+    chunk_fwd_kernel_h_split[grid](
+        k=k,
+        v=v,
+        g=g,
+        gk=gk,
+        gv=gv,
+        hs=hs,
+        hr=hr,
+        h0=h0,
+        ht=ht,
+        offsets=offsets,
+        split_indices=split_indices,
+        T=T,
+        S=S,
+        H=H,
+        K=K,
+        V=V,
+        BT=BT,
+        USE_G=g is not None,
+        USE_GK=gk is not None,
+        USE_GV=gv is not None,
+        HEAD_FIRST=head_first
+    )
+    def grid(meta): return (triton.cdiv(K, meta['BK']), triton.cdiv(V, meta['BV']), N * H)
+    chunk_fwd_kernel_h_reduction[grid](
+        g=g,
+        gk=gk,
+        gv=gv,
+        hs=hs,
+        hr=hr,
+        ht=ht,
+        offsets=offsets,
+        split_offsets=split_offsets,
+        T=T,
+        S=S,
+        H=H,
+        K=K,
+        V=V,
+        BT=BT,
+        USE_G=g is not None,
+        USE_GK=gk is not None,
+        USE_GV=gv is not None,
+        HEAD_FIRST=head_first
+    )
+    return hr, ht
+
+
+def chunk_bwd_dh(
+    q: torch.Tensor,
+    k: torch.Tensor,
+    v: torch.Tensor,
+    g: torch.Tensor,
+    gk: torch.Tensor,
+    gv: torch.Tensor,
+    do: torch.Tensor,
+    h0: torch.Tensor,
+    dht: torch.Tensor,
+    scale: float,
+    offsets: Optional[torch.Tensor] = None,
+    split_offsets: Optional[torch.Tensor] = None,
+    split_indices: Optional[torch.Tensor] = None,
+    head_first: bool = True,
+    chunk_size: int = 64,
+    split_size: int = 256,
+    states_in_fp32: bool = True
+) -> Tuple[torch.Tensor, torch.Tensor]:
+    if head_first:
+        B, H, T, K, V = *k.shape, v.shape[-1]
+        HQ = q.shape[1]
+    else:
+        B, T, H, K, V = *k.shape, v.shape[-1]
+        HQ = q.shape[2]
+    # B: batch size
+    # N: the actual number of sequences in the batch
+    # H: number of heads
+    # T: sequence length, can be variable across sequences
+    # S: split size, a multiple of chunk size
+    # BT: chunk size
+    S, BT = max(chunk_size, min(split_size, triton.next_power_of_2(T))), chunk_size
+    assert S % BT == 0, f"The `split_size` (got {S}) must be a multiple of `chunk_size` {BT}"
+    if offsets is None:
+        N = B
+        NS = N * triton.cdiv(T, S)
+    else:
+        N = len(offsets) - 1
+        NS = split_offsets[-1]
+    # number of groups in GQA
+    NG = HQ // H
+
+    dhs = q.new_empty(NS, HQ, K, V, dtype=torch.float)
+    dhr = q.new_empty(NS, HQ, K, V, dtype=torch.float if states_in_fp32 else k.dtype)
+    dh0 = torch.empty_like(h0, dtype=torch.float) if h0 is not None else None
+
+    # parallelized over splits
+    def grid(meta): return (triton.cdiv(K, meta['BK']), triton.cdiv(V, meta['BV']), NS * HQ)
+    chunk_bwd_kernel_dh_split[grid](
+        q=q,
+        g=g,
+        gk=gk,
+        gv=gv,
+        do=do,
+        dht=dht,
+        dhs=dhs,
+        dhr=dhr,
+        dh0=dh0,
+        offsets=offsets,
+        split_indices=split_indices,
+        scale=scale,
+        T=T,
+        S=S,
+        HQ=HQ,
+        H=H,
+        K=K,
+        V=V,
+        BT=BT,
+        NG=NG,
+        USE_G=g is not None,
+        USE_GK=gk is not None,
+        USE_GV=gv is not None,
+        HEAD_FIRST=head_first,
+    )
+
+    def grid(meta): return (triton.cdiv(K, meta['BK']), triton.cdiv(V, meta['BV']), N * HQ)
+    chunk_bwd_kernel_dh_reduction[grid](
+        g=g,
+        gk=gk,
+        gv=gv,
+        dhs=dhs,
+        dhr=dhr,
+        dh0=dh0,
+        offsets=offsets,
+        split_offsets=split_offsets,
+        T=T,
+        S=S,
+        HQ=HQ,
+        H=H,
+        K=K,
+        V=V,
+        BT=BT,
+        NG=NG,
+        USE_G=g is not None,
+        USE_GK=gk is not None,
+        USE_GV=gv is not None,
+        HEAD_FIRST=head_first
+    )
+    return dhr, dh0

