Daily Papers

Transformer model with multi-head attention requires caching intermediate results for efficient inference in generation tasks. However, cache brings new memory-related costs and prevents leveraging larger batch size for faster speed. We propose memory-efficient lossless attention (called EL-attention) to address this issue. It avoids heavy operations for building multi-head keys and values, cache for them is not needed. EL-attention constructs an ensemble of attention results by expanding query while keeping key and value shared. It produces the same result as multi-head attention with less GPU memory and faster inference speed. We conduct extensive experiments on Transformer, BART, and GPT-2 for summarization and question generation tasks. The results show EL-attention speeds up existing models by 1.6x to 5.3x without accuracy loss.

Adam is the go-to optimizer for training modern machine learning models, but it requires additional memory to maintain the moving averages of the gradients and their squares. While various low-memory optimizers have been proposed that sometimes match the performance of Adam, their lack of reliability has left Adam as the default choice. In this work, we apply a simple layer-wise Signal-to-Noise Ratio (SNR) analysis to quantify when second-moment tensors can be effectively replaced by their means across different dimensions. Our SNR analysis reveals how architecture, training hyperparameters, and dataset properties impact compressibility along Adam's trajectory, naturally leading to SlimAdam, a memory-efficient Adam variant. SlimAdam compresses the second moments along dimensions with high SNR when feasible, and leaves when compression would be detrimental. Through experiments across a diverse set of architectures and training scenarios, we show that SlimAdam matches Adam's performance and stability while saving up to 98% of total second moments. Code for SlimAdam is available at https://github.com/dayal-kalra/low-memory-adam.

We explore reinforcement learning (RL) techniques to enhance reasoning within targeted problem spaces in large language models (LLMs) under memory and compute constraints. Our focus is on critic-free methods compatible with LoRA fine-tuning on a single 40GB GPU, a common limitation in academic settings. We introduce S-GRPO, a memory-efficient variant of Group Relative Policy Optimization, and T-SPMO, a token-level prefix matching strategy for fine-grained credit assignment. Despite limited resources, when used to fine-tune Qwen2-1.5B both methods significantly improve SVAMP benchmark accuracy from 46% to above 70% using LoRA training. T-SPMO also excels in multi-digit multiplication tasks, underscoring the potential of RL fine-tuning under hardware constraints. Additionally, we find that our full-token GRPO baseline under LoRA fine-tuning did not improve model performance (compared to base model) on either task, suggesting that our memory-efficient methods may act as a form of regularization that stabilizes training when only a small subset of parameters are updated.

Transformers consist of diverse building blocks, such as embedding layers, normalization layers, self-attention mechanisms, and point-wise feedforward networks. Thus, understanding the differences and interactions among these blocks is important. In this paper, we uncover a clear Sharpness Disparity across these blocks, which emerges early in training and intriguingly persists throughout the training process. Motivated by this finding, we propose Blockwise Learning Rate (LR), a strategy that tailors the LR to each block's sharpness, accelerating large language model (LLM) pre-training. By integrating Blockwise LR into AdamW, we consistently achieve lower terminal loss and nearly 2times speedup compared to vanilla AdamW. We demonstrate this acceleration across GPT-2 and LLaMA, with model sizes ranging from 0.12B to 1.1B and datasets of OpenWebText and MiniPile. Finally, we incorporate Blockwise LR into Adam-mini (Zhang et al., 2024), a recently proposed memory-efficient variant of Adam, achieving a combined 2times speedup and 2times memory saving. These results underscore the potential of exploiting the sharpness disparity to improve LLM training.

Interactive digital agents (IDAs) leverage APIs of stateful digital environments to perform tasks in response to user requests. While IDAs powered by instruction-tuned large language models (LLMs) can react to feedback from interface invocations in multi-step exchanges, they have not been trained in their respective digital environments. Prior methods accomplish less than half of tasks in sophisticated benchmarks such as AppWorld. We present a reinforcement learning (RL) approach that trains IDAs directly in their target environments. We formalize this training as a partially observable Markov decision process and derive LOOP, a data- and memory-efficient variant of proximal policy optimization. LOOP uses no value network and maintains exactly one copy of the underlying LLM in memory, making its implementation straightforward and as memory-efficient as fine-tuning a single LLM. A 32-billion-parameter agent trained with LOOP in the AppWorld environment outperforms the much larger OpenAI o1 agent by 9 percentage points (15% relative). To our knowledge, this is the first reported application of RL to IDAs that interact with a stateful, multi-domain, multi-app environment via direct API calls. Our analysis sheds light on the effectiveness of RL in this area, showing that the agent learns to consult the API documentation, avoid unwarranted assumptions, minimize confabulation, and recover from setbacks.

Training LLMs presents significant memory challenges due to growing size of data, weights, and optimizer states. Techniques such as data and model parallelism, gradient checkpointing, and offloading strategies address this issue but are often infeasible due to hardware constraints. To mitigate memory usage, alternative methods like Parameter-Efficient-Fine-Tuning (PEFT) and GaLore approximate weights or optimizer states. PEFT methods, such as LoRA, have gained popularity for fine-tuning LLMs, though they require a full-rank warm start. In contrast, GaLore allows full-parameter learning while being more memory-efficient. This work introduces Natural GaLore, a simple drop in replacement for AdamW, which efficiently applies the inverse Empirical Fisher Information Matrix to low-rank gradients using Woodbury's Identity. We demonstrate that incorporating second-order information speeds up optimization significantly, especially when the iteration budget is limited. Empirical pretraining on 60M, 130M, 350M, and 1.1B parameter Llama models on C4 data demonstrate significantly lower perplexity over GaLore without additional memory overhead. By fine-tuning RoBERTa on the GLUE benchmark using Natural GaLore, we demonstrate significant reduction in gap 86.05% vs 86.28% for full-finetuning. Furthermore, fine-tuning the TinyLlama 1.1B model for function calling using the TinyAgent framework shows that Natural GaLore achieving 83.09% accuracy on the TinyAgent dataset, significantly outperforms 16-bit LoRA at 80.06% and even surpasses GPT4-Turbo by 4%, all while using 30% less memory. All code to reproduce the results are available at: https://github.com/selfsupervised-ai/Natural-GaLore.git