fla/ops/common/chunk_o.py

@@ -0,0 +1,668 @@
+# -*- coding: utf-8 -*-
+# Copyright (c) 2023-2025, Songlin Yang, Yu Zhang
+
+from typing import Optional, Tuple
+
+import torch
+import triton
+import triton.language as tl
+
+from fla.ops.utils.op import exp, safe_exp
+from fla.utils import check_shared_mem, is_nvidia_hopper
+
+BKV_LIST = [64, 128] if check_shared_mem() else [32, 64]
+NUM_WARPS = [2, 4] if is_nvidia_hopper else [2, 4, 8]
+
+
+@triton.heuristics({
+    'USE_G': lambda args: args['g'] is not None,
+    'USE_OFFSETS': lambda args: args['offsets'] is not None
+})
+@triton.autotune(
+    configs=[
+        triton.Config({'BK': BK, 'BV': BV}, num_warps=num_warps, num_stages=num_stages)
+        for BK in BKV_LIST
+        for BV in BKV_LIST
+        for num_warps in NUM_WARPS
+        for num_stages in [2, 3, 4]
+    ],
+    key=['H', 'K', 'V', 'BT'],
+)
+@triton.jit(do_not_specialize=['T'])
+def chunk_fwd_kernel_o(
+    q,
+    k,
+    v,
+    h,
+    g,
+    o,
+    offsets,
+    indices,
+    scale,
+    T,
+    H: tl.constexpr,
+    K: tl.constexpr,
+    V: tl.constexpr,
+    BT: tl.constexpr,
+    BK: tl.constexpr,
+    BV: tl.constexpr,
+    USE_G: tl.constexpr,
+    USE_OFFSETS: tl.constexpr,
+    HEAD_FIRST: tl.constexpr
+):
+    i_v, i_t, i_bh = tl.program_id(0), tl.program_id(1), tl.program_id(2)
+    i_b, i_h = i_bh // H, i_bh % H
+
+    if USE_OFFSETS:
+        i_tg = i_t
+        i_n, i_t = tl.load(indices + i_t * 2).to(tl.int32), tl.load(indices + i_t * 2 + 1).to(tl.int32)
+        bos, eos = tl.load(offsets + i_n).to(tl.int32), tl.load(offsets + i_n + 1).to(tl.int32)
+        T = eos - bos
+        NT = tl.cdiv(T, BT)
+    else:
+        NT = tl.cdiv(T, BT)
+        i_tg = i_b * NT + i_t
+        bos, eos = i_b * T, i_b * T + T
+
+    s_qk = K if HEAD_FIRST else H*K
+    s_vo = V if HEAD_FIRST else H*V
+    s_g = 1 if HEAD_FIRST else H
+    # offset calculation
+    q += (i_bh * T*K) if HEAD_FIRST else ((bos * H + i_h) * K)
+    k += (i_bh * T*K) if HEAD_FIRST else ((bos * H + i_h) * K)
+    v += (i_bh * T*V) if HEAD_FIRST else ((bos * H + i_h) * V)
+    o += (i_bh * T*V) if HEAD_FIRST else ((bos * H + i_h) * V)
+    h += ((i_bh * NT + i_t).to(tl.int64) * K*V) if HEAD_FIRST else ((i_tg * H + i_h).to(tl.int64) * K*V)
+
+    b_o = tl.zeros([BT, BV], dtype=tl.float32)
+    b_A = tl.zeros([BT, BT], dtype=tl.float32)
+
+    for i_k in range(tl.cdiv(K, BK)):
+        p_q = tl.make_block_ptr(q, (T, K), (s_qk, 1), (i_t * BT, i_k * BK), (BT, BK), (1, 0))
+        p_k = tl.make_block_ptr(k, (K, T), (1, s_qk), (i_k * BK, i_t * BT), (BK, BT), (0, 1))
+        p_h = tl.make_block_ptr(h, (K, V), (V, 1), (i_k * BK, i_v * BV), (BK, BV), (1, 0))
+        # [BT, BK]
+        b_q = tl.load(p_q, boundary_check=(0, 1))
+        # [BK, BT]
+        b_k = tl.load(p_k, boundary_check=(0, 1))
+        # [BK, BV]
+        b_h = tl.load(p_h, boundary_check=(0, 1))
+
+        # [BT, BK] @ [BK, BV] -> [BT, BV]
+        b_o += tl.dot(b_q, b_h)
+        # [BT, BK] @ [BK, BT] -> [BT, BT]
+        b_A += tl.dot(b_q, b_k)
+
+    if USE_G:
+        g += (i_bh * T) if HEAD_FIRST else (bos * H + i_h)
+        p_g = tl.make_block_ptr(g, (T,), (s_g,), (i_t * BT,), (BT,), (0,))
+        b_g = tl.load(p_g, boundary_check=(0,))
+        b_o = b_o * exp(b_g)[:, None]
+        b_A = b_A * safe_exp(b_g[:, None] - b_g[None, :])
+
+    o_i = tl.arange(0, BT)
+    m_A = o_i[:, None] >= o_i[None, :]
+    b_A = tl.where(m_A, b_A, 0)
+
+    p_v = tl.make_block_ptr(v, (T, V), (s_vo, 1), (i_t * BT, i_v * BV), (BT, BV), (1, 0))
+    p_o = tl.make_block_ptr(o, (T, V), (s_vo, 1), (i_t * BT, i_v * BV), (BT, BV), (1, 0))
+    b_v = tl.load(p_v, boundary_check=(0, 1))
+
+    # to fix mma -> mma layout conversion
+    # already solved by triton v3.2 or higher
+    b_o = b_o * scale + tl.dot(b_A.to(b_v.dtype), b_v) * scale
+    tl.store(p_o, b_o.to(p_o.dtype.element_ty), boundary_check=(0, 1))
+
+
+@triton.heuristics({
+    'USE_OFFSETS': lambda args: args['offsets'] is not None,
+    'USE_G': lambda args: args['g'] is not None,
+    'USE_DW': lambda args: args['dw'] is not None
+})
+@triton.autotune(
+    configs=[
+        triton.Config({}, num_warps=num_warps, num_stages=num_stages)
+        for num_warps in NUM_WARPS
+        for num_stages in [2, 3, 4]
+    ],
+    key=['H', 'K', 'V', 'BT', 'BK', 'BV', 'USE_G', 'USE_DW'],
+)
+@triton.jit(do_not_specialize=['T'])
+def chunk_bwd_kernel_dqkwg(
+    q,
+    k,
+    v,
+    h,
+    g,
+    do,
+    dh,
+    dq,
+    dk,
+    dg,
+    w,
+    dv,
+    dw,
+    offsets,
+    indices,
+    scale,
+    B: tl.constexpr,
+    T,
+    H: tl.constexpr,
+    K: tl.constexpr,
+    V: tl.constexpr,
+    BT: tl.constexpr,
+    BK: tl.constexpr,
+    BV: tl.constexpr,
+    USE_G: tl.constexpr,
+    USE_DW: tl.constexpr,
+    USE_OFFSETS: tl.constexpr,
+    HEAD_FIRST: tl.constexpr
+):
+    i_k, i_t, i_bh = tl.program_id(0), tl.program_id(1), tl.program_id(2)
+    i_b, i_h = i_bh // H, i_bh % H
+    if USE_G:
+        dg += i_k * B * H * T
+    if USE_OFFSETS:
+        i_tg = i_t
+        i_n, i_t = tl.load(indices + i_t * 2).to(tl.int32), tl.load(indices + i_t * 2 + 1).to(tl.int32)
+        bos, eos = tl.load(offsets + i_n).to(tl.int32), tl.load(offsets + i_n + 1).to(tl.int32)
+        T = eos - bos
+        NT = tl.cdiv(T, BT)
+    else:
+        NT = tl.cdiv(T, BT)
+        i_tg = i_b * NT + i_t
+        bos, eos = i_b * T, i_b * T + T
+
+    # offset calculation
+    v += i_bh * T*V if HEAD_FIRST else (bos * H + i_h) * V
+    do += i_bh * T*V if HEAD_FIRST else (bos * H + i_h) * V
+    h += (i_bh * NT + i_t).to(tl.int64) * K*V if HEAD_FIRST else (i_tg * H + i_h).to(tl.int64) * K*V
+    dh += (i_bh * NT + i_t).to(tl.int64) * K*V if HEAD_FIRST else (i_tg * H + i_h).to(tl.int64) * K*V
+    q += i_bh * T*K if HEAD_FIRST else (bos * H + i_h) * K
+    k += i_bh * T*K if HEAD_FIRST else (bos * H + i_h) * K
+    dq += i_bh * T*K if HEAD_FIRST else (bos * H + i_h) * K
+    dk += i_bh * T*K if HEAD_FIRST else (bos * H + i_h) * K
+    s_qk = K if HEAD_FIRST else H*K
+    s_vo = V if HEAD_FIRST else H*V
+    s_g = 1 if HEAD_FIRST else H
+
+    # for delta rule only
+    if USE_DW:
+        dw += i_bh * T*K if HEAD_FIRST else (bos * H + i_h) * K
+        dv += i_bh * T*V if HEAD_FIRST else (bos * H + i_h) * V
+        w += i_bh * T*K if HEAD_FIRST else (bos * H + i_h) * K
+
+    b_dq = tl.zeros([BT, BK], dtype=tl.float32)
+    b_dk = tl.zeros([BT, BK], dtype=tl.float32)
+    b_ds = tl.zeros([BT, BT], dtype=tl.float32)
+    b_dg_last = tl.zeros([1,], dtype=tl.float32) if USE_G else None
+    b_dw = tl.zeros([BT, BK], dtype=tl.float32) if USE_DW else None
+
+    for i_v in range(tl.cdiv(V, BV)):
+        p_v = tl.make_block_ptr(v, (T, V), (s_vo, 1), (i_t * BT, i_v * BV), (BT, BV), (1, 0))
+        p_do = tl.make_block_ptr(do, (T, V), (s_vo, 1), (i_t * BT, i_v * BV), (BT, BV), (1, 0))
+        p_h = tl.make_block_ptr(h, (V, K), (1, V), (i_v * BV, i_k * BK), (BV, BK), (0, 1))
+        p_dh = tl.make_block_ptr(dh, (V, K), (1, V), (i_v * BV, i_k * BK), (BV, BK), (0, 1))
+        # [BT, BV]
+        b_v = tl.load(p_v, boundary_check=(0, 1))
+        b_do = tl.load(p_do, boundary_check=(0, 1))
+        # [BV, BK]
+        b_h = tl.load(p_h, boundary_check=(0, 1))
+        b_dh = tl.load(p_dh, boundary_check=(0, 1))
+        if USE_G:
+            b_dg_last += (tl.sum(b_h * b_dh))
+        # [BT, BV] @ [BV, BT] -> [BT, BT]
+        b_ds += tl.dot(b_do, tl.trans(b_v))
+        # [BT, BV] @ [BV, BK] -> [BT, BK]
+        b_dq += tl.dot(b_do, b_h.to(b_do.dtype))
+        # [BT, BV] @ [BV, BK] -> [BT, BK]
+        b_dk += tl.dot(b_v, b_dh.to(b_v.dtype))
+        if USE_DW:
+            p_dv = tl.make_block_ptr(dv, (T, V), (s_vo, 1), (i_t * BT, i_v * BV), (BT, BV), (1, 0))
+            b_dv = tl.load(p_dv, boundary_check=(0, 1))
+            b_dw += tl.dot(b_dv.to(b_v.dtype), b_h.to(b_v.dtype))
+
+    if USE_DW and not USE_G:
+        p_dw = tl.make_block_ptr(dw, (T, K), (s_qk, 1), (i_t * BT, i_k * BK), (BT, BK), (1, 0))
+        tl.store(p_dw, -b_dw.to(p_dw.dtype.element_ty), boundary_check=(0, 1))
+
+    tl.debug_barrier()
+    o_i = tl.arange(0, BT)
+    p_q = tl.make_block_ptr(q, (T, K), (s_qk, 1), (i_t * BT, i_k * BK), (BT, BK), (1, 0))
+    p_k = tl.make_block_ptr(k, (T, K), (s_qk, 1), (i_t * BT, i_k * BK), (BT, BK), (1, 0))
+    b_q = tl.load(p_q, boundary_check=(0, 1))
+    b_k = tl.load(p_k, boundary_check=(0, 1))
+
+    p_dq = tl.make_block_ptr(dq, (T, K), (s_qk, 1), (i_t * BT, i_k * BK), (BT, BK), (1, 0))
+    p_dk = tl.make_block_ptr(dk, (T, K), (s_qk, 1), (i_t * BT, i_k * BK), (BT, BK), (1, 0))
+
+    if USE_G:
+        b_dg = tl.zeros([BT,], dtype=tl.float32)
+        g += i_bh * T if HEAD_FIRST else bos * H + i_h
+        dg += i_bh * T if HEAD_FIRST else bos * H + i_h
+        p_g = tl.make_block_ptr(g, (T,), (s_g,), (i_t * BT,), (BT,), (0,))
+        b_g = tl.load(p_g, boundary_check=(0,))
+        b_g_last = tl.load(g + (min(i_t * BT + BT, T) - 1) * s_g)
+        b_dg_last *= exp(b_g_last)
+
+        if USE_DW:
+            p_w = tl.make_block_ptr(w, (T, K), (s_qk, 1), (i_t * BT, i_k * BK), (BT, BK), (1, 0))
+            p_dw = tl.make_block_ptr(dw, (T, K), (s_qk, 1), (i_t * BT, i_k * BK), (BT, BK), (1, 0))
+            b_w = tl.load(p_w, boundary_check=(0, 1))
+            b_dw = b_dw * exp(b_g)[:, None]
+            tl.store(p_dw, -b_dw.to(p_dw.dtype.element_ty), boundary_check=(0, 1))
+            b_dg -= tl.sum(b_w * b_dw, axis=1)
+
+        b_dq = b_dq * exp(b_g)[:, None] * scale
+        b_dg += tl.sum(b_dq * b_q, axis=1)
+
+        b_dk = b_dk * safe_exp(-b_g + b_g_last)[:, None]
+        b_dg -= tl.sum(b_k * b_dk, axis=1)
+        b_dg_last += tl.sum(b_dk * b_k)
+
+        b_ds = tl.where(o_i[:, None] >= o_i[None, :], b_ds * safe_exp(b_g[:, None] - b_g[None, :]), 0) * scale
+        b_ds2 = b_ds * tl.dot(b_q, tl.trans(b_k))
+        b_dg += tl.sum(b_ds2, axis=1)
+        b_dg -= tl.sum(b_ds2, axis=0)
+
+        b_ds = b_ds.to(b_k.dtype)
+        # [BT, BK]
+        b_dq += tl.dot(b_ds, b_k)
+        b_dk += tl.dot(tl.trans(b_ds), b_q)
+        p_dg = tl.make_block_ptr(dg, (T,), (s_g,), (i_t * BT,), (BT,), (0,))
+        # (SY 09/21) revcumsum in a separate kernel due to strange triton compiler issue
+        # b_dg = tl.dot(tl.where(o_i[:, None] <= o_i[None, :], 1., 0.), b_dg, allow_tf32=False) + b_dg_last)
+        b_dg = tl.where(o_i < min(BT, T-i_t*BT) - 1, b_dg, b_dg + b_dg_last)
+        tl.store(p_dq, b_dq.to(p_dq.dtype.element_ty), boundary_check=(0, 1))
+        tl.store(p_dk, b_dk.to(p_dk.dtype.element_ty), boundary_check=(0, 1))
+        tl.store(p_dg, b_dg.to(p_dg.dtype.element_ty), boundary_check=(0,))
+    else:
+        b_ds = tl.where(o_i[:, None] >= o_i[None, :], b_ds, 0)
+        b_ds = b_ds.to(b_k.dtype)
+        b_dq += tl.dot(b_ds, b_k)
+        b_dk += tl.dot(tl.trans(b_ds), b_q) * scale
+        b_dq *= scale
+        tl.store(p_dq, b_dq.to(p_dq.dtype.element_ty), boundary_check=(0, 1))
+        tl.store(p_dk, b_dk.to(p_dk.dtype.element_ty), boundary_check=(0, 1))
+
+
+@triton.heuristics({
+    'USE_OFFSETS': lambda args: args['offsets'] is not None,
+    'USE_G': lambda args: args['g'] is not None,
+})
+@triton.autotune(
+    configs=[
+        triton.Config({}, num_warps=num_warps, num_stages=num_stages)