Auto-regressive inference of transformers benefit greatly from Key-Value (KV) caching, but can lead to major memory bottlenecks as model size, batch size, and sequence length grow at scale. We introduce Multi-Layer Key-Value (MLKV) sharing, a novel approach extending KV sharing across transformer layers to reduce memory usage beyond what was possible with Multi-Query Attention (MQA) and Grouped-Query Attention (GQA). Evaluations on various NLP benchmarks and inference metrics using uptrained Pythia-160M variants demonstrate that MLKV significantly reduces memory usage with minimal performance loss, reducing KV cache size down to a factor of 6x compared to MQA. These results highlight MLKV's potential for efficient deployment of transformer models at scale. We provide code at https://github.com/zaydzuhri/pythia-mlkv

Parameter-efficient fine-tuning (PEFT) of pre-trained language models (PLMs) has emerged as a highly successful approach, with training only a small number of parameters without sacrificing performance and becoming the de-facto learning paradigm with the increasing size of PLMs. However, existing PEFT methods are not memory-efficient, because they still require caching most of the intermediate activations for the gradient calculation, akin to fine-tuning. One effective way to reduce the activation memory is to apply a reversible model, so the intermediate activations are not necessary to be cached and can be recomputed. Nevertheless, modifying a PLM to its reversible variant is not straightforward, since the reversible model has a distinct architecture from the currently released PLMs. In this paper, we first investigate what is a key factor for the success of existing PEFT methods, and realize that it's essential to preserve the PLM's starting point when initializing a PEFT method. With this finding, we propose memory-efficient fine-tuning (MEFT) that inserts adapters into a PLM, preserving the PLM's starting point and making it reversible without additional pre-training. We evaluate MEFT on the GLUE benchmark and five question-answering tasks with various backbones, BERT, RoBERTa, BART and OPT. MEFT significantly reduces the activation memory up to 84% of full fine-tuning with a negligible amount of trainable parameters. Moreover, MEFT achieves the same score on GLUE and a comparable score on the question-answering tasks as full fine-tuning. A similar finding is also observed for the image classification task.

We present BlockBERT, a lightweight and efficient BERT model for better modeling long-distance dependencies. Our model extends BERT by introducing sparse block structures into the attention matrix to reduce both memory consumption and training/inference time, which also enables attention heads to capture either short- or long-range contextual information. We conduct experiments on language model pre-training and several benchmark question answering datasets with various paragraph lengths. BlockBERT uses 18.7-36.1% less memory and 12.0-25.1% less time to learn the model. During testing, BlockBERT saves 27.8% inference time, while having comparable and sometimes better prediction accuracy, compared to an advanced BERT-based model, RoBERTa.

Spiking Neural Networks (SNNs) are promising energy-efficient models for neuromorphic computing. For training the non-differentiable SNN models, the backpropagation through time (BPTT) with surrogate gradients (SG) method has achieved high performance. However, this method suffers from considerable memory cost and training time during training. In this paper, we propose the Spatial Learning Through Time (SLTT) method that can achieve high performance while greatly improving training efficiency compared with BPTT. First, we show that the backpropagation of SNNs through the temporal domain contributes just a little to the final calculated gradients. Thus, we propose to ignore the unimportant routes in the computational graph during backpropagation. The proposed method reduces the number of scalar multiplications and achieves a small memory occupation that is independent of the total time steps. Furthermore, we propose a variant of SLTT, called SLTT-K, that allows backpropagation only at K time steps, then the required number of scalar multiplications is further reduced and is independent of the total time steps. Experiments on both static and neuromorphic datasets demonstrate superior training efficiency and performance of our SLTT. In particular, our method achieves state-of-the-art accuracy on ImageNet, while the memory cost and training time are reduced by more than 70% and 50%, respectively, compared with BPTT.

Visual Auto-Regressive (VAR) models significantly reduce inference steps through the "next-scale" prediction paradigm. However, progressive multi-scale generation incurs substantial memory overhead due to cumulative KV caching, limiting practical deployment. We observe a scale-depth asymmetric dependency in VAR: early scales exhibit extreme sensitivity to network depth, while later scales remain robust to depth reduction. Inspired by this, we propose VARiant: by equidistant sampling, we select multiple subnets ranging from 16 to 2 layers from the original 30-layer VAR-d30 network. Early scales are processed by the full network, while later scales utilize subnet. Subnet and the full network share weights, enabling flexible depth adjustment within a single model. However, weight sharing between subnet and the entire network can lead to optimization conflicts. To address this, we propose a progressive training strategy that breaks through the Pareto frontier of generation quality for both subnets and the full network under fixed-ratio training, achieving joint optimality. Experiments on ImageNet demonstrate that, compared to the pretrained VAR-d30 (FID 1.95), VARiant-d16 and VARiant-d8 achieve nearly equivalent quality (FID 2.05/2.12) while reducing memory consumption by 40-65%. VARiant-d2 achieves 3.5 times speedup and 80% memory reduction at moderate quality cost (FID 2.97). In terms of deployment, VARiant's single-model architecture supports zero-cost runtime depth switching and provides flexible deployment options from high quality to extreme efficiency, catering to diverse application scenarios.