+        for num_warps in [2, 4, 8]
+        for num_stages in [2, 3, 4]
+    ],
+    key=['H', 'K', 'V', 'BT', 'BK', 'BV', 'USE_G'],
+)
+@triton.jit(do_not_specialize=['T'])
+def chunk_bwd_kernel_dv(
+    q,
+    k,
+    g,
+    do,
+    dv,
+    dh,
+    offsets,
+    indices,
+    scale,
+    T,
+    H: tl.constexpr,
+    K: tl.constexpr,
+    V: tl.constexpr,
+    BT: tl.constexpr,
+    BK: tl.constexpr,
+    BV: tl.constexpr,
+    USE_G: tl.constexpr,
+    USE_OFFSETS: tl.constexpr,
+    HEAD_FIRST: tl.constexpr
+):
+    i_v, i_t, i_bh = tl.program_id(0), tl.program_id(1), tl.program_id(2)
+    i_b, i_h = i_bh // H, i_bh % H
+    if USE_OFFSETS:
+        i_tg = i_t
+        i_n, i_t = tl.load(indices + i_t * 2).to(tl.int32), tl.load(indices + i_t * 2 + 1).to(tl.int32)
+        bos, eos = tl.load(offsets + i_n).to(tl.int32), tl.load(offsets + i_n + 1).to(tl.int32)
+        T = eos - bos
+        NT = tl.cdiv(T, BT)
+    else:
+        NT = tl.cdiv(T, BT)
+        i_tg = i_b * NT + i_t
+        bos, eos = i_b * T, i_b * T + T
+
+    b_dv = tl.zeros([BT, BV], dtype=tl.float32)
+
+    # offset calculation
+    q += i_bh * T*K if HEAD_FIRST else (bos * H + i_h) * K
+    k += i_bh * T*K if HEAD_FIRST else (bos * H + i_h) * K
+    do += i_bh * T*V if HEAD_FIRST else (bos * H + i_h) * V
+    dv += i_bh * T*V if HEAD_FIRST else (bos * H + i_h) * V
+    s_qk = K if HEAD_FIRST else H*K
+    s_vo = V if HEAD_FIRST else H*V
+    s_g = 1 if HEAD_FIRST else H
+    dh += (i_bh * NT + i_t).to(tl.int64) * K*V if HEAD_FIRST else (i_tg * H + i_h).to(tl.int64) * K*V
+
+    b_A = tl.zeros([BT, BT], dtype=tl.float32)
+    for i_k in range(tl.cdiv(K, BK)):
+        p_k = tl.make_block_ptr(k, (T, K), (s_qk, 1), (i_t * BT, i_k * BK), (BT, BK), (1, 0))
+        p_q = tl.make_block_ptr(q, (K, T), (1, s_qk), (i_k * BK, i_t * BT), (BK, BT), (0, 1))
+        b_q = tl.load(p_q, boundary_check=(0, 1))
+        b_k = tl.load(p_k, boundary_check=(0, 1))
+        b_A += tl.dot(b_k, b_q)
+        p_dh = tl.make_block_ptr(dh, (K, V), (V, 1), (i_k * BK, i_v * BV), (BK, BV), (1, 0))
+        b_dh = tl.load(p_dh, boundary_check=(0, 1))
+        b_dv += tl.dot(b_k, b_dh.to(b_k.dtype))
+
+    if USE_G:
+        g += (i_bh * T) if HEAD_FIRST else (bos * H + i_h)
+        p_g = tl.make_block_ptr(g, (T,), (s_g,), (i_t * BT,), (BT,), (0,))
+        b_g = tl.load(p_g, boundary_check=(0,))
+        b_g_last = tl.load(g + (min(i_t * BT + BT, T) - 1) * s_g)
+        b_dv *= safe_exp(-b_g + b_g_last)[:, None]
+
+    mask = (tl.arange(0, BT)[:, None] <= tl.arange(0, BT)[None, :])
+    if USE_G:
+        b_A = tl.where(mask, b_A * safe_exp(b_g[None, :] - b_g[:, None]) * scale, 0).to(do.dtype.element_ty)
+    else:
+        b_A = tl.where(mask, b_A * scale, 0).to(do.dtype.element_ty)
+    p_do = tl.make_block_ptr(do, (T, V), (s_vo, 1), (i_t * BT, i_v * BV), (BT, BV), (1, 0))
+    p_dv = tl.make_block_ptr(dv, (T, V), (s_vo, 1), (i_t * BT, i_v * BV), (BT, BV), (1, 0))
+    b_do = tl.load(p_do, boundary_check=(0, 1))
+    b_dv += tl.dot(b_A.to(b_do.dtype), b_do)
+    tl.store(p_dv, b_dv.to(p_dv.dtype.element_ty), boundary_check=(0, 1))
+
+
+@triton.heuristics({
+    'USE_G': lambda args: args['g'] is not None,
+    'USE_OFFSETS': lambda args: args['offsets'] is not None,
+})
+@triton.autotune(
+    configs=[
+        triton.Config({}, num_warps=num_warps, num_stages=num_stages)
+        for num_warps in NUM_WARPS
+        for num_stages in [2, 3, 4]
+    ],
+    key=['H', 'K', 'V', 'BT', 'BK', 'BV', 'USE_G'],
+)
+@triton.jit(do_not_specialize=['T'])
+def chunk_bwd_kernel_dv_local(
+    q,
+    k,
+    g,
+    do,
+    dv,
+    offsets,
+    indices,
+    scale,
+    T,
+    H: tl.constexpr,
+    K: tl.constexpr,
+    V: tl.constexpr,
+    BT: tl.constexpr,
+    BK: tl.constexpr,
+    BV: tl.constexpr,
+    USE_G: tl.constexpr,
+    USE_OFFSETS: tl.constexpr,
+    HEAD_FIRST: tl.constexpr
+):
+    i_t, i_bh = tl.program_id(0), tl.program_id(1)
+    i_b, i_h = i_bh // H, i_bh % H
+    if USE_OFFSETS:
+        i_n, i_t = tl.load(indices + i_t * 2).to(tl.int32), tl.load(indices + i_t * 2 + 1).to(tl.int32)
+        bos, eos = tl.load(offsets + i_n).to(tl.int32), tl.load(offsets + i_n + 1).to(tl.int32)
+        T = eos - bos
+    else:
+        bos, eos = i_b * T, i_b * T + T
+
+    # offset calculation
+    q += i_bh * T*K if HEAD_FIRST else (bos * H + i_h) * K
+    k += i_bh * T*K if HEAD_FIRST else (bos * H + i_h) * K
+    do += i_bh * T*V if HEAD_FIRST else (bos * H + i_h) * V
+    dv += i_bh * T*V if HEAD_FIRST else (bos * H + i_h) * V
+    s_qk = K if HEAD_FIRST else H*K
+    s_vo = V if HEAD_FIRST else H*V
+    s_g = 1 if HEAD_FIRST else H
+
+    b_A = tl.zeros([BT, BT], dtype=tl.float32)
+    for i_k in range(tl.cdiv(K, BK)):
+        p_k = tl.make_block_ptr(k, (T, K), (s_qk, 1), (i_t * BT, i_k * BK), (BT, BK), (1, 0))
+        p_q = tl.make_block_ptr(q, (K, T), (1, s_qk), (i_k * BK, i_t * BT), (BK, BT), (0, 1))
+        b_q = tl.load(p_q, boundary_check=(0, 1))
+        b_k = tl.load(p_k, boundary_check=(0, 1))
+        b_A += tl.dot(b_k, b_q)
+
+    if USE_G:
+        g += (i_bh * T) if HEAD_FIRST else (bos * H + i_h)
+        p_g = tl.make_block_ptr(g, (T,), (s_g,), (i_t * BT,), (BT,), (0,))
+        b_g = tl.load(p_g, boundary_check=(0,))
+
+    mask = (tl.arange(0, BT)[:, None] <= tl.arange(0, BT)[None, :])
+    if USE_G:
+        b_A = tl.where(mask, b_A * safe_exp(b_g[None, :] - b_g[:, None]) * scale, 0).to(do.dtype.element_ty)
+    else:
+        b_A = tl.where(mask, b_A * scale, 0).to(do.dtype.element_ty)
+
+    for i_v in range(tl.cdiv(V, BV)):
+        p_do = tl.make_block_ptr(do, (T, V), (s_vo, 1), (i_t * BT, i_v * BV), (BT, BV), (1, 0))
+        p_dv = tl.make_block_ptr(dv, (T, V), (s_vo, 1), (i_t * BT, i_v * BV), (BT, BV), (1, 0))
+        b_do = tl.load(p_do, boundary_check=(0, 1))
+        b_dv = tl.dot(b_A.to(b_do.dtype), b_do)
+        tl.store(p_dv, b_dv.to(p_dv.dtype.element_ty), boundary_check=(0, 1))
+
+
+def chunk_fwd_o(
+    q: torch.Tensor,
+    k: torch.Tensor,
+    v: torch.Tensor,
+    h: torch.Tensor,
+    g: Optional[torch.Tensor] = None,  # cumsum of log decay
+    scale: Optional[float] = None,
+    offsets: Optional[torch.LongTensor] = None,
+    indices: Optional[torch.LongTensor] = None,
+    head_first: bool = True,
+    chunk_size: int = 64
+) -> torch.Tensor:
+    if head_first:
+        B, H, T, K, V = *q.shape, v.shape[-1]
+    else:
+        B, T, H, K, V = *q.shape, v.shape[-1]
+    if scale is None:
+        scale = k.shape[-1] ** -0.5
+    BT = min(chunk_size, max(16, triton.next_power_of_2(T)))
+    NT = triton.cdiv(T, BT) if offsets is None else len(indices)
+
+    o = torch.empty_like(v)
+
+    def grid(meta): return (triton.cdiv(V, meta['BV']), NT, B * H)
+    chunk_fwd_kernel_o[grid](
+        q,
+        k,
+        v,
+        h,
+        g,
+        o,
+        offsets,
+        indices,
+        scale,
+        T=T,
+        H=H,
+        K=K,
+        V=V,
+        BT=BT,
+        HEAD_FIRST=head_first
+    )
+    return o
+
+
+def chunk_bwd_dv(
+    q: torch.Tensor,
+    k: torch.Tensor,
+    g: torch.Tensor,
+    do: torch.Tensor,
+    dh: torch.Tensor,
+    scale: float,
+    offsets: Optional[torch.LongTensor] = None,
+    indices: Optional[torch.LongTensor] = None,
+    head_first: bool = True,
+    chunk_size: int = 64
+) -> torch.Tensor:
+    if head_first:
+        B, H, T, K, V = *k.shape, do.shape[-1]
+    else:
+        B, T, H, K, V = *k.shape, do.shape[-1]
+    BT = min(chunk_size, max(16, triton.next_power_of_2(T)))
+    # H100 can have larger block size
+    if check_shared_mem('hopper', k.device.index):
+        CONST_TILING = 128
+    elif check_shared_mem:
+        CONST_TILING = 64
+    else:
+        CONST_TILING = 32
+    BK = min(triton.next_power_of_2(K), CONST_TILING)
+    BV = min(triton.next_power_of_2(V), CONST_TILING)
+    NT = triton.cdiv(T, BT) if offsets is None else len(indices)
+    NV = triton.cdiv(V, BV)
+
+    dv = torch.empty_like(do)
+    grid = (NV, NT, B * H)
+    chunk_bwd_kernel_dv[grid](
+        q,
+        k,
+        g,
+        do,
+        dv,
+        dh,
+        offsets,
+        indices,
+        scale,
+        T=T,
+        H=H,
+        K=K,
+        V=V,
+        BT=BT,
+        BK=BK,
+        BV=BV,
+        HEAD_FIRST=head_first
+    )
+    return dv
+
+
+def chunk_bwd_dv_local(
+    q: torch.Tensor,
+    k: torch.Tensor,
+    g: torch.Tensor,
+    do: torch.Tensor,
+    dh: torch.Tensor,
+    scale: float,
+    offsets: Optional[torch.LongTensor] = None,
+    indices: Optional[torch.LongTensor] = None,
+    head_first: bool = True,
+    chunk_size: int = 64
+) -> torch.Tensor:
+    if head_first:
+        B, H, T, K, V = *k.shape, do.shape[-1]
+    else:
+        B, T, H, K, V = *k.shape, do.shape[-1]
+    BT = min(chunk_size, max(16, triton.next_power_of_2(T)))
+    # H100 can have larger block size
+    if check_shared_mem('hopper', k.device.index):
+        CONST_TILING = 128
+    elif check_shared_mem:
+        CONST_TILING = 64
+    else:
+        CONST_TILING = 32
+    BK = min(triton.next_power_of_2(K), CONST_TILING)
+    BV = min(triton.next_power_of_2(V), CONST_TILING)
+    NT = triton.cdiv(T, BT) if offsets is None else len(indices)
+
+    dv = torch.empty_like(do)
+    grid = (NT, B * H)
+    chunk_bwd_kernel_dv_local[grid](
+        q,
+        k,
+        g,
+        do,
+        dv,
+        offsets,
+        indices,
+        scale,
+        T=T,
+        H=H,
+        K=K,
+        V=V,
+        BT=BT,
+        BK=BK,
+        BV=BV,
+        HEAD_FIRST=head_first
+    )
+    return dv
+
+
+def chunk_bwd_dqkwg(
+    q: torch.Tensor,
+    k: torch.Tensor,
+    v: torch.Tensor,
+    g: torch.Tensor,
+    do: torch.Tensor,
+    h: torch.Tensor,
+    dh: torch.Tensor,
+    dv: Optional[torch.Tensor] = None,
+    w: Optional[torch.Tensor] = None,
+    offsets: Optional[torch.LongTensor] = None,
+    indices: Optional[torch.LongTensor] = None,
+    chunk_size: int = 64,
+    scale: float = 1.0,
+    head_first: bool = True,
+) -> Tuple[torch.Tensor, torch.Tensor, torch.Tensor]:
+
+    if head_first:
+        B, H, T, K, V = *k.shape, v.shape[-1]
+    else:
+        B, T, H, K, V = *k.shape, v.shape[-1]
+    BT = min(chunk_size, max(16, triton.next_power_of_2(T)))
+    NT = triton.cdiv(T, BT) if offsets is None else len(indices)
+
+    CONST_TILING = 64 if check_shared_mem() else 32
+    BK = min(triton.next_power_of_2(K), CONST_TILING)
+    BV = min(triton.next_power_of_2(V), CONST_TILING)
+    NK = triton.cdiv(K, BK)
+    dq = torch.empty_like(q)
+    dk = torch.empty_like(k)
+    dg = torch.empty(NK, *g.shape, dtype=torch.float32, device=g.device) if g is not None else None
+    dw = torch.empty_like(w) if w is not None else None
+
+    grid = (NK, NT, B * H)
+    chunk_bwd_kernel_dqkwg[grid](
+        q=q,
+        k=k,
+        v=v,
+        h=h,
+        g=g,
+        do=do,
+        dh=dh,
+        dv=dv,
+        w=w,
+        dw=dw,
+        dq=dq,
+        dk=dk,
+        dg=dg,
+        offsets=offsets,
+        indices=indices,
+        scale=scale,
+        B=B,
+        T=T,
+        H=H,
+        K=K,
+        V=V,
+        BT=BT,
+        BK=BK,
+        BV=BV,
+        HEAD_FIRST=head_first
+    )
+
+    if dg is not None:
+        dg = dg.sum(0)
+    return dq, dk, dw, dg