Low-Rank Adaptation (LoRA) has gained popularity for fine-tuning large foundation models, leveraging low-rank matrices A and B to represent weight changes (i.e., Delta W = B A). This method reduces trainable parameters and mitigates heavy memory consumption associated with full delta matrices by sequentially multiplying A and B with the activation. Despite its success, the intrinsic low-rank characteristic may limit its performance. Although several variants have been proposed to address this issue, they often overlook the crucial computational and memory efficiency brought by LoRA. In this paper, we propose Circular Convolution Adaptation (C^3A), which not only achieves high-rank adaptation with enhanced performance but also excels in both computational power and memory utilization. Extensive experiments demonstrate that C^3A consistently outperforms LoRA and its variants across various fine-tuning tasks.

Multi-headed Attention's (MHA) quadratic compute and linearly growing KV-cache make long-context transformers expensive to train and serve. Prior works such as Grouped Query Attention (GQA) and Multi-Latent Attention (MLA) shrink the cache, speeding decode, but leave compute, which determines prefill and training speed, largely unchanged. We introduce Compressed Convolutional Attention (CCA), a novel attention method which down-projects queries, keys, and values and performs the entire attention operation inside the shared latent space. This simple design dramatically cuts parameters, KV-cache, and FLOPs all at once by the desired compression factor. Because CCA is orthogonal to head-sharing, we combine the two to form Compressed Convolutional Grouped Query Attention (CCGQA), which further tightens the compute-bandwidth Pareto frontier so that users can tune compression toward either FLOP or memory limits without sacrificing quality. Experiments show that CCGQA consistently outperforms both GQA and MLA at equal KV-cache compression on dense and MoE models. Additionally, we show that CCGQA outperforms all other attention methods on MoE models with half the KV-cache of GQA and MLA, achieving an 8x KV-cache compression with no drop in performance compared to standard MHA. CCA and CCGQA also dramatically reduce the FLOP cost of attention which leads to substantially faster training and prefill than existing methods. On H100 GPUs, our fused CCA/CCGQA kernel reduces prefill latency by about 1.7x at a sequence length of 16k relative to MHA, and accelerates backward by about 1.3x.

While transformers and their variant conformers show promising performance in speech recognition, the parameterized property leads to much memory cost during training and inference. Some works use cross-layer weight-sharing to reduce the parameters of the model. However, the inevitable loss of capacity harms the model performance. To address this issue, this paper proposes a parameter-efficient conformer via sharing sparsely-gated experts. Specifically, we use sparsely-gated mixture-of-experts (MoE) to extend the capacity of a conformer block without increasing computation. Then, the parameters of the grouped conformer blocks are shared so that the number of parameters is reduced. Next, to ensure the shared blocks with the flexibility of adapting representations at different levels, we design the MoE routers and normalization individually. Moreover, we use knowledge distillation to further improve the performance. Experimental results show that the proposed model achieves competitive performance with 1/3 of the parameters of the encoder, compared with the full-parameter model.

A recent trend in explainable AI research has focused on surrogate modeling, where neural networks are approximated as simpler ML algorithms such as kernel machines. A second trend has been to utilize kernel functions in various explain-by-example or data attribution tasks. In this work, we combine these two trends to analyze approximate empirical neural tangent kernels (eNTK) for data attribution. Approximation is critical for eNTK analysis due to the high computational cost to compute the eNTK. We define new approximate eNTK and perform novel analysis on how well the resulting kernel machine surrogate models correlate with the underlying neural network. We introduce two new random projection variants of approximate eNTK which allow users to tune the time and memory complexity of their calculation. We conclude that kernel machines using approximate neural tangent kernel as the kernel function are effective surrogate models, with the introduced trace NTK the most consistent performer. Open source software allowing users to efficiently calculate kernel functions in the PyTorch framework is available (https://github.com/pnnl/projection\_ntk).

Low-Rank Adaptation (LoRA) and its variants have shown impressive results in reducing the number of trainable parameters and memory requirements of large transformer networks while maintaining fine-tuning performance. However, the low-rank nature of the weight update inherently limits the representation power of fine-tuned models, potentially compromising performance on complex tasks. This raises a critical question: when a performance gap between LoRA and standard fine-tuning is observed, is it due to the reduced number of trainable parameters or the rank deficiency? This paper aims to answer this question by introducing RandLoRA, a parameter-efficient method that performs full-rank updates using a learned linear combinations of low-rank, non-trainable random matrices. Our method limits the number of trainable parameters by restricting optimization to diagonal scaling matrices applied to the fixed random matrices. This allows us to effectively overcome the low-rank limitations while maintaining parameter and memory efficiency during training. Through extensive experimentation across vision, language, and vision-language benchmarks, we systematically evaluate the limitations of LoRA and existing random basis methods. Our findings reveal that full-rank updates are beneficial across vision and language tasks individually, and even more so for vision-language tasks, where RandLoRA significantly reduces -- and sometimes eliminates -- the performance gap between standard fine-tuning and LoRA, demonstrating its efficacy.

Learning discriminative deep feature embeddings by using million-scale in-the-wild datasets and margin-based softmax loss is the current state-of-the-art approach for face recognition. However, the memory and computing cost of the Fully Connected (FC) layer linearly scales up to the number of identities in the training set. Besides, the large-scale training data inevitably suffers from inter-class conflict and long-tailed distribution. In this paper, we propose a sparsely updating variant of the FC layer, named Partial FC (PFC). In each iteration, positive class centers and a random subset of negative class centers are selected to compute the margin-based softmax loss. All class centers are still maintained throughout the whole training process, but only a subset is selected and updated in each iteration. Therefore, the computing requirement, the probability of inter-class conflict, and the frequency of passive update on tail class centers, are dramatically reduced. Extensive experiments across different training data and backbones (e.g. CNN and ViT) confirm the effectiveness, robustness and efficiency of the proposed PFC. The source code is available at \https://github.com/deepinsight/insightface/tree/master/recognition.

Driven by the rapid growth of model parameters, parameter-efficient fine-tuning (PEFT) has become essential for adapting large models to diverse downstream tasks under constrained computational resources. Within this paradigm, orthogonal fine-tuning and its variants preserve semantic representations of pre-trained models, but struggle to achieve both expressiveness and efficiency in terms of parameter counts, memory, and computation. To overcome this limitation, we propose efficient Orthogonal Fine-Tuning with Principal Subspace adaptation (PSOFT), which confines orthogonal transformations to the principal subspace of pre-trained weights. Specifically, PSOFT constructs this subspace via matrix decomposition to enable compatible transformations with higher effective rank, establishes a theoretical condition that strictly maintains the geometry of this subspace for essential semantic preservation, and introduces efficient tunable vectors that gradually relax orthogonality during training to enhance adaptability. Extensive experiments on 35 NLP and CV tasks across four representative models demonstrate that PSOFT offers a practical and scalable solution to simultaneously achieve semantic preservation, expressiveness, and multi-dimensional efficiency in PEFT. The code is publicly available at https://github.com/fei407/PSOFT.

Prompt tuning (PT), where a small amount of trainable soft (continuous) prompt vectors is affixed to the input of language models (LM), has shown promising results across various tasks and models for parameter-efficient fine-tuning (PEFT). PT stands out from other PEFT approaches because it maintains competitive performance with fewer trainable parameters and does not drastically scale up its parameters as the model size expands. However, PT introduces additional soft prompt tokens, leading to longer input sequences, which significantly impacts training and inference time and memory usage due to the Transformer's quadratic complexity. Particularly concerning for Large Language Models (LLMs) that face heavy daily querying. To address this issue, we propose Decomposed Prompt Tuning (DePT), which decomposes the soft prompt into a shorter soft prompt and a pair of low-rank matrices that are then optimised with two different learning rates. This allows DePT to achieve better performance while saving over 20% memory and time costs compared to vanilla PT and its variants, without changing trainable parameter sizes. Through extensive experiments on 23 natural language processing (NLP) and vision-language (VL) tasks, we demonstrate that DePT outperforms state-of-the-art PEFT approaches, including the full fine-tuning baseline in some scenarios. Additionally, we empirically show that DEPT grows more efficient as the model size increases. Our further study reveals that DePT integrates seamlessly with parameter-efficient transfer learning in the few-shot learning setting and highlights its adaptability to various model architectures and sizes.

Dense retrieval overcome the lexical gap and has shown great success in ad-hoc information retrieval (IR). Despite their success, dense retrievers are expensive to serve across practical use cases. For use cases requiring to search from millions of documents, the dense index becomes bulky and requires high memory usage for storing the index. More recently, learning-to-hash (LTH) techniques, for e.g., BPR and JPQ, produce binary document vectors, thereby reducing the memory requirement to efficiently store the dense index. LTH techniques are supervised and finetune the retriever using a ranking loss. They outperform their counterparts, i.e., traditional out-of-the-box vector compression techniques such as PCA or PQ. A missing piece from prior work is that existing techniques have been evaluated only in-domain, i.e., on a single dataset such as MS MARCO. In our work, we evaluate LTH and vector compression techniques for improving the downstream zero-shot retrieval accuracy of the TAS-B dense retriever while maintaining efficiency at inference. Our results demonstrate that, unlike prior work, LTH strategies when applied naively can underperform the zero-shot TAS-B dense retriever on average by up to 14% nDCG@10 on the BEIR benchmark. To solve this limitation, in our work, we propose an easy yet effective solution of injecting domain adaptation with existing supervised LTH techniques. We experiment with two well-known unsupervised domain adaptation techniques: GenQ and GPL. Our domain adaptation injection technique can improve the downstream zero-shot retrieval effectiveness for both BPR and JPQ variants of the TAS-B model by on average 11.5% and 8.2% nDCG@10 while both maintaining 32times memory efficiency and 14times and 2times speedup respectively in CPU retrieval latency on BEIR. All our code, models, and data are publicly available at https://github.com/thakur-nandan/income.

Transformer has achieved remarkable success in language, image, and speech processing. Recently, various efficient attention architectures have been proposed to improve transformer's efficiency while largely preserving its efficacy, especially in modeling long sequences. A widely-used benchmark to test these efficient methods' capability on long-range modeling is Long Range Arena (LRA). However, LRA only focuses on the standard bidirectional (or noncausal) self attention, and completely ignores cross attentions and unidirectional (or causal) attentions, which are equally important to downstream applications. Although designing cross and causal variants of an attention method is straightforward for vanilla attention, it is often challenging for efficient attentions with subquadratic time and memory complexity. In this paper, we propose Comprehensive Attention Benchmark (CAB) under a fine-grained attention taxonomy with four distinguishable attention patterns, namely, noncausal self, causal self, noncausal cross, and causal cross attentions. CAB collects seven real-world tasks from different research areas to evaluate efficient attentions under the four attention patterns. Among these tasks, CAB validates efficient attentions in eight backbone networks to show their generalization across neural architectures. We conduct exhaustive experiments to benchmark the performances of nine widely-used efficient attention architectures designed with different philosophies on CAB. Extensive experimental results also shed light on the fundamental problems of efficient attentions, such as efficiency length against vanilla attention, performance consistency across attention patterns, the benefit of attention mechanisms, and interpolation/extrapolation on long-context language modeling.