fla/ops/common/chunk_scaled_dot_kkt.py

@@ -0,0 +1,126 @@
+# -*- coding: utf-8 -*-
+# Copyright (c) 2023-2025, Songlin Yang, Yu Zhang
+
+from typing import Optional
+
+import torch
+import triton
+import triton.language as tl
+
+from fla.ops.common.utils import prepare_chunk_indices
+
+
+@triton.heuristics({
+    'USE_OFFSETS': lambda args: args['offsets'] is not None
+})
+@triton.autotune(
+    configs=[
+        triton.Config({'BK': BK}, num_warps=num_warps, num_stages=num_stages)
+        for BK in [32, 64, 128]
+        for num_warps in [2, 4, 8]
+        for num_stages in [2, 3, 4]
+    ],
+    key=['H', 'K', 'BT', 'USE_OFFSETS'],
+)
+@triton.jit(do_not_specialize=['T'])
+def chunk_scaled_dot_kkt_fwd_kernel(
+    k,
+    beta,
+    A,
+    offsets,
+    indices,
+    T,
+    H: tl.constexpr,
+    K: tl.constexpr,
+    BT: tl.constexpr,
+    BK: tl.constexpr,
+    HEAD_FIRST: tl.constexpr,
+    USE_OFFSETS: tl.constexpr,
+):
+    i_t, i_bh = tl.program_id(0), tl.program_id(1)
+    i_b, i_h = i_bh // H, i_bh % H
+    if USE_OFFSETS:
+        i_n, i_t = tl.load(indices + i_t * 2).to(tl.int32), tl.load(indices + i_t * 2 + 1).to(tl.int32)
+        bos, eos = tl.load(offsets + i_n).to(tl.int32), tl.load(offsets + i_n + 1).to(tl.int32)
+        T = eos - bos
+    else:
+        bos, eos = i_b * T, i_b * T + T
+    o_t = tl.arange(0, BT)
+
+    if HEAD_FIRST:
+        p_beta = tl.make_block_ptr(beta + i_bh * T, (T,), (1,), (i_t * BT,), (BT,), (0,))
+    else:
+        p_beta = tl.make_block_ptr(beta + bos*H + i_h, (T,), (H,), (i_t * BT,), (BT,), (0,))
+    b_beta = tl.load(p_beta, boundary_check=(0,))
+
+    b_A = tl.zeros([BT, BT], dtype=tl.float32)
+    for i_k in range(tl.cdiv(K, BK)):
+        if HEAD_FIRST:
+            p_k = tl.make_block_ptr(k + i_bh * T*K, (T, K), (K, 1), (i_t * BT, i_k * BK), (BT, BK), (1, 0))
+        else:
+            p_k = tl.make_block_ptr(k + (bos*H + i_h) * K, (T, K), (H*K, 1), (i_t * BT, i_k * BK), (BT, BK), (1, 0))
+        b_k = tl.load(p_k, boundary_check=(0, 1))
+        b_kb = b_k * b_beta[:, None]
+        b_A += tl.dot(b_kb.to(b_k.dtype), tl.trans(b_k))
+
+    b_A = tl.where(o_t[:, None] > o_t[None, :], b_A, 0)
+    if HEAD_FIRST:
+        p_A = tl.make_block_ptr(A + i_bh * T*BT, (T, BT), (BT, 1), (i_t * BT, 0), (BT, BT), (1, 0))
+    else:
+        p_A = tl.make_block_ptr(A + (bos*H + i_h) * BT, (T, BT), (BT*H, 1), (i_t * BT, 0), (BT, BT), (1, 0))
+    tl.store(p_A, b_A.to(p_A.dtype.element_ty), boundary_check=(0, 1))
+
+
+def chunk_scaled_dot_kkt_fwd(
+    k: torch.Tensor,
+    beta: torch.Tensor,
+    cu_seqlens: Optional[torch.LongTensor],
+    head_first: bool = False,
+    chunk_size: int = 64,
+    output_dtype: torch.dtype = torch.float32
+) -> torch.Tensor:
+    r"""
+    Compute beta * K * K^T.
+
+    Args:
+        k (torch.Tensor):
+            The key tensor of shape `[B, T, H, K]` if not `head_first` else `[B, H, T, K]`.
+        beta (torch.Tensor):
+            The beta tensor of shape `[B, T, H]` if not `head_first` else `[B, H, T]`.
+        cu_seqlens (torch.LongTensor):
+            The cumulative sequence lengths of the input tensor.
+            Default: None
+        head_first (bool):
+            If False, the input/output tensor is in the shape of `[B, T, H, K]`.
+            If True, the input/output tensor is in the shape of `[B, H, T, K]`.
+            Default: False
+        chunk_size (int):
+            The chunk size. Default: 64.
+        output_dtype (torch.dtype):
+            The dtype of the output tensor. Default: `torch.float32`
+
+    Returns:
+        beta * K * K^T of shape `[B, T, H, BT]` if not `head_first` else `[B, H, T, BT]`,
+        where `BT` is the chunk size.
+    """
+    if head_first:
+        B, H, T, K = k.shape
+    else:
+        B, T, H, K = k.shape
+    BT = chunk_size
+    indices = prepare_chunk_indices(cu_seqlens, BT) if cu_seqlens is not None else None
+    NT = triton.cdiv(T, BT) if cu_seqlens is None else len(indices)
+    A = torch.empty(B, *((H, T) if head_first else (T, H)), BT, device=k.device, dtype=output_dtype)
+    chunk_scaled_dot_kkt_fwd_kernel[(NT, B * H)](
+        k=k,
+        beta=beta,
+        A=A,
+        offsets=cu_seqlens,
+        indices=indices,
+        T=T,
+        H=H,
+        K=K,
+        BT=BT,
+        HEAD_FIRST=head_first
+    )
+    return A

fla/ops/common/utils.py

@@ -0,0 +1,69 @@
+# -*- coding: utf-8 -*-
+# Copyright (c) 2023-2025, Songlin Yang, Yu Zhang
+
+import torch
+import triton
+import triton.language as tl
+
+from fla.utils import tensor_cache
+
+
+@triton.autotune(
+    configs=[
+        triton.Config({}, num_warps=num_warps)
+        for num_warps in [4, 8, 16, 32]
+    ],
+    key=['B'],
+)
+@triton.jit
+def prepare_position_ids_kernel(
+    y,
+    offsets,
+    B: tl.constexpr
+):
+    i_n = tl.program_id(0)
+    bos, eos = tl.load(offsets + i_n).to(tl.int32), tl.load(offsets + i_n + 1).to(tl.int32)
+    T = eos - bos
+
+    o = tl.arange(0, B)
+    for i in range(0, tl.cdiv(T, B) * B, B):
+        o_i = o + i
+        tl.store(y + bos + o_i, o_i, o_i < T)
+
+
+@tensor_cache
+def prepare_lens(offsets: torch.LongTensor) -> torch.LongTensor:
+    return offsets[1:] - offsets[:-1]
+
+
+@tensor_cache
+def prepare_position_ids(offsets: torch.LongTensor) -> torch.LongTensor:
+    return torch.cat([torch.arange(n, dtype=offsets.dtype, device=offsets.device) for n in prepare_lens(offsets).unbind()])
+
+
+@tensor_cache
+def prepare_sequence_ids(position_ids: torch.LongTensor) -> torch.LongTensor:
+    return position_ids.eq(0).cumsum(0) - 1
+
+
+@tensor_cache
+def prepare_token_indices(offsets: torch.LongTensor) -> torch.LongTensor:
+    position_ids = prepare_position_ids(offsets)
+    return torch.stack([prepare_sequence_ids(position_ids), position_ids], 1).to(offsets)
+
+
+@tensor_cache
+def prepare_chunk_indices(
+    offsets: torch.LongTensor,
+    chunk_size: int
+) -> torch.LongTensor:
+    indices = torch.cat([torch.arange(n) for n in triton.cdiv(prepare_lens(offsets), chunk_size).tolist()])
+    return torch.stack([prepare_sequence_ids(indices), indices], 1).to(offsets)
+
+
+@tensor_cache
+def prepare_chunk_offsets(
+    offsets: torch.LongTensor,
+    chunk_size: int
+) -> torch.LongTensor:
+    return torch.cat([offsets.new_tensor([0]), triton.cdiv(prepare_lens(offsets), chunk_size)]).cumsum(-1)

fla/ops/delta_rule/README.md

@@ -0,0 +1,90 @@
+# Chunkwise-form Parallelism of DeltaNet
+
+This section expands on the formulation presented in Appendix B of the DeltaNet paper.[^1]
+
+To reduce notational clutter, we focus on the first chunk, denoting $\mathbf{S}^r=\mathbf{S}_{[1]}^r$. By partially expanding the recurrence, we have:
+```math
+\begin{equation}
+\begin{aligned}
+\mathbf{S}^r &= \underbrace{\left(\prod_{i=1}^r \mathbf{I} - \beta^i \boldsymbol{k}^i \boldsymbol{k}^{i\top} \right)}_{:= \mathbf{P}^r} \cdot\mathbf{S}^{0} + \overbrace{\sum_{i=1}^{r} \underbrace{\left(\prod_{j=i+1}^r \mathbf{I} - \beta^j \boldsymbol{k}^j \boldsymbol{k}^{j\top} \right)}_{:= \mathbf{P}_{i+1}^r}\beta^i \boldsymbol{k}^i\boldsymbol{v}^{i\top}}^{:=\mathbf{H}^r} \\
+&=\mathbf{P}^r \cdot \mathbf{S}^{0} + \mathbf{H}^r
+\end{aligned}
+\end{equation}
+```
+
+where $\mathbf{P}_i^r$ involves cumulative products of generalized Householder matrices.
+We abbreviate $\mathbf{P}_1^r$ as $\mathbf{P}^r$.
+This can be optimized using the classical WY representation:
+```math
+\begin{equation}
+\mathbf{P}^{r} = \mathbf{I} - \sum_{i=1}^{r}\boldsymbol{k}^i\boldsymbol{w}^{i\top}  \in \mathbb{R}^{d_k \times d_k};\qquad
+\boldsymbol{w}^r = \beta^r \left(\boldsymbol{k}^r -  \sum_{i=1}^{r-1} \left(\boldsymbol{k}^{r\top}\boldsymbol{k}^i \right)\boldsymbol{w}^i  \right) \in \mathbb{R}^{d_k}
+\end{equation}
+```
+
+We prove this by induction:
+```math
+\begin{align*}
+\mathbf{P}^{r} &= \prod_{i=1}^r \mathbf{I} - \beta^i \boldsymbol{k}^i \boldsymbol{k}^{i\top} \\
+&= \left(\mathbf{I} - \beta^r \boldsymbol{k}^r \boldsymbol{k}^{r\top}\right)\mathbf{P}^{r-1} \\
+&= \left(\mathbf{I} - \beta^r \boldsymbol{k}^r \boldsymbol{k}^{r\top}\right)\left(\mathbf{I} - \sum_{i=1}^{r-1}\boldsymbol{k}^i\boldsymbol{w}^{i\top}\right) \\
+&= \mathbf{I} - \sum_{i=1}^{r-1}\boldsymbol{k}^i\boldsymbol{w}^{i\top} - \beta^r \boldsymbol{k}^r \boldsymbol{k}^{r\top} + \beta^r\boldsymbol{k}^r \boldsymbol{k}^{r\top} \left(\sum_{i=1}^{r-1}\boldsymbol{k}^i\boldsymbol{w}^{i\top}\right) \\
+&= \mathbf{I} - \sum_{i=1}^{r-1}\boldsymbol{k}^i\boldsymbol{w}^{i\top} - \beta^r \boldsymbol{k}^r \left(\boldsymbol{k}^{r} - \left(\sum_{i=1}^{r-1}\left(\boldsymbol{k}^{r\top} \boldsymbol{k}^i\right)\boldsymbol{w}^{i}\right) \right)^\top \\
+&= \mathbf{I} - \sum_{i=1}^{r}\boldsymbol{k}^i\boldsymbol{w}^{i\top}
+\end{align*}
+```
+
+Similarly, $\mathbf{H}^r$ can be represented as:
+```math
+\begin{equation}
+\mathbf{H}^{r} = \sum_{i=1}^{r} \boldsymbol{k}^i \boldsymbol{u}^{i\top}  \in \mathbb{R}^{d_k \times d_v};\qquad \boldsymbol{u}^r = \beta^r \left(\boldsymbol{v}^r -  \sum_{i=1}^{r-1} \left(\boldsymbol{k}^{r\top}\boldsymbol{k}^i\right) \boldsymbol{u}^i \right)\in \mathbb{R}^{d_v}
+\end{equation}
+```
+
+This can also be proven by induction:
+```math
+\begin{align*}
+\mathbf{H}^{r} &= \sum_{i=1}^{r} \mathbf{P}_{i+1}^r \beta^i \boldsymbol{k}^i \boldsymbol{v}^{i\top}\\
+&= \left(\mathbf{I} - \beta^r \boldsymbol{k}^r \boldsymbol{k}^{r\top}\right) \mathbf{H}^{r-1} +  \beta^r \boldsymbol{k}^r \boldsymbol{v}^{r\top}\\
+&= \sum_{i=1}^{r-1}\boldsymbol{k}^i \boldsymbol{u}^{i\top} - \beta^r \boldsymbol{k}^r \boldsymbol{k}^{r\top} \sum_{i=1}^{r-1}\boldsymbol{k}^i \boldsymbol{u}^{i\top} +\beta^r \boldsymbol{k}^r \boldsymbol{v}^{r\top}\\
+&= \sum_{i=1}^{r-1}\boldsymbol{k}^i \boldsymbol{u}^{i\top} + \boldsymbol{k}^r \left(\beta^r \boldsymbol{v}^{r\top}-\beta^r \boldsymbol{k}^{r\top} \sum_{i=1}^{r-1}\boldsymbol{k}^i \boldsymbol{u}^{i\top}\right) \\
+&= \sum_{i=1}^{r-1}\boldsymbol{k}^i \boldsymbol{u}^{i\top} + \boldsymbol{k}^r \beta^r\left(\boldsymbol{v}^{r}-\sum_{i=1}^{r-1}\left(\boldsymbol{k}^{r\top}\boldsymbol{k}^{i}\right)\boldsymbol{u}^{i} \right)^\top \\
+&=\sum_{i=1}^{r} \boldsymbol{k}^i \boldsymbol{u}^{i\top}
+\end{align*}
+```
+
+In matrix form, $\mathbf{P}$ and $\mathbf{H}$ can be written as:
+```math
+\begin{equation}
+\mathbf{P}=\mathbf{I}-\mathbf{K}^\top\mathbf{W} \in \mathbb{R}^{d_k \times d_k}, \qquad\mathbf{H}=\mathbf{K}^\top\mathbf{U} \in \mathbb{R}^{d_k\times d_v}
+\end{equation}
+```
+
+Now we can derive the matrix form of $\mathbf{W}$ and $\mathbf{U}$:
+```math
+\begin{align*}
+\mathbf{W} &= \mathrm{diag}(\beta) \mathbf{K} - \mathrm{tril}(\mathrm{diag}(\beta) \mathbf{K}\mathbf{K}^\top, -1)\mathbf{W}\\
+\left(\mathbf{I} + \mathrm{tril}(\mathrm{diag}(\beta) \mathbf{K}\mathbf{K}^\top, -1)\right) \mathbf{W} &= \mathrm{diag}(\beta) \mathbf{K}
+\end{align*}
+```
+A similar process holds for $\mathbf{U}$. We can further write $\mathbf{W}$ and $\mathbf{U}$ in matrix form:
+```math
+\begin{align*}
+\mathbf{T} &= \left(\mathbf{I} + \mathrm{tril}\left(\mathrm{diag}(\beta)\mathbf{K} \mathbf{K}^\top,-1\right)\right)^{-1}\mathrm{diag}\left(\beta\right)\in \mathbb{R}^{C \times C}\\
+\mathbf{W} &= \mathbf{T} \mathbf{K}\in \mathbb{R}^{C \times d_k}\\
+\mathbf{U} &= \mathbf{T}\mathbf{V}\in \mathbb{R}^{C \times d_v}
+\end{align*}
+```
+
+Substituting these back into the original equations yields a hardware-efficient chunkwise algorithm for DeltaNet that leverages matrix multiplications, enabling tensor core based GPU optimization:
+```math
+\begin{equation}
+\begin{aligned}
+\mathbf{S} &= \mathbf{P}\cdot\mathbf{S}^0 + \mathbf{H} \\
+&= \mathbf{S}^0 + \mathbf{K}^\top (\mathbf{U} -\mathbf{W} \mathbf{S}^0) \in \mathbb{R}^{d_k \times d_v}\\
+\mathbf{O} &= \mathbf{Q} \mathbf{S}^0 + (\mathbf{Q} \mathbf{K}^{\top} \odot \mathbf{M}) \left(\mathbf{U} - \mathbf{W} \mathbf{S}^0\right) \in \mathbb{R}^{C \times d_v}
+\end{aligned}
+\end{equation}
+```
+
+[^1]: https://arxiv.org/abs/2406.06484

fla/ops/delta_rule/chunk.py

@@ -0,0 +1,373 @@
+# -*- coding: utf-8 -*-
+# Copyright (c) 2023-2025, Songlin Yang, Yu Zhang
+
+from typing import Optional
+
+import torch
+import triton
+from einops import rearrange
+
+from fla.modules.l2norm import l2norm_bwd, l2norm_fwd
+from fla.ops.common.chunk_delta_h import chunk_gated_delta_rule_bwd_dhu, chunk_gated_delta_rule_fwd_h
+from fla.ops.common.chunk_o import chunk_bwd_dqkwg, chunk_bwd_dv_local, chunk_fwd_o
+from fla.ops.common.utils import prepare_chunk_indices
+from fla.ops.delta_rule.wy_fast import bwd_prepare_wy_repr, fwd_prepare_wy_repr, fwd_recompute_w_u
+from fla.utils import autocast_custom_bwd, autocast_custom_fwd, input_guard
+
+
+def chunk_delta_rule_fwd(
+    q: torch.Tensor,
+    k: torch.Tensor,
+    v: torch.Tensor,
+    beta: torch.Tensor,
+    scale: float,
+    initial_state: torch.Tensor,
+    output_final_state: bool,
+    offsets: Optional[torch.LongTensor] = None,
+    indices: Optional[torch.LongTensor] = None,
+    head_first: bool = True,
+    chunk_size: int = 64
+):
+    T = q.shape[2] if head_first else q.shape[1]
+    BT = min(chunk_size, max(triton.next_power_of_2(T), 16))
+    # obtain WY representation. u is actually the new v.
+    w, u, A = fwd_prepare_wy_repr(
+        k=k,
+        v=v,
+        beta=beta,
+        offsets=offsets,
+        indices=indices,
+        head_first=head_first,
+        chunk_size=BT
+    )
+
+    h, v_new, final_state = chunk_gated_delta_rule_fwd_h(
+        k=k,
+        w=w,
+        u=u,
+        g=None,
+        initial_state=initial_state,
+        output_final_state=output_final_state,
+        offsets=offsets,
+        indices=indices,
+        head_first=head_first,
+        chunk_size=BT
+    )
+    o = chunk_fwd_o(
+        q=q,
+        k=k,
+        v=v_new,
+        h=h,
+        g=None,
+        scale=scale,
+        offsets=offsets,
+        indices=indices,
+        head_first=head_first,
+        chunk_size=BT
+    )
+    return o, A, final_state
+
+
+def chunk_delta_rule_bwd(
+    q: torch.Tensor,
+    k: torch.Tensor,
+    v: torch.Tensor,
+    beta: torch.Tensor,
+    A: torch.Tensor,
+    scale: float,
+    initial_state: torch.Tensor,
+    do: torch.Tensor,
+    dht: torch.Tensor,
+    offsets: Optional[torch.LongTensor] = None,
+    indices: Optional[torch.LongTensor] = None,
+    head_first: bool = True,
+    chunk_size: int = 64
+):
+    T = q.shape[2] if head_first else q.shape[1]
+    BT = min(chunk_size, max(triton.next_power_of_2(T), 16))
+    w, u = fwd_recompute_w_u(
+        k=k,
+        v=v,
+        beta=beta,
+        A=A,
+        offsets=offsets,
+        indices=indices,
+        head_first=head_first,
+        chunk_size=BT
+    )
+    h, v_new, _ = chunk_gated_delta_rule_fwd_h(
+        k=k,
+        w=w,
+        u=u,
+        g=None,
+        initial_state=initial_state,
+        output_final_state=False,
+        offsets=offsets,
+        indices=indices,
+        head_first=head_first,
+        chunk_size=BT
+    )
+    dv = chunk_bwd_dv_local(
+        q=q,
+        k=k,
+        do=do,
+        g=None,
+        dh=None,
+        scale=scale,
+        offsets=offsets,
+        indices=indices,
+        head_first=head_first,
+        chunk_size=BT
+    )
+    dh, dh0, dv = chunk_gated_delta_rule_bwd_dhu(
+        q=q,
+        k=k,
+        w=w,
+        g=None,
+        h0=initial_state,
+        dht=dht,
+        do=do,
+        dv=dv,
+        scale=scale,
+        offsets=offsets,
+        indices=indices,
+        head_first=head_first,
+        chunk_size=BT
+    )
+    dq, dk, dw, _ = chunk_bwd_dqkwg(
+        q=q,
+        k=k,
+        v=v_new,
+        h=h,
+        w=w,
+        dv=dv,
+        do=do,
+        dh=dh,
+        g=None,
+        scale=scale,
+        offsets=offsets,
+        indices=indices,
+        head_first=head_first,
+        chunk_size=BT
+    )
+    dk2, dv, db = bwd_prepare_wy_repr(
+        k=k,
+        v=v,
+        beta=beta,
+        A=A,
+        dw=dw,
+        du=dv,
+        offsets=offsets,
+        indices=indices,
+        head_first=head_first,
+        chunk_size=BT
+    )
+    dk.add_(dk2)
+    return dq, dk, dv, db, dh0
+
+
+class ChunkDeltaRuleFunction(torch.autograd.Function):
+
+    @staticmethod
+    @input_guard
+    @autocast_custom_fwd
+    def forward(
+        ctx,
+        q: torch.Tensor,
+        k: torch.Tensor,
+        v: torch.Tensor,
+        beta: torch.Tensor,
+        scale: float,
+        initial_state: torch.Tensor,
+        output_final_state: bool,
+        offsets: Optional[torch.LongTensor] = None,
+        head_first: bool = True,
+        use_qk_l2norm_in_kernel: bool = True
+    ):
+        T = q.shape[2] if head_first else q.shape[1]
+        chunk_size = min(64, max(triton.next_power_of_2(T), 16))
+
+        q_orig = q
+        k_orig = k
+
+        if use_qk_l2norm_in_kernel:
+            q = l2norm_fwd(q)
+            k = l2norm_fwd(k)
+
+        # 2-d indices denoting the offsets of chunks in each sequence
+        # for example, if the passed `offsets` is [0, 100, 356] and `chunk_size` is 64,
+        # then there are 2 and 4 chunks in the 1st and 2nd sequences respectively, and `indices` will be
+        # [[0, 0], [0, 1], [1, 0], [1, 1], [1, 2], [1, 3]]
+        indices = prepare_chunk_indices(offsets, chunk_size) if offsets is not None else None
+
+        o, A, final_state = chunk_delta_rule_fwd(
+            q=q,
+            k=k,
+            v=v,
+            beta=beta,
+            scale=scale,
+            initial_state=initial_state,
+            output_final_state=output_final_state,
+            offsets=offsets,
+            indices=indices,
+            head_first=head_first,
+            chunk_size=chunk_size
+        )
+        ctx.save_for_backward(q_orig, k_orig, v, beta, A, initial_state)
+        ctx.chunk_size = chunk_size
+        ctx.scale = scale
+        ctx.offsets = offsets
+        ctx.indices = indices
+        ctx.head_first = head_first
+        ctx.use_qk_l2norm_in_kernel = use_qk_l2norm_in_kernel
+        return o.to(q.dtype), final_state
+
+    @staticmethod
+    @input_guard
+    @autocast_custom_bwd
+    def backward(
+        ctx,
+        do: torch.Tensor,
+        dht: torch.Tensor
+    ):
+        q, k, v, beta, A, initial_state = ctx.saved_tensors
+        use_qk_l2norm_in_kernel = ctx.use_qk_l2norm_in_kernel
+        if use_qk_l2norm_in_kernel:
+            q, q_orig = l2norm_fwd(q), q
+            k, k_orig = l2norm_fwd(k), k
+
+        dq, dk, dv, db, dh0 = chunk_delta_rule_bwd(
+            q=q,
+            k=k,
+            v=v,
+            beta=beta,
+            A=A,
+            scale=ctx.scale,
+            initial_state=initial_state,
+            do=do,
+            dht=dht,
+            offsets=ctx.offsets,
+            indices=ctx.indices,
+            head_first=ctx.head_first,
+            chunk_size=ctx.chunk_size
+        )
+        if use_qk_l2norm_in_kernel:
+            dq = l2norm_bwd(q_orig, dq)
+            dk = l2norm_bwd(k_orig, dk)
+        return dq.to(q.dtype), dk.to(k.dtype), dv.to(v.dtype), db.to(beta.dtype), None, dh0, None, None, None, None, None, None
+
+
+@torch.compiler.disable
+def chunk_delta_rule(
+    q: torch.Tensor,
+    k: torch.Tensor,
+    v: torch.Tensor,
+    beta: torch.Tensor,
+    scale: float = None,
+    initial_state: torch.Tensor = None,
+    output_final_state: bool = False,
+    cu_seqlens: Optional[torch.LongTensor] = None,
+    head_first: bool = False,
+    use_qk_l2norm_in_kernel: bool = False
+):
+    r"""
+    Args:
+        q (torch.Tensor):
+            queries of shape `[B, T, H, K]` if `head_first=False` else `[B, H, T, K]`.
+        k (torch.Tensor):
+            keys of shape `[B, T, H, K]` if `head_first=False` else `[B, H, T, K]`.
+        v (torch.Tensor):
+            values of shape `[B, T, H, V]` if `head_first=False` else `[B, H, T, V]`.
+        beta (torch.Tensor):
+            betas of shape `[B, T, H]` if `head_first=False` else `[B, H, T]`.
+        scale (Optional[int]):
+            Scale factor for the RetNet attention scores.
+            If not provided, it will default to `1 / sqrt(K)`. Default: `None`.
+        initial_state (Optional[torch.Tensor]):
+            Initial state of shape `[N, H, K, V]` for `N` input sequences.
+            For equal-length input sequences, `N` equals the batch size `B`.
+            Default: `None`.
+        output_final_state (Optional[bool]):
+            Whether to output the final state of shape `[N, H, K, V]`. Default: `False`.
+        cu_seqlens (torch.LongTensor):
+            Cumulative sequence lengths of shape `[N+1]` used for variable-length training,
+            consistent with the FlashAttention API.
+        head_first (Optional[bool]):
+            Whether the inputs are in the head-first format, which is not supported for variable-length inputs.
+            Default: `False`.
+        use_qk_l2norm_in_kernel (Optional[bool]):
+            Whether to use qk l2norm within the kernel for saving GPU memory.
+            Default: `False`.
+
+    Returns:
+        o (torch.Tensor):
+            Outputs of shape `[B, T, H, V]` if `head_first=False` else `[B, H, T, V]`.
+        final_state (torch.Tensor):
+            Final state of shape `[N, H, K, V]` if `output_final_state=True` else `None`.
+
+    Examples::
+        >>> import torch
+        >>> import torch.nn.functional as F
+        >>> from einops import rearrange
+        >>> from fla.ops.delta_rule import chunk_delta_rule
+        # inputs with equal lengths
+        >>> B, T, H, K, V = 4, 2048, 4, 512, 512
+        >>> q = torch.randn(B, T, H, K, dtype=torch.bfloat16, device='cuda')
+        >>> k = F.normalize(torch.randn(B, T, H, K, dtype=torch.bfloat16, device='cuda'), p=2, dim=-1)
+        >>> v = torch.randn(B, T, H, V, dtype=torch.bfloat16, device='cuda')
+        >>> beta = torch.rand(B, T, H, dtype=torch.bfloat16, device='cuda').sigmoid()
+        >>> h0 = torch.randn(B, H, K, V, dtype=torch.bfloat16, device='cuda')
+        >>> o, ht = chunk_delta_rule(
+            q, k, v, beta,
+            initial_state=h0,
+            output_final_state=True
+        )
+        # for variable-length inputs, the batch size `B` is expected to be 1 and `cu_seqlens` is required
+        >>> q, k, v, beta = map(lambda x: rearrange(x, 'b t ... -> 1 (b t) ...'), (q, k, v, beta))
+        # for a batch with 4 sequences, `cu_seqlens` with 5 start/end positions are expected
+        >>> cu_seqlens = q.new_tensor([0, 2048, 4096, 6144, 8192], dtype=torch.long)
+        >>> o_var, ht_var = chunk_delta_rule(
+            q, k, v, beta,
+            initial_state=h0,
+            output_final_state=True,
+            cu_seqlens=cu_seqlens
+        )
+    """
+    assert q.dtype == k.dtype == v.dtype
+    assert q.dtype != torch.float32, "ChunkDeltaRuleFunction does not support float32. Please use bfloat16."
+    assert len(beta.shape) == 3, "beta must be of shape (batch size, num of head, seq len)."
+
+    if cu_seqlens is not None:
+        if q.shape[0] != 1:
+            raise ValueError(
+                f"The batch size is expected to be 1 rather than {q.shape[0]} when using `cu_seqlens`."
+                f"Please flatten variable-length inputs before processing."
+            )
+        if head_first:
+            raise RuntimeError(
+                "Sequences with variable lengths are not supported for head-first mode"
+            )
+        if initial_state is not None and initial_state.shape[0] != len(cu_seqlens) - 1:
+            raise ValueError(
+                f"The number of initial states is expected to be equal to the number of input sequences, "
+                f"i.e., {len(cu_seqlens) - 1} rather than {initial_state.shape[0]}."
+            )
+    if head_first:
+        q, k, v = map(lambda x: rearrange(x, 'b h t d -> b t h d'), (q, k, v))
+        beta = rearrange(beta, 'b h t -> b t h')
+    scale = k.shape[-1] ** -0.5 if scale is None else scale
+    o, final_state = ChunkDeltaRuleFunction.apply(
+        q,
+        k,
+        v,
+        beta,
+        scale,
+        initial_state,
+        output_final_state,
+        cu_seqlens,
+        False,
+        use_qk_l2norm_in_kernel
+    )
+    if head_first:
+        o = rearrange(o, 'b t h v -> b h t v')
+    return o, final_state