In modern neural networks like Transformers, linear layers require significant memory to store activations during backward pass. This study proposes a memory reduction approach to perform backpropagation through linear layers. Since the gradients of linear layers are computed by matrix multiplications, we consider methods for randomized matrix multiplications and demonstrate that they require less memory with a moderate decrease of the test accuracy. Also, we investigate the variance of the gradient estimate induced by the randomized matrix multiplication. We compare this variance with the variance coming from gradient estimation based on the batch of samples. We demonstrate the benefits of the proposed method on the fine-tuning of the pre-trained RoBERTa model on GLUE tasks.

Remote photoplethysmography (rPPG), enabling non-contact physiological monitoring through facial light reflection analysis, faces critical computational bottlenecks as deep learning introduces performance gains at the cost of prohibitive resource demands. This paper proposes ME-rPPG, a memory-efficient algorithm built on temporal-spatial state space duality, which resolves the trilemma of model scalability, cross-dataset generalization, and real-time constraints. Leveraging a transferable state space, ME-rPPG efficiently captures subtle periodic variations across facial frames while maintaining minimal computational overhead, enabling training on extended video sequences and supporting low-latency inference. Achieving cross-dataset MAEs of 5.38 (MMPD), 0.70 (VitalVideo), and 0.25 (PURE), ME-rPPG outperforms all baselines with improvements ranging from 21.3% to 60.2%. Our solution enables real-time inference with only 3.6 MB memory usage and 9.46 ms latency -- surpassing existing methods by 19.5%-49.7% accuracy and 43.2% user satisfaction gains in real-world deployments. The code and demos are released for reproducibility on https://health-hci-group.github.io/ME-rPPG-demo/.

Advances in latent diffusion models (LDMs) have revolutionized high-resolution image generation, but the design space of the autoencoder that is central to these systems remains underexplored. In this paper, we introduce LiteVAE, a family of autoencoders for LDMs that leverage the 2D discrete wavelet transform to enhance scalability and computational efficiency over standard variational autoencoders (VAEs) with no sacrifice in output quality. We also investigate the training methodologies and the decoder architecture of LiteVAE and propose several enhancements that improve the training dynamics and reconstruction quality. Our base LiteVAE model matches the quality of the established VAEs in current LDMs with a six-fold reduction in encoder parameters, leading to faster training and lower GPU memory requirements, while our larger model outperforms VAEs of comparable complexity across all evaluated metrics (rFID, LPIPS, PSNR, and SSIM).

Recently, 3D Gaussian Splatting (3DGS) has emerged as a powerful alternative to NeRF-based approaches, enabling real-time, high-quality novel view synthesis through explicit, optimizable 3D Gaussians. However, 3DGS suffers from significant memory overhead due to its reliance on per-Gaussian parameters to model view-dependent effects and anisotropic shapes. While recent works propose compressing 3DGS with neural fields, these methods struggle to capture high-frequency spatial variations in Gaussian properties, leading to degraded reconstruction of fine details. We present Hybrid Radiance Fields (HyRF), a novel scene representation that combines the strengths of explicit Gaussians and neural fields. HyRF decomposes the scene into (1) a compact set of explicit Gaussians storing only critical high-frequency parameters and (2) grid-based neural fields that predict remaining properties. To enhance representational capacity, we introduce a decoupled neural field architecture, separately modeling geometry (scale, opacity, rotation) and view-dependent color. Additionally, we propose a hybrid rendering scheme that composites Gaussian splatting with a neural field-predicted background, addressing limitations in distant scene representation. Experiments demonstrate that HyRF achieves state-of-the-art rendering quality while reducing model size by over 20 times compared to 3DGS and maintaining real-time performance. Our project page is available at https://wzpscott.github.io/hyrf/.

With the rapid growth in model size, fine-tuning the large pre-trained language model has become increasingly difficult due to its extensive memory usage. Previous works usually focus on reducing the number of trainable parameters in the network. While the model parameters do contribute to memory usage, the primary memory bottleneck during training arises from storing feature maps, also known as activations, as they are crucial for gradient calculation. Notably, neural networks are usually trained using stochastic gradient descent. We argue that in stochastic optimization, models can handle noisy gradients as long as the gradient estimator is unbiased with reasonable variance. Following this motivation, we propose a new family of unbiased estimators called WTA-CRS, for matrix production with reduced variance, which only requires storing the sub-sampled activations for calculating the gradient. Our work provides both theoretical and experimental evidence that, in the context of tuning transformers, our proposed estimators exhibit lower variance compared to existing ones. By replacing the linear operation with our approximated one in transformers, we can achieve up to 2.7times peak memory reduction with almost no accuracy drop and enables up to 6.4times larger batch size. Under the same hardware, WTA-CRS enables better down-streaming task performance by applying larger models and/or faster training speed with larger batch sizes.

Video Object Segmentation (VOS) is foundational to numerous computer vision applications, including surveillance, autonomous driving, robotics and generative video editing. However, existing VOS models often struggle with precise mask delineation, deformable objects, topologically transforming objects, tracking drift and long video sequences. In this paper, we introduce HQ-SMem, for High Quality video segmentation and tracking using Smart Memory, a novel method that enhances the performance of VOS base models by addressing these limitations. Our approach incorporates three key innovations: (i) leveraging SAM with High-Quality masks (SAM-HQ) alongside appearance-based candidate-selection to refine coarse segmentation masks, resulting in improved object boundaries; (ii) implementing a dynamic smart memory mechanism that selectively stores relevant key frames while discarding redundant ones, thereby optimizing memory usage and processing efficiency for long-term videos; and (iii) dynamically updating the appearance model to effectively handle complex topological object variations and reduce drift throughout the video. These contributions mitigate several limitations of existing VOS models including, coarse segmentations that mix-in background pixels, fixed memory update schedules, brittleness to drift and occlusions, and prompt ambiguity issues associated with SAM. Extensive experiments conducted on multiple public datasets and state-of-the-art base trackers demonstrate that our method consistently ranks among the top two on VOTS and VOTSt 2024 datasets. Moreover, HQ-SMem sets new benchmarks on Long Video Dataset and LVOS, showcasing its effectiveness in challenging scenarios characterized by complex multi-object dynamics over extended temporal durations.

Recent work has shown that attention-based language models excel at recall, the ability to ground generations in tokens previously seen in context. However, the efficiency of attention-based models is bottle-necked during inference by the KV-cache's aggressive memory consumption. In this work, we explore whether we can improve language model efficiency (e.g. by reducing memory consumption) without compromising on recall. By applying experiments and theory to a broad set of architectures, we identify a key tradeoff between a model's state size and recall ability. We show that efficient alternatives to attention (e.g. H3, Mamba, RWKV) maintain a fixed-size recurrent state, but struggle at recall. We propose BASED a simple architecture combining linear and sliding window attention. By varying BASED window size and linear attention feature dimension, we can dial the state size and traverse the pareto frontier of the recall-memory tradeoff curve, recovering the full quality of attention on one end and the small state size of attention-alternatives on the other. We train language models up to 1.3b parameters and show that BASED matches the strongest sub-quadratic models (e.g. Mamba) in perplexity and outperforms them on real-world recall-intensive tasks by 6.22 accuracy points. Implementations of linear attention are often less efficient than optimized standard attention implementations. To make BASED competitive, we develop IO-aware algorithms that enable 24x higher throughput on language generation than FlashAttention-2, when generating 1024 tokens using 1.3b parameter models. Code for this work is provided at: https://github.com/HazyResearch/based.

We present a very simple algorithm for attention that requires O(1) memory with respect to sequence length and an extension to self-attention that requires O(log n) memory. This is in contrast with the frequently stated belief that self-attention requires O(n^2) memory. While the time complexity is still O(n^2), device memory rather than compute capability is often the limiting factor on modern accelerators. Thus, reducing the memory requirements of attention allows processing of longer sequences than might otherwise be feasible. We provide a practical implementation for accelerators that requires O(n) memory, is numerically stable, and is within a few percent of the runtime of the standard implementation of attention. We also demonstrate how to differentiate the function while remaining memory-efficient. For sequence length 16384, the memory overhead of self-attention is reduced by 59X for inference and by 32X for differentiation.

Training large language models (LLMs) typically relies on adaptive optimizers such as Adam, which require significant memory to maintain first- and second-moment matrices, known as optimizer states. While recent works such as GaLore, Fira, and APOLLO have proposed state-compressed variants to reduce memory consumption, a fundamental question remains: What is the minimal amount of optimizer state that is truly necessary to retain state-of-the-art performance in LLM pretraining? In this work, we systematically investigate this question using a bottom-up approach. We find that two memory- and compute-efficient optimization techniques are particularly effective: (1) column-wise gradient normalization significantly boosts the performance of plain SGD without requiring momentum; and (2) adding first-order momentum only to the output layer - where gradient variance is highest - yields performance competitive with fully adaptive methods such as Muon. Based on these insights, we propose SCALE (Stochastic Column-normalized Last-layer Momentum), a new optimizer that combines column-normalized SGD with last-layer momentum, where column normalization refers to normalizing the gradient along the output dimension. Across multiple LLaMA models (60M-1B), SCALE matches or exceeds the performance of Adam while using only 35-45% of the total memory. It also consistently outperforms memory-efficient optimizers such as GaLore, Fira, and APOLLO, making it a strong candidate for large-scale pretraining under memory constraints. For the LLaMA 7B model, SCALE outperforms the state-of-the-art method APOLLO in terms of both perplexity and memory consumption. In addition, our method serves as a minimalist baseline for more sophisticated optimizer design.