fla/ops/delta_rule/fused_recurrent.py

@@ -0,0 +1,607 @@
+# -*- coding: utf-8 -*-
+# Copyright (c) 2023-2025, Songlin Yang, Yu Zhang
+
+from typing import Optional, Tuple
+
+import torch
+import triton
+import triton.language as tl
+from einops import rearrange
+
+from fla.modules.l2norm import l2norm_bwd, l2norm_fwd
+from fla.utils import input_guard
+
+
+@triton.heuristics({
+    'USE_INITIAL_STATE': lambda args: args['h0'] is not None,
+    'STORE_FINAL_STATE': lambda args: args['ht'] is not None,
+    'USE_OFFSETS': lambda args: args['offsets'] is not None
+})
+@triton.jit(do_not_specialize=['T'])
+def fused_recurrent_delta_rule_fwd_kernel(
+    q,
+    k,
+    v,
+    u,
+    beta,
+    o,
+    h0,
+    ht,
+    offsets,
+    scale,
+    T,
+    B: tl.constexpr,
+    H: tl.constexpr,
+    K: tl.constexpr,
+    V: tl.constexpr,
+    BK: tl.constexpr,
+    BV: tl.constexpr,
+    USE_INITIAL_STATE: tl.constexpr,
+    STORE_FINAL_STATE: tl.constexpr,
+    IS_BETA_HEADWISE: tl.constexpr,
+    USE_OFFSETS: tl.constexpr,
+    HEAD_FIRST: tl.constexpr
+):
+    i_v, i_k, i_nh = tl.program_id(0), tl.program_id(1), tl.program_id(2)
+    i_n, i_h = i_nh // H, i_nh % H
+    if USE_OFFSETS:
+        bos, eos = tl.load(offsets + i_n).to(tl.int64), tl.load(offsets + i_n + 1).to(tl.int64)
+        all = T
+        T = eos - bos
+    else:
+        bos, eos = i_n * T, i_n * T + T
+        all = B * T
+
+    if HEAD_FIRST:
+        p_q = q + i_nh * T*K + i_k * BK + tl.arange(0, BK)
+        p_k = k + i_nh * T*K + i_k * BK + tl.arange(0, BK)
+        p_v = v + i_nh * T*V + i_v * BV + tl.arange(0, BV)
+        p_u = u + i_nh * T*V + i_v * BV + tl.arange(0, BV)
+        if IS_BETA_HEADWISE:
+            p_beta = beta + i_nh * T*V + i_v * BV + tl.arange(0, BV)
+        else:
+            p_beta = beta + i_nh * T
+        p_o = o + (i_k * B*H + i_nh) * T*V + i_v * BV + tl.arange(0, BV)
+    else:
+        p_q = q + (bos * H + i_h) * K + i_k * BK + tl.arange(0, BK)
+        p_k = k + (bos * H + i_h) * K + i_k * BK + tl.arange(0, BK)
+        p_v = v + (bos * H + i_h) * V + i_v * BV + tl.arange(0, BV)
+        p_u = u + (bos * H + i_h) * V + i_v * BV + tl.arange(0, BV)
+        if IS_BETA_HEADWISE:
+            p_beta = beta + (bos * H + i_h) * V + i_v * BV + tl.arange(0, BV)
+        else:
+            p_beta = beta + bos * H + i_h
+        p_o = o + ((i_k * all + bos) * H + i_h) * V + i_v * BV + tl.arange(0, BV)
+
+    mask_k = (i_k * BK + tl.arange(0, BK)) < K
+    mask_v = (i_v * BV + tl.arange(0, BV)) < V
+    mask_h = mask_k[None, :] & mask_v[:, None]
+
+    b_h = tl.zeros([BV, BK], dtype=tl.float32)
+    if USE_INITIAL_STATE:
+        p_h0 = h0 + i_nh * K * V + (i_k * BK + tl.arange(0, BK)[None, :]) * V + (i_v * BV + tl.arange(0, BV)[:, None])
+        b_h += tl.load(p_h0, mask=mask_h, other=0).to(tl.float32)
+
+    for _ in range(0, T):
+        b_k = tl.load(p_k, mask=mask_k, other=0).to(tl.float32)
+        b_v = tl.load(p_v, mask=mask_v, other=0).to(tl.float32)
+        b_q = tl.load(p_q, mask=mask_k, other=0).to(tl.float32) * scale
+        b_v_minus = tl.sum(b_h * b_k[None, :], axis=1)
+        b_v -= b_v_minus
+        if IS_BETA_HEADWISE:
+            b_beta = tl.load(p_beta, mask=mask_v, other=0).to(tl.float32)
+        else:
+            b_beta = tl.load(p_beta).to(tl.float32)
+        tl.store(p_u, b_v.to(p_v.dtype.element_ty), mask=mask_v)
+        b_v *= b_beta
+        b_h += b_k[None, :] * b_v[:, None]
+        b_o = b_h * b_q[None, :]
+        b_o = tl.sum(b_o, axis=1)
+        tl.store(p_o, b_o.to(p_o.dtype.element_ty), mask=mask_v)
+
+        p_q += K if HEAD_FIRST else H*K
+        p_k += K if HEAD_FIRST else H*K
+        p_o += V if HEAD_FIRST else H*V
+        p_v += V if HEAD_FIRST else H*V
+        p_u += V if HEAD_FIRST else H*V
+        p_beta += (1 if HEAD_FIRST else H) * (V if IS_BETA_HEADWISE else 1)
+
+    if STORE_FINAL_STATE:
+        p_ht = ht + i_nh * K * V + (i_k * BK + tl.arange(0, BK)[None, :]) * V + (i_v * BV + tl.arange(0, BV)[:, None])
+        tl.store(p_ht, b_h.to(p_ht.dtype.element_ty), mask=mask_h)
+
+
+@triton.heuristics({
+    'USE_INITIAL_STATE': lambda args: args['h0'] is not None,
+    'USE_FINAL_STATE_GRADIENT': lambda args: args['dht'] is not None,
+    'USE_OFFSETS': lambda args: args['offsets'] is not None
+})
+@triton.jit(do_not_specialize=['T'])
+def fused_recurrent_delta_rule_bwd_kernel(
+    q,
+    k,
+    v,
+    beta,
+    h0,
+    dh0,
+    dht,
+    do,
+    dq,
+    dk,
+    dv,
+    db,
+    offsets,
+    scale,
+    B: tl.constexpr,
+    T,
+    H: tl.constexpr,
+    K: tl.constexpr,
+    V: tl.constexpr,
+    BK: tl.constexpr,
+    BV: tl.constexpr,
+    NK: tl.constexpr,
+    IS_BETA_HEADWISE: tl.constexpr,  # whether beta is headwise vector or scalar
+    USE_INITIAL_STATE: tl.constexpr,  # whether to use dh0
+    USE_FINAL_STATE_GRADIENT: tl.constexpr,  # whether to use dht
+    USE_OFFSETS: tl.constexpr,
+    HEAD_FIRST: tl.constexpr
+):
+    i_v, i_k, i_nh = tl.program_id(0), tl.program_id(1), tl.program_id(2)
+    i_n, i_h = i_nh // H, i_nh % H
+    if USE_OFFSETS:
+        bos, eos = tl.load(offsets + i_n).to(tl.int64), tl.load(offsets + i_n + 1).to(tl.int64)
+        all = T
+        T = eos - bos
+    else:
+        bos, eos = i_n * T, i_n * T + T
+        all = B * T
+
+    mask_k = i_k * BK + tl.arange(0, BK) < K
+    mask_v = i_v * BV + tl.arange(0, BV) < V
+
+    if HEAD_FIRST:
+        p_q = q + i_nh * T*K + i_k * BK + tl.arange(0, BK) + (T - 1) * K
+        p_k = k + i_nh * T*K + i_k * BK + tl.arange(0, BK) + (T - 1) * K
+        p_v = v + i_nh * T*V + i_v * BV + tl.arange(0, BV) + (T - 1) * V
+        p_do = do + i_nh * T*V + i_v * BV + tl.arange(0, BV) + (T - 1) * V
+        p_dk = dk + (i_v * B*H + i_nh) * T*K + i_k * BK + tl.arange(0, BK) + (T - 1) * K
+        p_dv = dv + (i_k * B*H + i_nh) * T*V + i_v * BV + tl.arange(0, BV) + (T - 1) * V
+        if IS_BETA_HEADWISE:
+            p_beta = beta + i_nh * T*V + i_v * BV + tl.arange(0, BV) + (T - 1) * V
+            p_dbeta = db + (i_v * NK*B*H + i_k * B*H + i_nh) * T*V + tl.arange(0, BV) + (T - 1) * V
+        else:
+            p_beta = beta + i_nh * T + T - 1
+            p_dbeta = db + (i_v * B*H + i_nh) * T + T - 1
+    else:
+        p_q = q + (bos * H + i_h) * K + i_k * BK + tl.arange(0, BK) + (T - 1) * H*K
+        p_k = k + (bos * H + i_h) * K + i_k * BK + tl.arange(0, BK) + (T - 1) * H*K
+        p_v = v + (bos * H + i_h) * V + i_v * BV + tl.arange(0, BV) + (T - 1) * H*V
+        p_do = do + (bos * H + i_h) * V + i_v * BV + tl.arange(0, BV) + (T - 1) * H*V
+        p_dk = dk + ((i_v * all + bos) * H + i_h) * K + i_k * BK + tl.arange(0, BK) + (T - 1) * H*K
+        p_dv = dv + ((i_k * all + bos) * H + i_h) * V + i_v * BV + tl.arange(0, BV) + (T - 1) * H*V
+        if IS_BETA_HEADWISE:
+            p_beta = beta + (bos + T - 1) * H*V + i_h * V + i_v * BV + tl.arange(0, BV)
+            p_dbeta = db + ((i_v * NK + i_k) * all + bos + T - 1) * H*V + i_h * V + tl.arange(0, BV)
+        else:
+            p_beta = beta + (bos + T - 1) * H + i_h
+            p_dbeta = db + (i_v * all + bos + T - 1) * H + i_h
+
+    b_dh = tl.zeros([BK, BV], dtype=tl.float32)
+    if USE_FINAL_STATE_GRADIENT:
+        p_ht = dht + i_nh * K * V + (i_k * BK + tl.arange(0, BK)[:, None]) * V + (i_v * BV + tl.arange(0, BV)[None, :])
+        b_dh += tl.load(p_ht, mask=mask_k[:, None] & mask_v[None, :], other=0).to(tl.float32)
+
+    for _ in range(T):
+        b_q = tl.load(p_q, mask=mask_k, other=0).to(tl.float32) * scale
+        b_k = tl.load(p_k, mask=mask_k, other=0).to(tl.float32)
+        b_v = tl.load(p_v, mask=mask_v, other=0).to(tl.float32)
+        b_do = tl.load(p_do, mask=mask_v, other=0).to(tl.float32)
+        if IS_BETA_HEADWISE:
+            b_beta = tl.load(p_beta, mask=mask_v, other=0).to(tl.float32)
+        else:
+            b_beta = tl.load(p_beta).to(tl.float32)
+        b_dh += b_q[:, None] * b_do[None, :]
+        b_dk = tl.sum(b_dh * (b_v * b_beta)[None, :], axis=1)
+        b_dv = tl.sum(b_dh * b_k[:, None], axis=0)
+
+        b_db = b_dv * b_v if IS_BETA_HEADWISE else tl.sum(b_dv * b_v)
+        b_dv = b_dv * b_beta
+
+        tl.store(p_dk, b_dk.to(p_dk.dtype.element_ty), mask=mask_k)
+        tl.store(p_dv, b_dv.to(p_dv.dtype.element_ty), mask=mask_v)
+        if IS_BETA_HEADWISE:
+            tl.store(p_dbeta, b_db.to(p_dbeta.dtype.element_ty), mask=mask_v)
+        else:
+            tl.store(p_dbeta, b_db.to(p_dbeta.dtype.element_ty))
+
+        b_dh -= b_k[:, None] * b_dv[None, :]
+
+        p_q -= K if HEAD_FIRST else H*K
+        p_k -= K if HEAD_FIRST else H*K
+        p_v -= V if HEAD_FIRST else H*V
+        p_do -= V if HEAD_FIRST else H*V
+        p_dk -= K if HEAD_FIRST else H*K
+        p_dv -= V if HEAD_FIRST else H*V
+        p_dbeta -= (1 if HEAD_FIRST else H) * (V if IS_BETA_HEADWISE else 1)
+        p_beta -= (1 if HEAD_FIRST else H) * (V if IS_BETA_HEADWISE else 1)
+
+    if USE_INITIAL_STATE:
+        p_dh0 = dh0 + i_nh * K * V + (i_k * BK + tl.arange(0, BK)[:, None]) * V + (i_v * BV + tl.arange(0, BV)[None, :])
+        tl.store(p_dh0, b_dh.to(p_dh0.dtype.element_ty), mask=mask_k[:, None] & mask_v[None, :])
+
+    tl.debug_barrier()
+
+    b_h = tl.zeros([BK, BV], dtype=tl.float32)
+
+    if HEAD_FIRST:
+        p_q = q + i_nh * T*K + i_k * BK + tl.arange(0, BK)
+        p_k = k + i_nh * T*K + i_k * BK + tl.arange(0, BK)
+        p_v = v + i_nh * T*V + i_v * BV + tl.arange(0, BV)
+        if IS_BETA_HEADWISE:
+            p_beta = beta + i_nh * T*V + i_v * BV + tl.arange(0, BV)
+        else:
+            p_beta = beta + i_nh * T
+        p_do = do + i_nh * T*V + i_v * BV + tl.arange(0, BV)
+        p_dq = dq + (i_v * B*H + i_nh) * T*K + i_k * BK + tl.arange(0, BK)
+        p_dk = dk + (i_v * B*H + i_nh) * T*K + i_k * BK + tl.arange(0, BK)
+        p_dv = dv + (i_k * B*H + i_nh) * T*V + i_v * BV + tl.arange(0, BV)
+    else:
+        p_q = q + (bos * H + i_h) * K + i_k * BK + tl.arange(0, BK)
+        p_k = k + (bos * H + i_h) * K + i_k * BK + tl.arange(0, BK)
+        p_v = v + (bos * H + i_h) * V + i_v * BV + tl.arange(0, BV)
+        if IS_BETA_HEADWISE:
+            p_beta = beta + (bos * H + i_h) * V + i_v * BV + tl.arange(0, BV)
+        else:
+            p_beta = beta + bos * H + i_h
+        p_do = do + (bos * H + i_h) * V + i_v * BV + tl.arange(0, BV)
+        p_dq = dq + ((i_v * all + bos) * H + i_h) * K + i_k * BK + tl.arange(0, BK)
+        p_dk = dk + ((i_v * all + bos) * H + i_h) * K + i_k * BK + tl.arange(0, BK)
+        p_dv = dv + ((i_k * all + bos) * H + i_h) * V + i_v * BV + tl.arange(0, BV)
+
+    if USE_INITIAL_STATE:
+        mask_h = mask_k[:, None] & mask_v[None, :]
+        p_h0 = h0 + i_nh * K * V + (i_k * BK + tl.arange(0, BK)[:, None]) * V + (i_v * BV + tl.arange(0, BV)[None, :])
+        b_h += tl.load(p_h0, mask=mask_h, other=0).to(tl.float32)
+
+    for _ in range(0, T):
+        b_dk = tl.load(p_dk, mask=mask_k, other=0).to(tl.float32)
+        b_dv = tl.load(p_dv, mask=mask_v, other=0).to(tl.float32)
+        b_dk -= tl.sum(b_dv[None, :] * b_h, axis=1)
+        tl.store(p_dk, b_dk.to(p_dk.dtype.element_ty), mask=mask_k)
+
+        b_k = tl.load(p_k, mask=mask_k, other=0).to(tl.float32)
+        b_v = tl.load(p_v, mask=mask_v, other=0).to(tl.float32)
+        b_do = tl.load(p_do, mask=mask_v, other=0).to(tl.float32)
+        if IS_BETA_HEADWISE:
+            b_beta = tl.load(p_beta, mask=mask_v, other=0).to(tl.float32)
+        else:
+            b_beta = tl.load(p_beta).to(tl.float32)
+        b_v *= b_beta
+
+        b_h += b_k[:, None] * b_v[None, :]
+        b_dq = b_h * b_do[None, :]
+        d_q = tl.sum(b_dq, axis=1) * scale
+        tl.store(p_dq, d_q.to(p_dq.dtype.element_ty), mask=mask_k)
+
+        p_k += K if HEAD_FIRST else H*K
+        p_v += V if HEAD_FIRST else H*V
+        p_do += V if HEAD_FIRST else H*V
+        p_dq += K if HEAD_FIRST else H*K
+        p_dk += K if HEAD_FIRST else H*K
+        p_dv += V if HEAD_FIRST else H*V
+        p_beta += (1 if HEAD_FIRST else H) * (V if IS_BETA_HEADWISE else 1)
+
+
+def fused_recurrent_delta_rule_fwd(
+    q: torch.Tensor,
+    k: torch.Tensor,
+    v: torch.Tensor,
+    beta: torch.Tensor,
+    scale: float,
+    initial_state: torch.Tensor,
+    output_final_state: bool,
+    offsets: Optional[torch.LongTensor] = None,
+    head_first: bool = True
+) -> Tuple[torch.Tensor, torch.Tensor]:
+    if head_first:
+        B, H, T, K, V = *k.shape, v.shape[-1]
+    else:
+        B, T, H, K, V = *k.shape, v.shape[-1]
+    N = B if offsets is None else len(offsets) - 1
+    BK, BV = triton.next_power_of_2(K), min(triton.next_power_of_2(V), 8)
+    NK, NV = triton.cdiv(K, BK), triton.cdiv(V, BV)
+    assert NK == 1, "NK > 1 is not supported yet"
+    num_stages = 1
+    num_warps = 1
+
+    o = q.new_empty(NK, *v.shape)
+    if output_final_state:
+        final_state = q.new_empty(N, H, K, V, dtype=torch.float32)
+    else:
+        final_state = None
+
+    grid = (NV, NK, N * H)
+    u = torch.empty_like(v)
+    fused_recurrent_delta_rule_fwd_kernel[grid](
+        q,
+        k,
+        v,
+        u,
+        beta,
+        o,
+        initial_state,
+        final_state,
+        offsets,
+        scale,
+        T=T,
+        B=B,
+        H=H,
+        K=K,
+        V=V,
+        BK=BK,
+        BV=BV,
+        IS_BETA_HEADWISE=beta.ndim == v.ndim,
+        HEAD_FIRST=head_first,
+        num_warps=num_warps,
+        num_stages=num_stages,
+    )
+    o = o.squeeze(0)
+    return o, u, final_state
+
+
+def fused_recurrent_delta_rule_bwd(
+    q: torch.Tensor,
+    k: torch.Tensor,
+    v: torch.Tensor,
+    beta: torch.Tensor,
+    dht: torch.Tensor,
+    do: torch.Tensor,
+    scale: float,
+    initial_state: torch.Tensor,
+    offsets: Optional[torch.LongTensor] = None,
+    head_first: bool = True
+) -> Tuple[torch.Tensor, torch.Tensor, torch.Tensor, torch.Tensor, torch.Tensor]:
+    if head_first:
+        B, H, T, K, V = *k.shape, v.shape[-1]
+    else:
+        B, T, H, K, V = *k.shape, v.shape[-1]
+    N = B if offsets is None else len(offsets) - 1
+    BK, BV = triton.next_power_of_2(K), min(triton.next_power_of_2(V), 32)
+    NK, NV = triton.cdiv(K, BK), triton.cdiv(V, BV)
+    assert NK == 1, "NK > 1 is not supported yet"
+    num_stages = 1
+    num_warps = 2
+
+    beta_vector = beta.ndim == v.ndim
+
+    dq = q.new_empty(NV, *q.shape)
+    dk = q.new_empty(NV, *k.shape)
+    dv = q.new_empty(NK, *v.shape)
+    if beta_vector:
+        db = q.new_empty(NV, NK, B, H, T, V) if head_first else q.new_empty(NV, NK, B, T, H, V)
+    else:
+        db = q.new_empty(NV, B, H, T) if head_first else q.new_empty(NV, B, T, H)
+    grid = (NV, NK, N * H)
+
+    if initial_state is not None and initial_state.requires_grad:
+        dh0 = torch.empty_like(initial_state, dtype=torch.float32)
+    else:
+        dh0 = None
+
+    fused_recurrent_delta_rule_bwd_kernel[grid](
+        q,
+        k,
+        v,
+        beta,
+        initial_state,
+        dh0,
+        dht,
+        do,
+        dq,
+        dk,
+        dv,
+        db,
+        offsets,
+        scale,
+        T=T,
+        B=B,
+        H=H,
+        K=K,
+        V=V,
+        BK=BK,
+        BV=BV,
+        NK=NK,
+        IS_BETA_HEADWISE=beta_vector,
+        HEAD_FIRST=head_first,
+        num_warps=num_warps,
+        num_stages=num_stages
+    )
+    dq = dq.sum(0)
+    dk = dk.sum(0)
+    dv = dv.sum(0)
+    db = db.sum((0, 1)) if beta_vector else db.sum(0)
+
+    return dq, dk, dv, db, dh0
+
+
+class FusedRecurrentFunction(torch.autograd.Function):
+
+    @staticmethod
+    @input_guard
+    def forward(
+        ctx,
+        q: torch.Tensor,
+        k: torch.Tensor,
+        v: torch.Tensor,
+        beta: torch.Tensor,
+        scale: float,
+        initial_state: torch.Tensor,
+        output_final_state: bool,
+        offsets: Optional[torch.LongTensor] = None,
+        head_first: bool = True,
+        use_qk_l2norm_in_kernel: bool = False
+    ):
+        q_orig = q
+        k_orig = k
+
+        if use_qk_l2norm_in_kernel:
+            q = l2norm_fwd(q)
+            k = l2norm_fwd(k)
+
+        o, u, final_state = fused_recurrent_delta_rule_fwd(
+            q=q,
+            k=k,
+            v=v,
+            beta=beta,
+            scale=scale,
+            initial_state=initial_state,
+            output_final_state=output_final_state,
+            offsets=offsets,
+            head_first=head_first
+        )
+
+        ctx.save_for_backward(q_orig, k_orig, u, beta, initial_state)
+        ctx.scale = scale
+        ctx.offsets = offsets
+        ctx.head_first = head_first
+        ctx.use_qk_l2norm_in_kernel = use_qk_l2norm_in_kernel
+        return o, final_state
+
+    @staticmethod
+    @input_guard
+    def backward(ctx, do, dht):
+        q, k, v, beta, initial_state = ctx.saved_tensors
+        if ctx.use_qk_l2norm_in_kernel:
+            q, q_orig = l2norm_fwd(q), q
+            k, k_orig = l2norm_fwd(k), k
+        dq, dk, dv, db, dh0 = fused_recurrent_delta_rule_bwd(
+            q=q,
+            k=k,
+            v=v,
+            beta=beta,
+            dht=dht,
+            do=do,
+            scale=ctx.scale,
+            initial_state=initial_state,
+            offsets=ctx.offsets,
+            head_first=ctx.head_first
+        )
+        if ctx.use_qk_l2norm_in_kernel:
+            dq, dk = l2norm_bwd(q_orig, dq), l2norm_bwd(k_orig, dk)
+        return dq.to(q), dk.to(k), dv.to(v), db.to(beta), None, dh0, None, None, None, None
+
+
+@torch.compiler.disable
+def fused_recurrent_delta_rule(
+    q: torch.Tensor,
+    k: torch.Tensor,
+    v: torch.Tensor,
+    beta: torch.Tensor = None,
+    scale: float = None,
+    initial_state: torch.Tensor = None,
+    output_final_state: bool = False,
+    cu_seqlens: Optional[torch.LongTensor] = None,
+    head_first: bool = True,
+    use_qk_l2norm_in_kernel: bool = False
+) -> Tuple[torch.Tensor, torch.Tensor]:
+    r"""
+    Args:
+        q (torch.Tensor):
+            queries of shape `[B, T, H, K]` if `head_first=False` else `[B, H, T, K]`.
+        k (torch.Tensor):
+            keys of shape `[B, T, H, K]` if `head_first=False` else `[B, H, T, K]`.
+        v (torch.Tensor):
+            values of shape `[B, T, H, V]` if `head_first=False` else `[B, H, T, V]`.
+        beta (torch.Tensor):
+             betas of shape `[B, T, H]` if `head_first=False` else `(B, H, T)`.
+        scale (Optional[int]):
+            Scale factor for the RetNet attention scores.
+            If not provided, it will default to `1 / sqrt(K)`. Default: `None`.
+        initial_state (Optional[torch.Tensor]):
+            Initial state of shape `[N, H, K, V]` for `N` input sequences.
+            For equal-length input sequences, `N` equals the batch size `B`.
+            Default: `None`.
+        output_final_state (Optional[bool]):
+            Whether to output the final state of shape `[N, H, K, V]`. Default: `False`.
+        cu_seqlens (torch.LongTensor):
+            Cumulative sequence lengths of shape `[N+1]` used for variable-length training,
+            consistent with the FlashAttention API.
+        head_first (Optional[bool]):
+            Whether the inputs are in the head-first format, which is not supported for variable-length inputs.
+            Default: `False`.
+
+    Returns:
+        o (torch.Tensor):
+            Outputs of shape `[B, T, H, V]` if `head_first=False` else `[B, H, T, V]`.
+        final_state (torch.Tensor):
+            Final state of shape `[N, H, K, V]` if `output_final_state=True` else `None`.
+
+    Examples::
+        >>> import torch
+        >>> import torch.nn.functional as F
+        >>> from einops import rearrange
+        >>> from fla.ops.delta_rule import fused_recurrent_delta_rule
+        # inputs with equal lengths
+        >>> B, T, H, K, V = 4, 2048, 4, 512, 512
+        >>> q = torch.randn(B, T, H, K, device='cuda')
+        >>> k = F.normalize(torch.randn(B, T, H, K, device='cuda'), p=2, dim=-1)
+        >>> v = torch.randn(B, T, H, V, device='cuda')
+        >>> beta = torch.rand(B, T, H, device='cuda').sigmoid()
+        >>> h0 = torch.randn(B, H, K, V, device='cuda')
+        >>> o, ht = fused_recurrent_delta_rule(
+            q, k, v, beta,
+            initial_state=h0,
+            output_final_state=True
+        )
+        # for variable-length inputs, the batch size `B` is expected to be 1 and `cu_seqlens` is required
+        >>> q, k, v, beta = map(lambda x: rearrange(x, 'b t ... -> 1 (b t) ...'), (q, k, v, beta))
+        # for a batch with 4 sequences, `cu_seqlens` with 5 start/end positions are expected
+        >>> cu_seqlens = q.new_tensor([0, 2048, 4096, 6144, 8192], dtype=torch.long)
+        >>> o_var, ht_var = fused_recurrent_delta_rule(
+            q, k, v, beta,
+            initial_state=h0,
+            output_final_state=True,
+            cu_seqlens=cu_seqlens
+        )
+        >>> assert o.allclose(o_var.view(o.shape))
+        >>> assert ht.allclose(ht_var)
+    """
+    if cu_seqlens is not None:
+        if q.shape[0] != 1:
+            raise ValueError(
+                f"The batch size is expected to be 1 rather than {q.shape[0]} when using `cu_seqlens`."
+                f"Please flatten variable-length inputs before processing."
+            )
+        if head_first:
+            raise RuntimeError(
+                "Sequences with variable lengths are not supported for head-first mode"
+            )
+        if initial_state is not None and initial_state.shape[0] != len(cu_seqlens) - 1:
+            raise ValueError(
+                f"The number of initial states is expected to be equal to the number of input sequences, "
+                f"i.e., {len(cu_seqlens) - 1} rather than {initial_state.shape[0]}."
+            )
+    if scale is None:
+        scale = k.shape[-1] ** -0.5
+    else:
+        assert scale > 0, "scale must be positive"
+    if beta is None:
+        beta = torch.ones_like(q[..., 0])
+    if head_first:
+        q, k, v = map(lambda x: rearrange(x, 'b h t d -> b t h d'), (q, k, v))
+        beta = rearrange(beta, 'b h t -> b t h')
+    o, final_state = FusedRecurrentFunction.apply(
+        q,
+        k,
+        v,
+        beta,
+        scale,
+        initial_state,
+        output_final_state,
+        cu_seqlens,
+        False,
+        use_qk_l2norm_in_kernel
+    )
+    if head_first:
+        o = rearrange(o, 'b t h v -> b h t v')
+    return o, final_state