High throughput serving of large language models (LLMs) requires batching sufficiently many requests at a time. However, existing systems struggle because the key-value cache (KV cache) memory for each request is huge and grows and shrinks dynamically. When managed inefficiently, this memory can be significantly wasted by fragmentation and redundant duplication, limiting the batch size. To address this problem, we propose PagedAttention, an attention algorithm inspired by the classical virtual memory and paging techniques in operating systems. On top of it, we build vLLM, an LLM serving system that achieves (1) near-zero waste in KV cache memory and (2) flexible sharing of KV cache within and across requests to further reduce memory usage. Our evaluations show that vLLM improves the throughput of popular LLMs by 2-4times with the same level of latency compared to the state-of-the-art systems, such as FasterTransformer and Orca. The improvement is more pronounced with longer sequences, larger models, and more complex decoding algorithms. vLLM's source code is publicly available at https://github.com/vllm-project/vllm

As LLMs have become capable of processing more complex types of inputs, researchers have recently studied how to efficiently and affordably process possibly arbitrarily long sequences. One effective approach is to use a FIFO memory to store keys and values of an attention sublayer from past chunks to allow subsequent queries to attend. However, this approach requires a large memory and/or takes into the consideration the specific LM architecture. Moreover, due to the causal nature between the key-values in prior context and the queries at present, this approach cannot be extended to bidirectional attention such as in an encoder-decoder or PrefixLM decoder-only architecture. In this paper, we propose to use eviction policies, such as LRA and LFA, to reduce the memory size and adapt to various architectures, and we also propose the Attendre layer, a wait-to-attend mechanism by retrieving the key-value memory (K/V memory) with evicted queries in the query memory (Q memory). As a first step, we evaluate this method in the context length extension setup using the TriviaQA reading comprehension task, and show the effectiveness of the approach.

Context-augmented generation (CAG) techniques, including RAG and ICL, require the efficient combination of multiple contexts to generate responses to user queries. Directly inputting these contexts as a sequence introduces a considerable computational burden by re-encoding the combined selection of contexts for every request. To address this, we explore the promising potential of parallel encoding to independently pre-compute and cache each context's KV states. This approach enables the direct loading of cached states during inference while accommodating more contexts through position reuse across contexts. However, due to misalignments in attention distribution, directly applying parallel encoding results in a significant performance drop. To enable effective and efficient CAG, we propose Adaptive Parallel Encoding (APE), which brings shared prefix, attention temperature, and scaling factor to align the distribution of parallel encoding with sequential encoding. Results on RAG and ICL tasks demonstrate that APE can preserve 98% and 93% sequential encoding performance using the same inputs while outperforming parallel encoding by 3.6% and 7.9%, respectively. It also scales to many-shot CAG, effectively encoding hundreds of contexts in parallel. Efficiency evaluation shows that APE can achieve an end-to-end 4.5times speedup by reducing 28times prefilling time for a 128K-length context.

Many computational factors limit broader deployment of large language models. In this paper, we focus on a memory bottleneck imposed by the key-value (KV) cache, a computational shortcut that requires storing previous KV pairs during decoding. While existing KV cache methods approach this problem by pruning or evicting large swaths of relatively less important KV pairs to dramatically reduce the memory footprint of the cache, they can have limited success in tasks that require recollecting a majority of previous tokens. To alleviate this issue, we propose LESS, a simple integration of a (nearly free) constant sized cache with eviction-based cache methods, such that all tokens can be queried at later decoding steps. Its ability to retain information throughout time shows merit on a variety of tasks where we demonstrate LESS can help reduce the performance gap from caching everything, sometimes even matching it, all while being efficient.

Large language models face significant computational and memory challenges when processing long contexts. During inference, efficient management of the key-value (KV) cache, which stores intermediate activations for autoregressive generation, is critical to reducing memory overhead and improving computational efficiency. Traditional token-level efficient KV caching methods overlook semantic information, treating tokens independently without considering their semantic relationships. Meanwhile, existing semantic-preserving KV cache management approaches often suffer from substantial memory usage and high time-to-first-token. To address these limitations, we propose SentenceKV, a novel sentence-level semantic KV caching approach designed to enhance inference efficiency while preserving semantic coherence. During prefilling, SentenceKV groups tokens based on sentence-level semantic similarity, compressing sentence representations into concise semantic vectors stored directly on the GPU, while individual KV pairs are offloaded to CPU. During decoding, SentenceKV generates tokens by selectively retrieving semantically relevant sentence-level KV entries, leveraging the semantic similarity between the prefilling-stage semantic vectors and decoding-stage queries. This ensures efficient and contextually accurate predictions, minimizing the loading of redundant or irrelevant data into GPU memory and significantly reducing memory overhead while maintaining stable inference latency, even for extremely long contexts. Extensive evaluations on benchmarks including PG-19, LongBench, and Needle-In-A-Haystack demonstrate that SentenceKV significantly outperforms state-of-the-art methods in both efficiency and memory usage, without compromising model accuracy.

Large Language Models (LLMs) have revolutionized the field of natural language processing, achieving unprecedented performance across a variety of applications by leveraging increased model sizes and sequence lengths. However, the associated rise in computational and memory costs poses significant challenges, particularly in managing long sequences due to the quadratic complexity of the transformer attention mechanism. This paper focuses on the long-context scenario, addressing the inefficiencies in KV cache memory consumption during inference. Unlike existing approaches that optimize the memory based on the sequence lengths, we uncover that the channel dimension of the KV cache exhibits significant redundancy, characterized by unbalanced magnitude distribution and low-rank structure in attention weights. Based on these observations, we propose ThinK, a novel query-dependent KV cache pruning method designed to minimize attention weight loss while selectively pruning the least significant channels. Our approach not only maintains or enhances model accuracy but also achieves a reduction in memory costs by over 20% compared with vanilla KV cache eviction methods. Extensive evaluations on the LLaMA3 and Mistral models across various long-sequence datasets confirm the efficacy of ThinK, setting a new precedent for efficient LLM deployment without compromising performance. We also outline the potential of extending our method to value cache pruning, demonstrating ThinK's versatility and broad applicability in reducing both memory and computational overheads.