fla/ops/forgetting_attn/__init__.py

@@ -0,0 +1,7 @@
+# -*- coding: utf-8 -*-
+
+from .parallel import parallel_forgetting_attn
+
+__all__ = [
+    'parallel_forgetting_attn'
+]

fla/ops/gated_delta_rule/chunk.py

@@ -0,0 +1,392 @@
+# -*- coding: utf-8 -*-
+# Copyright (c) 2023-2025, Songlin Yang, Yu Zhang
+
+from typing import Optional
+
+import torch
+import triton
+from einops import rearrange
+
+from fla.modules.l2norm import l2norm_bwd, l2norm_fwd
+from fla.ops.common.chunk_delta_h import chunk_gated_delta_rule_bwd_dhu, chunk_gated_delta_rule_fwd_h
+from fla.ops.common.chunk_o import chunk_bwd_dqkwg, chunk_bwd_dv_local, chunk_fwd_o
+from fla.ops.gated_delta_rule.wy_fast import bwd_prepare_wy_repr, fwd_prepare_wy_repr, fwd_recompute_w_u
+from fla.ops.utils import chunk_local_cumsum
+from fla.utils import autocast_custom_bwd, autocast_custom_fwd, input_guard
+
+
+def chunk_gated_delta_rule_fwd(
+    q: torch.Tensor,
+    k: torch.Tensor,
+    v: torch.Tensor,
+    g: torch.Tensor,
+    beta: torch.Tensor,
+    scale: float,
+    initial_state: torch.Tensor,
+    output_final_state: bool,
+    offsets: Optional[torch.LongTensor] = None,
+    indices: Optional[torch.LongTensor] = None,
+    head_first: bool = True,
+    chunk_size: int = 64
+):
+    g = chunk_local_cumsum(g, chunk_size, offsets=offsets, indices=indices, head_first=head_first)
+    # obtain WY representation. u is actually the new v.
+    w, u, Aw, Au = fwd_prepare_wy_repr(
+        k=k,
+        v=v,
+        beta=beta,
+        g=g,
+        offsets=offsets,
+        indices=indices,
+        head_first=head_first,
+        chunk_size=chunk_size
+    )
+
+    h, v_new, final_state = chunk_gated_delta_rule_fwd_h(
+        k=k,
+        w=w,
+        u=u,
+        g=g,
+        initial_state=initial_state,
+        output_final_state=output_final_state,
+        offsets=offsets,
+        indices=indices,
+        head_first=head_first,
+        chunk_size=chunk_size
+    )
+
+    # obtain output
+    o = chunk_fwd_o(
+        q=q,
+        k=k,
+        v=v_new,
+        h=h,
+        g=g,
+        scale=scale,
+        offsets=offsets,
+        indices=indices,
+        head_first=head_first,
+        chunk_size=chunk_size
+    )
+    return g, o, Aw, Au, final_state
+
+
+def chunk_gated_delta_rule_bwd(
+    q: torch.Tensor,
+    k: torch.Tensor,
+    v: torch.Tensor,
+    g: torch.Tensor,
+    beta: torch.Tensor,
+    Aw: torch.Tensor,
+    Au: torch.Tensor,
+    scale: float,
+    initial_state: torch.Tensor,
+    do: torch.Tensor,
+    dht: torch.Tensor,
+    offsets: Optional[torch.LongTensor] = None,
+    indices: Optional[torch.LongTensor] = None,
+    head_first: bool = True,
+    chunk_size: int = 64
+):
+    T = q.shape[2] if head_first else q.shape[1]
+    BT = min(chunk_size, max(triton.next_power_of_2(T), 16))
+    w, u = fwd_recompute_w_u(
+        k=k,
+        v=v,
+        beta=beta,
+        Aw=Aw,
+        Au=Au,
+        offsets=offsets,
+        indices=indices,
+        head_first=head_first,
+        chunk_size=BT
+    )
+    h, v_new, _ = chunk_gated_delta_rule_fwd_h(
+        k=k,
+        w=w,
+        u=u,
+        g=g,
+        initial_state=initial_state,
+        output_final_state=False,
+        offsets=offsets,
+        indices=indices,
+        head_first=head_first,
+        chunk_size=BT
+    )
+    dv = chunk_bwd_dv_local(
+        q=q,
+        k=k,
+        g=g,
+        do=do,
+        dh=None,
+        scale=scale,
+        offsets=offsets,
+        indices=indices,
+        head_first=head_first,
+        chunk_size=BT
+    )
+    dh, dh0, dv = chunk_gated_delta_rule_bwd_dhu(
+        q=q,
+        k=k,
+        w=w,
+        g=g,
+        h0=initial_state,
+        dht=dht,
+        do=do,
+        dv=dv,
+        scale=scale,
+        offsets=offsets,
+        indices=indices,
+        head_first=head_first,
+        chunk_size=BT
+    )
+    dq, dk, dw, dg = chunk_bwd_dqkwg(
+        q=q,
+        k=k,
+        v=v_new,
+        w=w,
+        g=g,
+        h=h,
+        dv=dv,
+        do=do,
+        dh=dh,
+        scale=scale,
+        offsets=offsets,
+        indices=indices,
+        head_first=head_first,
+        chunk_size=BT
+    )
+    dk2, dv, db, dg2 = bwd_prepare_wy_repr(
+        k=k,
+        v=v,
+        beta=beta,
+        g=g,
+        Aw=Aw,
+        Au=Au,
+        dw=dw,
+        du=dv,
+        offsets=offsets,
+        indices=indices,
+        head_first=head_first,
+        chunk_size=BT
+    )
+    dk.add_(dk2)
+    dg.add_(dg2)
+    assert dg.dtype == torch.float32, "dg should be fp32"
+    dg = chunk_local_cumsum(dg, chunk_size, reverse=True, offsets=offsets, indices=indices, head_first=head_first)
+    return dq, dk, dv, db, dg, dh0
+
+
+class ChunkGatedDeltaRuleFunction(torch.autograd.Function):
+
+    @staticmethod
+    @input_guard
+    @autocast_custom_fwd
+    def forward(
+        ctx,
+        q: torch.Tensor,
+        k: torch.Tensor,
+        v: torch.Tensor,
+        g: torch.Tensor,
+        beta: torch.Tensor,
+        scale: float,
+        initial_state: torch.Tensor,
+        output_final_state: bool,
+        offsets: Optional[torch.LongTensor] = None,
+        head_first: bool = True,
+        use_qk_l2norm_in_kernel: bool = False
+    ):
+        chunk_size = 64
+        q_orig = q
+        k_orig = k
+
+        if use_qk_l2norm_in_kernel:
+            q = l2norm_fwd(q)
+            k = l2norm_fwd(k)
+
+        # 2-d indices denoting the offsets of chunks in each sequence
+        # for example, if the passed `offsets` is [0, 100, 356] and `chunk_size` is 64,
+        # then there are 2 and 4 chunks in the 1st and 2nd sequences respectively, and `indices` will be
+        # [[0, 0], [0, 1], [1, 0], [1, 1], [1, 2], [1, 3]]
+        indices = None
+        if offsets is not None:
+            indices = torch.cat([torch.arange(n) for n in triton.cdiv(offsets[1:] - offsets[:-1], chunk_size).tolist()])
+            indices = torch.stack([indices.eq(0).cumsum(0) - 1, indices], 1).to(offsets)
+
+        g, o, Aw, Au, final_state = chunk_gated_delta_rule_fwd(
+            q=q,
+            k=k,
+            v=v,
+            g=g,
+            beta=beta,
+            scale=scale,
+            initial_state=initial_state,
+            output_final_state=output_final_state,
+            offsets=offsets,
+            indices=indices,
+            head_first=head_first,
+            chunk_size=chunk_size,
+        )
+        ctx.save_for_backward(q_orig, k_orig, v, g, beta, Aw, Au, initial_state, offsets, indices)
+        ctx.chunk_size = chunk_size
+        ctx.scale = scale
+        ctx.head_first = head_first
+        ctx.use_qk_l2norm_in_kernel = use_qk_l2norm_in_kernel
+        return o.to(q.dtype), final_state
+
+    @staticmethod
+    @input_guard
+    @autocast_custom_bwd
+    def backward(
+        ctx,
+        do: torch.Tensor,
+        dht: torch.Tensor
+    ):
+        q, k, v, g, beta, Aw, Au, initial_state, offsets, indices = ctx.saved_tensors
+        if ctx.use_qk_l2norm_in_kernel:
+            q, q_orig = l2norm_fwd(q), q
+            k, k_orig = l2norm_fwd(k), k
+        dq, dk, dv, db, dg, dh0 = chunk_gated_delta_rule_bwd(
+            q=q,
+            k=k,
+            v=v,
+            g=g,
+            beta=beta,
+            Aw=Aw,
+            Au=Au,
+            scale=ctx.scale,
+            initial_state=initial_state,
+            do=do,
+            dht=dht,
+            offsets=offsets,
+            indices=indices,
+            head_first=ctx.head_first,
+            chunk_size=ctx.chunk_size
+        )
+        if ctx.use_qk_l2norm_in_kernel:
+            dq = l2norm_bwd(q_orig, dq)
+            dk = l2norm_bwd(k_orig, dk)
+        return dq.to(q), dk.to(k), dv.to(v), dg.to(g), db.to(beta), None, dh0, None, None, None, None
+
+
+@torch.compiler.disable
+def chunk_gated_delta_rule(
+    q: torch.Tensor,
+    k: torch.Tensor,
+    v: torch.Tensor,
+    g: torch.Tensor,
+    beta: torch.Tensor,
+    scale: float = None,
+    initial_state: torch.Tensor = None,
+    output_final_state: bool = False,
+    cu_seqlens: Optional[torch.LongTensor] = None,
+    head_first: bool = False,
+    use_qk_l2norm_in_kernel: bool = False
+):
+    r"""
+    Args:
+        q (torch.Tensor):
+            queries of shape `[B, T, H, K]` if `head_first=False` else `[B, H, T, K]`.
+        k (torch.Tensor):
+            keys of shape `[B, T, H, K]` if `head_first=False` else `[B, H, T, K]`.
+        v (torch.Tensor):
+            values of shape `[B, T, H, V]` if `head_first=False` else `[B, H, T, V]`.
+        g (torch.Tensor):
+            (forget) gating tensor (in log space!) of shape `[B, T, H]` if `head_first=False` else `[B, H, T]`.
+        beta (torch.Tensor):
+            betas of shape `[B, T, H]` if `head_first=False` else `[B, H, T]`.
+        scale (Optional[int]):
+            Scale factor for the RetNet attention scores.
+            If not provided, it will default to `1 / sqrt(K)`. Default: `None`.
+        initial_state (Optional[torch.Tensor]):
+            Initial state of shape `[N, H, K, V]` for `N` input sequences.
+            For equal-length input sequences, `N` equals the batch size `B`.
+            Default: `None`.
+        output_final_state (Optional[bool]):
+            Whether to output the final state of shape `[N, H, K, V]`. Default: `False`.
+        cu_seqlens (torch.LongTensor):
+            Cumulative sequence lengths of shape `[N+1]` used for variable-length training,
+            consistent with the FlashAttention API.
+        head_first (Optional[bool]):
+            Whether the inputs are in the head-first format, which is not supported for variable-length inputs.
+            Default: `False`.
+
+    Returns:
+        o (torch.Tensor):
+            Outputs of shape `[B, T, H, V]` if `head_first=False` else `[B, H, T, V]`.
+        final_state (torch.Tensor):
+            Final state of shape `[N, H, K, V]` if `output_final_state=True` else `None`.
+
+    Examples::
+        >>> import torch
+        >>> import torch.nn.functional as F
+        >>> from einops import rearrange
+        >>> from fla.ops.gated_delta_rule import chunk_gated_delta_rule
+        # inputs with equal lengths
+        >>> B, T, H, K, V = 4, 2048, 4, 512, 512
+        >>> q = torch.randn(B, T, H, K, dtype=torch.bfloat16, device='cuda')
+        >>> k = F.normalize(torch.randn(B, T, H, K, dtype=torch.bfloat16, device='cuda'), p=2, dim=-1)
+        >>> v = torch.randn(B, T, H, V, dtype=torch.bfloat16, device='cuda')
+        >>> beta = torch.rand(B, T, H, dtype=torch.bfloat16, device='cuda').sigmoid()
+        >>> g = F.logsigmoid(torch.rand(B, T, H, dtype=torch.bfloat16, device='cuda'))
+        >>> h0 = torch.randn(B, H, K, V, dtype=torch.bfloat16, device='cuda')
+        >>> o, ht = chunk_gated_delta_rule(
+            q, k, v, g, beta,
+            initial_state=h0,
+            output_final_state=True,
+            head_first=False
+        )
+        # for variable-length inputs, the batch size `B` is expected to be 1 and `cu_seqlens` is required
+        >>> q, k, v, beta, g = map(lambda x: rearrange(x, 'b t ... -> 1 (b t) ...'), (q, k, v, beta, g))
+        # for a batch with 4 sequences, `cu_seqlens` with 5 start/end positions are expected
+        >>> cu_seqlens = q.new_tensor([0, 2048, 4096, 6144, 8192], dtype=torch.long)
+        >>> o_var, ht_var = chunk_gated_delta_rule(
+            q, k, v, g, beta,
+            initial_state=h0,
+            output_final_state=True,
+            cu_seqlens=cu_seqlens,
+            head_first=False
+        )
+    """
+    assert q.dtype == k.dtype == v.dtype
+    assert q.dtype != torch.float32, "ChunkGatedDeltaRuleFunction does not support float32. Please use bfloat16."
+    assert len(beta.shape) == 3, "beta must be of shape [B, H, T] if head_first=True, or [B, T, H] if head_first=False."
+
+    if cu_seqlens is not None:
+        if q.shape[0] != 1:
+            raise ValueError(
+                f"The batch size is expected to be 1 rather than {q.shape[0]} when using `cu_seqlens`."
+                f"Please flatten variable-length inputs before processing."
+            )
+        if head_first:
+            raise RuntimeError(
+                "Sequences with variable lengths are not supported for head-first mode"
+            )
+        if initial_state is not None and initial_state.shape[0] != len(cu_seqlens) - 1:
+            raise ValueError(
+                f"The number of initial states is expected to be equal to the number of input sequences, "
+                f"i.e., {len(cu_seqlens) - 1} rather than {initial_state.shape[0]}."
+            )
+    if head_first:
+        q, k, v = map(lambda x: rearrange(x, 'b h t d -> b t h d'), (q, k, v))
+        beta, g = map(lambda x: rearrange(x, 'b h t -> b t h'), (beta, g))
+    if scale is None:
+        scale = k.shape[-1] ** -0.5
+    else:
+        assert scale > 0, "Scale must be positive."
+    o, final_state = ChunkGatedDeltaRuleFunction.apply(
+        q,
+        k,
+        v,
+        g,
+        beta,
+        scale,
+        initial_state,
+        output_final_state,
+        cu_seqlens,
+        False,
+        use_qk_l2norm_in_kernel
+    )
+    if head_first:
+        o = rearrange(o, 'b t h v -> b h t v')
+    return o, final_state

fla/ops/generalized_delta_rule/README.md

@@ -0,0 +1,37 @@
+# Generalized Delta Rule
+
+In delta rule we have the recurrence:
+
+```math
+\mathbf{S}_t = \mathbf{S}_{t-1}(\mathbf{I}-\beta_t \mathbf{k}_t\mathbf{k}_t^T) + \beta_t \mathbf{v}_t\mathbf{k}_t^T
+```
+
+This repository implements a delta rule variant where $\mathbf{I}$ is not necessarily an identity matrix; $\mathbf{k}_t$ in $\mathbf{I} - \beta_t \mathbf{k}_t\mathbf{k}_t^T$ might be different from input $\mathbf{k}_t$ in $\mathbf{v}_t\mathbf{k}_t^T$.
+
+## IPLR (Identity Plus Low Rank)
+
+The first variant is IPLR, where we have:
+
+```math
+\mathbf{S}_t = \mathbf{S}_{t-1}(\mathbf{I}+\mathbf{a}_t\mathbf{b}_t^T) + \mathbf{v}_t\mathbf{k}_t^T
+```
+
+When $\mathbf{a}_t = -\beta_t \mathbf{k}_t$, $\mathbf{b}_t = \mathbf{k}_t$, $\mathbf{v}_t= \beta_t \mathbf{v}_t$, we recover the original delta rule. Since here the transition matrix is identity-plus-low-rank, we refer to this variant as IPLR.
+
+### Numerical Stability
+
+$\mathbf{a}_t$ and $\mathbf{b}_t$ must be in opposite directions, that is, $\mathbf{b}_t = \lambda_t \mathbf{a}_t$ where $\lambda_t < 0$. For an understanding of why this is necessary, you can derive the eigenvalues of the transition matrix.
+
+## DPLR (Diagonal Plus Low Rank)
+
+The second variant is DPLR, where we have:
+
+```math
+\mathbf{S}_t = \mathbf{S}_{t-1}(\mathbf{D}_t+\mathbf{a}_t\mathbf{b}_t^T) + \mathbf{v}_t\mathbf{k}_t^T
+```
+
+Here, $\mathbf{I}$ is replaced by a diagonal matrix $\mathbf{D}_t$. This transition matrix structure has been utilized in RWKV7.
+
+## Efficient Chunkwise Implementation
+
+For detailed information about efficient chunkwise implementation, please refer to our [technical note](https://drive.google.com/file/d/1rJbO3dU4fe7OKG3w7Yg058z_BNIuavNF/view?usp=sharing).

fla/ops/generalized_delta_rule/__init__.py

@@ -0,0 +1,9 @@
+from .dplr import chunk_dplr_delta_rule, fused_recurrent_dplr_delta_rule
+from .iplr import chunk_iplr_delta_rule, fused_recurrent_iplr_delta_rule
+
+__all__ = [
+    'chunk_dplr_delta_rule',
+    'fused_recurrent_dplr_delta_rule',
+    'chunk_iplr_delta_rule',
+    'fused_recurrent_iplr_delta_rule'
+]

fla/ops/generalized_delta_rule/dplr/naive.py

@@ -0,0 +1,96 @@
+# -*- coding: utf-8 -*-
+
+import torch
+from einops import rearrange
+
+# S_t = S_t @ (I + alpha_t beta_t^T) + v_t k_t^T
+# q, k, alpha, beta [B, H, L, D_K]
+# v [B, H, L, D_V]
+
+
+def dplr_recurrence(q, k, v, alpha, beta, gk, initial_state=None, output_final_state=True):
+    orig_dtype = q.dtype
+    b, h, l, d_k = q.shape
+    q, k, v, beta, gk = map(lambda x: x.float(), [q, k, v, beta, gk])
+    d_v = v.shape[-1]
+    o = torch.zeros_like(v)
+    S = torch.zeros(b, h, d_k, d_v).to(v)
+    q = q * (d_k ** -0.5)
+
+    if initial_state is not None:
+        S += initial_state
+
+    for i in range(l):
+        _k = k[:, :, i]
+        _q = q[:, :, i]
+        _v = v[:, :, i]
+        _alpha = alpha[:, :, i].clone()
+        _beta = beta[:, :, i].clone()
+        _kv = _k[..., None] * _v[..., None, :] + (S.clone() * _alpha[..., None]).sum(-2, keepdim=True) * _beta[..., None]
+        S = S.clone() * gk[:, :, i].exp()[..., None] + _kv
+        o[:, :, i] = torch.einsum('bhd,bhdm->bhm', _q, S)
+    S = None if output_final_state is False else S
+    return o.to(orig_dtype), S
+
+
+def dplr_chunkwise(q, k, v, alpha, beta, gk, initial_state=None, output_final_state=True, chunk_size=32):
+    b, h, l, d_k = q.shape
+    d_v = v.shape[-1]
+    q = q * (d_k ** -0.5)
+    v = v
+    assert l % chunk_size == 0
+
+    S = k.new_zeros(b, h, d_k, d_v).to(q)
+    if initial_state is not None:
+        S += initial_state
+
+    # note that diagonal is masked.
+    mask = torch.triu(torch.ones(chunk_size, chunk_size, dtype=torch.bool, device=q.device), diagonal=0)
+    q, k, v, alpha, beta, gk = map(lambda x: rearrange(x, 'b h (n c) d -> b h n c d',
+                                   c=chunk_size).float(), [q, k, v, alpha, beta, gk])
+
+    gk_cumsum = gk.cumsum(-2)
+
+    # v2 = (alpha @ k.transpose(-1, -2)).masked_fill_(mask, 0) @ v
+    A_ab = torch.zeros(b, h, l // chunk_size, chunk_size, chunk_size).to(q.device)
+    A_qk = torch.zeros(b, h, l // chunk_size, chunk_size, chunk_size).to(q.device)
+    A_ak = torch.zeros(b, h, l // chunk_size, chunk_size, chunk_size).to(q.device)
+    A_qb = torch.zeros(b, h, l // chunk_size, chunk_size, chunk_size).to(q.device)
+
+    for i in range(chunk_size):
+        alpha_i = alpha[:, :, :, i, None]
+        q_i = q[:, :, :, i, None]
+        gk_i = gk_cumsum[:, :, :, i, None]
+        mask = (torch.arange(chunk_size) <= i).to(q.device)
+        attn_i = (gk_i - gk_cumsum).masked_fill(~mask.unsqueeze(-1), float('-inf')).exp()
+        A_qk[:, :, :, i, :] = (q_i * k * attn_i).sum(-1).clone()
+        A_qb[:, :, :, i, :] = (q_i * beta * attn_i).sum(-1).clone()
+        mask = (torch.arange(chunk_size) < i).to(q.device)
+        # shift by one.
+        attn_i = (gk_i - gk[:, :, :, i, None] - gk_cumsum).masked_fill(~mask.unsqueeze(-1), float('-inf')).exp()
+        A_ab[:, :, :, i, :] = (alpha_i * beta * attn_i).sum(-1).clone()
+        A_ak[:, :, :, i, :] = (alpha_i * k * attn_i).sum(-1).clone()
+
+    A_ab = A_ab
+    for i in range(1, chunk_size):
+        A_ab[..., i, :i] = A_ab[..., i, :i].clone() + (A_ab[..., i, :, None].clone() * A_ab[..., :, :i].clone()).sum(-2)
+
+    A_ab = A_ab + torch.eye(chunk_size, dtype=torch.float, device=q.device)
+    u = A_ab @ (A_ak @ v)
+    w = A_ab @ ((gk_cumsum-gk).exp() * alpha)
+
+    o = torch.zeros_like(v)
+    mask = torch.triu(torch.ones(chunk_size, chunk_size, dtype=torch.bool, device=q.device), diagonal=1)
+    for i in range(0, l // chunk_size):
+        q_i, k_i, v_i, u_i, w_i, beta_i = q[:, :, i], k[:, :, i], v[:, :, i], u[:, :, i], w[:, :, i], beta[:, :, i]
+        v2_i = u_i + w_i @ S
+
+        o_1 = A_qk[:, :, i] @ v_i
+        o_2 = A_qb[:, :, i] @ v2_i
+        o_3 = (q_i * gk_cumsum[:, :, i].exp()) @ S
+        o[:, :, i] = o_1 + o_2 + o_3
+        decay = (gk_cumsum[:, :, i, -1, None] - gk_cumsum[:, :, i]).exp()
+        S = S*gk_cumsum[:, :, i, -1, :, None].exp() + (k_i * decay).transpose(-1, -2) @ v_i + \
+            (beta_i * decay).transpose(-1, -2) @ v2_i
+    S = None if output_final_state is False else S
+    return rearrange(o, 'b h n c d -> b h (n c) d'), S

fla/ops/generalized_delta_rule/dplr/wy_fast_bwd.py

@@ -0,0 +1,184 @@
+# -*- coding: utf-8 -*-
+# Copyright (c) 2023-2025, Songlin Yang, Yu Zhang
+
+from typing import Optional, Tuple
+
+import torch
+import triton
+import triton.language as tl
+
+from fla.utils import check_shared_mem, is_intel_alchemist, use_cuda_graph
+
+# https://github.com/intel/intel-xpu-backend-for-triton/issues/3449
+triton_config = {'grf_mode': 'large'} if is_intel_alchemist else {}
+
+
+@triton.heuristics({
+    'USE_OFFSETS': lambda args: args['offsets'] is not None
+})
+@triton.autotune(
+    configs=[
+        triton.Config(triton_config, num_warps=num_warps, num_stages=num_stages)
+        for num_warps in [2, 4, 8, 16, 32]
+        for num_stages in [2, 3, 4]
+    ],
+    key=['BT', 'BK', 'BV'],
+    use_cuda_graph=use_cuda_graph,
+)
+@triton.jit(do_not_specialize=['T'])
+def bwd_prepare_wy_repr_kernel(
+    A_ab_inv,
+    A_ak,
+    ag,
+    v,
+    dw,
+    du,
+    dv,
+    dv0,
+    dag,
+    dAak,
+    dAab,
+    offsets,
+    indices,
+    T,
+    H: tl.constexpr,
+    K: tl.constexpr,
+    V: tl.constexpr,
+    BT: tl.constexpr,
+    BK: tl.constexpr,
+    BV: tl.constexpr,
+    USE_OFFSETS: tl.constexpr,
+    HEAD_FIRST: tl.constexpr
+):
+    i_t, i_bh = tl.program_id(0), tl.program_id(1)
+    i_b, i_h = i_bh // H, i_bh % H
+    if USE_OFFSETS:
+        i_n, i_t = tl.load(indices + i_t * 2).to(tl.int32), tl.load(indices + i_t * 2 + 1).to(tl.int32)
+        bos, eos = tl.load(offsets + i_n).to(tl.int32), tl.load(offsets + i_n + 1).to(tl.int32)
+        T = eos - bos
+    else:
+        bos, eos = i_b * T, i_b * T + T
+
+    if HEAD_FIRST:
+        p_Aab_inv_t = tl.make_block_ptr(A_ab_inv + i_bh * T * BT, (BT, T), (1, BT), (0, i_t * BT), (BT, BT), (0, 1))
+        p_Aak_t = tl.make_block_ptr(A_ak + i_bh * T * BT, (BT, T), (1, BT), (0, i_t * BT), (BT, BT), (0, 1))
+        p_dAak = tl.make_block_ptr(dAak + i_bh * T * BT, (T, BT), (BT, 1), (i_t * BT, 0), (BT, BT), (1, 0))
+        p_dAab = tl.make_block_ptr(dAab + i_bh * T * BT, (T, BT), (BT, 1), (i_t * BT, 0), (BT, BT), (1, 0))
+    else:
+        p_Aak_t = tl.make_block_ptr(A_ak + (bos*H + i_h) * BT,  (BT, T), (1, H*BT), (0, i_t * BT), (BT, BT), (0, 1))
+        p_Aab_inv_t = tl.make_block_ptr(A_ab_inv + (bos*H + i_h) * BT, (BT, T), (1, H*BT), (0, i_t * BT), (BT, BT), (0, 1))
+        p_dAak = tl.make_block_ptr(dAak + (bos*H + i_h) * BT, (T, BT), (H*BT, 1), (i_t * BT, 0), (BT, BT), (1, 0))
+        p_dAab = tl.make_block_ptr(dAab + (bos*H + i_h) * BT, (T, BT), (H*BT, 1), (i_t * BT, 0), (BT, BT), (1, 0))
+
+    b_A_ab_inv_t = tl.load(p_Aab_inv_t, boundary_check=(0, 1))
+    b_A_ak_t = tl.load(p_Aak_t, boundary_check=(0, 1))
+    b_A_ak_t = tl.where(tl.arange(0, BT)[:, None] < tl.arange(0, BT)[None, :], b_A_ak_t, 0)
+    b_A_ab_inv_t = tl.where(tl.arange(0, BT)[:, None] <= tl.arange(0, BT)[None, :], b_A_ab_inv_t, 0)
+    b_A_tmp_t = tl.dot(b_A_ak_t, b_A_ab_inv_t).to(v.dtype.element_ty)
+    b_dA_tmp = tl.zeros([BT, BT], dtype=tl.float32)
+
+    for i_v in range(tl.cdiv(V, BV)):
+        if HEAD_FIRST:
+            p_v = tl.make_block_ptr(v + i_bh * T*V, (T, V), (V, 1), (i_t * BT, i_v * BV), (BT, BV), (1, 0))
+            p_dv = tl.make_block_ptr(dv + i_bh * T*V, (T, V), (V, 1), (i_t * BT, i_v * BV), (BT, BV), (1, 0))
+            p_dv0 = tl.make_block_ptr(dv0 + i_bh * T*V, (T, V), (V, 1), (i_t * BT, i_v * BV), (BT, BV), (1, 0))
+            p_du = tl.make_block_ptr(du + i_bh * T*V, (T, V), (V, 1), (i_t * BT, i_v * BV), (BT, BV), (1, 0))
+        else:
+            p_v = tl.make_block_ptr(v + (bos*H + i_h) * V, (T, V), (H*V, 1), (i_t * BT, i_v * BV), (BT, BV), (1, 0))
+            p_dv = tl.make_block_ptr(dv + (bos*H + i_h) * V, (T, V), (H*V, 1), (i_t * BT, i_v * BV), (BT, BV), (1, 0))
+            p_dv0 = tl.make_block_ptr(dv0 + (bos*H + i_h) * V, (T, V), (H*V, 1), (i_t * BT, i_v * BV), (BT, BV), (1, 0))
+            p_du = tl.make_block_ptr(du + (bos*H + i_h) * V, (T, V), (H*V, 1), (i_t * BT, i_v * BV), (BT, BV), (1, 0))
+        b_v = tl.load(p_v, boundary_check=(0, 1))
+        b_du = tl.load(p_du, boundary_check=(0, 1))
+        b_dA_tmp += tl.dot(b_du.to(b_v.dtype), tl.trans(b_v))
+        b_dv0 = tl.load(p_dv0, boundary_check=(0, 1))
+        b_dv = b_dv0 + tl.dot(b_A_tmp_t, b_du)
+        tl.store(p_dv, b_dv.to(p_dv.dtype.element_ty), boundary_check=(0, 1))
+
+    b_dA_tmp = tl.where(tl.arange(0, BT)[:, None] > tl.arange(0, BT)[None, :], b_dA_tmp, 0)
+    b_dA_ak = tl.dot(b_A_ab_inv_t, b_dA_tmp)
+    b_dA_ak = tl.where(tl.arange(0, BT)[:, None] > tl.arange(0, BT)[None, :], b_dA_ak, 0)
+    tl.store(p_dAak, b_dA_ak, boundary_check=(0, 1))
+    b_dA_ab_inv = tl.dot(b_dA_tmp, b_A_ak_t)
+
+    for i_k in range(tl.cdiv(K, BK)):
+        if HEAD_FIRST:
+            p_ag = tl.make_block_ptr(ag + i_bh * T*K, (T, K), (K, 1), (i_t * BT, i_k * BK), (BT, BK), (1, 0))
+            p_dag = tl.make_block_ptr(dag + i_bh * T*K, (T, K), (K, 1), (i_t * BT, i_k * BK), (BT, BK), (1, 0))
+            p_dw = tl.make_block_ptr(dw + i_bh * T*K, (T, K), (K, 1), (i_t * BT, i_k * BK), (BT, BK), (1, 0))
+        else:
+            p_ag = tl.make_block_ptr(ag + (bos * H + i_h) * K, (T, K), (H*K, 1), (i_t * BT, i_k * BK), (BT, BK), (1, 0))
+            p_dag = tl.make_block_ptr(dag + (bos * H + i_h) * K, (T, K), (H*K, 1), (i_t * BT, i_k * BK), (BT, BK), (1, 0))
+            p_dw = tl.make_block_ptr(dw + (bos * H + i_h) * K, (T, K), (H*K, 1), (i_t * BT, i_k * BK), (BT, BK), (1, 0))
+        b_ag = tl.load(p_ag, boundary_check=(0, 1))
+        b_dw = tl.load(p_dw, boundary_check=(0, 1))
+        b_dA_ab_inv += tl.dot(b_dw, tl.trans(b_ag))
+        b_dag = tl.dot(b_A_ab_inv_t.to(b_dw.dtype), b_dw)
+        tl.store(p_dag, b_dag.to(p_dag.dtype.element_ty), boundary_check=(0, 1))
+
+    # if we know dL/dA^(-1), for dL/dA, we can use the following formula:
+    # dL/dA = -(A^(-1))^T @ (dL/dA^(-1)) @ (A^(-1))^T
+    # in the fwd pass we use fwd substitution to calculate (I-lower(A_ab))^-1.
+    # denote A = I - lower(A_ab), B = A^-1
+    # in the backward pass.
+    # dL/dA = -(B)^T @ (dL/dB) @ B^T
+    # dL/dA_ab = lower(B^T @ dL/dB @ B^T)
+    b_dA_ab_inv = tl.where(tl.arange(0, BT)[:, None] >= tl.arange(0, BT)[None, :], b_dA_ab_inv, 0)
+    b_dA_ab_inv = tl.dot(b_A_ab_inv_t, b_dA_ab_inv)
+    b_dA_ab_inv = tl.dot(b_dA_ab_inv, b_A_ab_inv_t)
+    b_dA_ab_inv = tl.where(tl.arange(0, BT)[:, None] > tl.arange(0, BT)[None, :], b_dA_ab_inv, 0)
+    tl.store(p_dAab, b_dA_ab_inv, boundary_check=(0, 1))
+
+
+def chunk_dplr_bwd_wy(
+    A_ab_inv: torch.Tensor,
+    A_ak: torch.Tensor,
+    v: torch.Tensor,
+    ag: torch.Tensor,
+    dw: torch.Tensor,
+    du: torch.Tensor,
+    dv0: torch.Tensor,
+    offsets: Optional[torch.LongTensor],
+    indices: Optional[torch.LongTensor],
+    head_first: bool,
+    chunk_size: int,
+) -> Tuple[torch.Tensor, torch.Tensor, torch.Tensor]:
+    A_ab_inv, A_ak, v, ag, dw, du = map(lambda x: x.contiguous(), [A_ab_inv, A_ak, v, ag, dw, du])
+    if head_first:
+        B, H, T, K, V = *dw.shape, du.shape[-1]
+    else:
+        B, T, H, K, V = *dw.shape, du.shape[-1]
+    BT = min(chunk_size, max(triton.next_power_of_2(T), 16))
+    NT = triton.cdiv(T, BT) if offsets is None else len(indices)
+    BK = min(triton.next_power_of_2(K), 64)
+    BV = min(triton.next_power_of_2(V), 64) if check_shared_mem() else min(triton.next_power_of_2(V), 32)
+
+    dA_ab = torch.empty_like(A_ab_inv, dtype=torch.float)
+    dA_ak = torch.empty_like(A_ak, dtype=torch.float)
+    dv = torch.empty_like(v)
+    dag = torch.empty_like(ag)
+
+    bwd_prepare_wy_repr_kernel[(NT, B * H)](
+        A_ab_inv=A_ab_inv,
+        A_ak=A_ak,
+        ag=ag,
+        v=v,
+        dw=dw,
+        du=du,
+        dv=dv,
+        dv0=dv0,
+        dag=dag,
+        dAak=dA_ak,
+        dAab=dA_ab,
+        offsets=offsets,
+        indices=indices,
+        T=T,
+        H=H,
+        K=K,
+        V=V,
+        BT=BT,
+        BK=BK,
+        BV=BV,
+        HEAD_FIRST=head_first
+    )
+    return dA_ab, dA_ak, dv, dag

fla/ops/gla/fused_recurrent.py

@@ -0,0 +1,113 @@
+# -*- coding: utf-8 -*-
+# Copyright (c) 2024, Songlin Yang, Yu Zhang
+
+from typing import Optional, Tuple
+
+import torch
+
+from fla.ops.common.fused_recurrent import fused_recurrent
+
+
+def fused_recurrent_gla(
+    q: torch.Tensor,
+    k: torch.Tensor,
+    v: torch.Tensor,
+    gk: Optional[torch.Tensor] = None,
+    gv: Optional[torch.Tensor] = None,
+    scale: Optional[int] = None,
+    initial_state: Optional[torch.Tensor] = None,
+    output_final_state: bool = False,
+    reverse: bool = False,
+    cu_seqlens: Optional[torch.LongTensor] = None,
+    head_first: bool = True
+) -> Tuple[torch.Tensor, torch.Tensor]:
+    r"""
+    Args:
+        q (torch.Tensor):
+            queries of shape `[B, H, T, K]` if `head_first=True` else `[B, T, H, K]`.
+        k (torch.Tensor):
+            keys of shape `[B, H, T, K]` if `head_first=True` else `[B, T, H, K]`.
+        v (torch.Tensor):
+            values of shape `[B, H, T, V]` if `head_first=True` else `[B, T, H, V]`.
+        gk (torch.Tensor):
+            Forget gates of shape `[B, H, T, K]` if `head_first=True` else `[B, T, H, K]` applied to keys.
+        gv (torch.Tensor):
+            Forget gates of shape `[B, H, T, V]` if `head_first=True` else `[B, T, H, V]` applied to values.
+        scale (Optional[int]):
+            Scale factor for the attention scores.
+            If not provided, it will default to `1 / sqrt(K)`. Default: `None`.
+        initial_state (Optional[torch.Tensor]):
+            Initial state of shape `[N, H, K, V]` for `N` input sequences.
+            For equal-length input sequences, `N` equals the batch size `B`.
+            Default: `None`.
+        output_final_state (Optional[bool]):
+            Whether to output the final state of shape `[N, H, K, V]`. Default: `False`.
+        reverse (Optional[bool]):
+            If `True`, process the state passing in reverse order. Default: `False`.
+        cu_seqlens (torch.LongTensor):
+            Cumulative sequence lengths of shape `[N+1]` used for variable-length training,
+            consistent with the FlashAttention API.
+        head_first (Optional[bool]):
+            Whether the inputs are in the head-first format, which is not supported for variable-length inputs.
+            Default: `True`.
+
+    Returns:
+        o (torch.Tensor):
+            Outputs of shape `[B, H, T, V]` if `head_first=True` else `[B, T, H, V]`.
+        final_state (torch.Tensor):
+            Final state of shape `[N, H, K, V]` if `output_final_state=True` else `None`.
+
+    Examples::
+        >>> import torch
+        >>> import torch.nn.functional as F
+        >>> from einops import rearrange
+        >>> from fla.ops.gla import fused_recurrent_gla
+        # inputs with equal lengths
+        >>> B, T, H, K, V = 4, 2048, 4, 512, 512
+        >>> q = torch.randn(B, T, H, K, device='cuda')
+        >>> k = torch.randn(B, T, H, K, device='cuda')
+        >>> v = torch.randn(B, T, H, V, device='cuda')
+        >>> g = F.logsigmoid(torch.randn(B, T, H, K, device='cuda'))
+        >>> h0 = torch.randn(B, H, K, V, device='cuda')
+        >>> o, ht = fused_recurrent_gla(q, k, v, g,
+                                        initial_state=h0,
+                                        output_final_state=True,
+                                        head_first=False)
+        # for variable-length inputs, the batch size `B` is expected to be 1 and `cu_seqlens` is required
+        >>> q, k, v, g = map(lambda x: rearrange(x, 'b t h d -> 1 (b t) h d'), (q, k, v, g))
+        # for a batch with 4 sequences, `cu_seqlens` with 5 start/end positions are expected
+        >>> cu_seqlens = q.new_tensor([0, 2048, 4096, 6144, 8192], dtype=torch.long)
+        >>> o_var, ht_var = fused_recurrent_gla(q, k, v, g,
+                                                initial_state=h0,
+                                                output_final_state=True,
+                                                cu_seqlens=cu_seqlens,
+                                                head_first=False)
+        >>> assert o.allclose(o_var.view(o.shape))
+        >>> assert ht.allclose(ht_var)
+    """
+    if cu_seqlens is not None:
+        if q.shape[0] != 1:
+            raise ValueError(f"The batch size is expected to be 1 rather than {q.shape[0]} when using `cu_seqlens`."
+                             f"Please flatten variable-length inputs before processing.")
+        if head_first:
+            raise RuntimeError("Sequences with variable lengths are not supported for head-first mode")
+        if initial_state is not None and initial_state.shape[0] != len(cu_seqlens) - 1:
+            raise ValueError(f"The number of initial states is expected to be equal to the number of input sequences, "
+                             f"i.e., {len(cu_seqlens) - 1} rather than {initial_state.shape[0]}.")
+    if scale is None:
+        scale = k.shape[-1] ** -0.5
+    o, final_state = fused_recurrent(
+        q=q,
+        k=k,
+        v=v,
+        g=None,
+        gk=gk,
+        gv=gv,
+        scale=scale,
+        initial_state=initial_state,
+        output_final_state=output_final_state,
+        reverse=reverse,
+        cu_seqlens=cu_seqlens,
+        head_first=head_first
+    )
+    return o, final_state