Long-context language models exhibit impressive performance but remain challenging to deploy due to high GPU memory demands during inference. We propose Memory-efficient Offloaded Mini-sequence Inference (MOM), a method that partitions critical layers into smaller "mini-sequences" and integrates seamlessly with KV cache offloading. Experiments on various Llama, Qwen, and Mistral models demonstrate that MOM reduces peak memory usage by over 50\% on average. On Meta-Llama-3.2-8B, MOM extends the maximum context length from 155k to 455k tokens on a single A100 80GB GPU, while keeping outputs identical and not compromising accuracy. MOM also maintains highly competitive throughput due to minimal computational overhead and efficient last-layer processing. Compared to traditional chunked prefill methods, MOM achieves a 35\% greater context length extension. More importantly, our method drastically reduces prefill memory consumption, eliminating it as the longstanding dominant memory bottleneck during inference. This breakthrough fundamentally changes research priorities, redirecting future efforts from prefill-stage optimizations to improving decode-stage residual KV cache efficiency.

Large language models rely heavily on prompts to specify tasks, recall knowledge and guide reasoning. However, this reliance is inefficient as prompts must be re-read at each step, scale poorly across tasks, and lack mechanisms for modular reuse. We introduce TokMem, a tokenized procedural memory that stores recurring procedures as compact, trainable embeddings. Each memory token encodes both an address to a procedure and a control signal that steers generation, enabling targeted behavior with constant-size overhead. To support continual adaptation, TokMem keeps the backbone model frozen, allowing new procedures to be added without interfering with existing ones. We evaluate TokMem on 1,000 tasks for atomic recall, and on function-calling tasks for compositional recall, where it consistently outperforms retrieval-augmented generation while avoiding repeated context overhead, and fine-tuning with far fewer parameters. These results establish TokMem as a scalable and modular alternative to prompt engineering and fine-tuning, offering an explicit procedural memory for LLMs.

Memory retention challenges in deep neural architectures have ongoing limitations in the ability to process and recall extended contextual information. Token dependencies degrade as sequence length increases, leading to a decline in coherence and factual consistency across longer outputs. A structured approach is introduced to mitigate this issue through the reweaving of latent states captured at different processing layers, reinforcing token representations over extended sequences. The proposed Contextual Memory Reweaving framework incorporates a Layered Latent State Reconstruction mechanism to systematically integrate past contextual embeddings without introducing external memory modules. Experimental results demonstrate improvements in recall accuracy across a range of sequence lengths, with notable gains in the retention of rarely occurring tokens and numerical reasoning consistency. Further analysis of computational efficiency indicates that the additional processing overhead remains within acceptable thresholds, enabling scalability across different model sizes. Evaluations in long-form text generation and ambiguous query resolution highlight the capacity of memory reweaving to enhance continuity and reduce inconsistencies over extended outputs. Attention weight distributions reveal more structured allocation patterns, suggesting that reweaved latent states contribute to improved contextual awareness. The findings establish a framework for refining memory retention mechanisms in language models, addressing long-standing challenges in handling complex, multi-step reasoning tasks.

Large Language Models (LLMs) have driven significant progress, yet their growing parameter counts and context windows incur prohibitive compute, energy, and monetary costs. We introduce EfficientLLM, a novel benchmark and the first comprehensive empirical study evaluating efficiency techniques for LLMs at scale. Conducted on a production-class cluster (48xGH200, 8xH200 GPUs), our study systematically explores three key axes: (1) architecture pretraining (efficient attention variants: MQA, GQA, MLA, NSA; sparse Mixture-of-Experts (MoE)), (2) fine-tuning (parameter-efficient methods: LoRA, RSLoRA, DoRA), and (3) inference (quantization methods: int4, float16). We define six fine-grained metrics (Memory Utilization, Compute Utilization, Latency, Throughput, Energy Consumption, Compression Rate) to capture hardware saturation, latency-throughput balance, and carbon cost. Evaluating over 100 model-technique pairs (0.5B-72B parameters), we derive three core insights: (i) Efficiency involves quantifiable trade-offs: no single method is universally optimal; e.g., MoE reduces FLOPs and improves accuracy but increases VRAM by 40%, while int4 quantization cuts memory/energy by up to 3.9x at a 3-5% accuracy drop. (ii) Optima are task- and scale-dependent: MQA offers optimal memory-latency trade-offs for constrained devices, MLA achieves lowest perplexity for quality-critical tasks, and RSLoRA surpasses LoRA efficiency only beyond 14B parameters. (iii) Techniques generalize across modalities: we extend evaluations to Large Vision Models (Stable Diffusion 3.5, Wan 2.1) and Vision-Language Models (Qwen2.5-VL), confirming effective transferability. By open-sourcing datasets, evaluation pipelines, and leaderboards, EfficientLLM provides essential guidance for researchers and engineers navigating the efficiency-performance landscape of next-generation foundation models.

KV caching significantly improves the efficiency of Large Language Model (LLM) inference by storing attention states from previously processed tokens, enabling faster generation of subsequent tokens. However, as sequence length increases, the KV cache quickly becomes a major memory bottleneck. To address this, we propose PagedEviction, a novel fine-grained, structured KV cache pruning strategy that enhances the memory efficiency of vLLM's PagedAttention. Unlike existing approaches that rely on attention-based token importance or evict tokens across different vLLM pages, PagedEviction introduces an efficient block-wise eviction algorithm tailored for paged memory layouts. Our method integrates seamlessly with PagedAttention without requiring any modifications to its CUDA attention kernels. We evaluate PagedEviction across Llama-3.1-8B-Instruct, Llama-3.2-1B-Instruct, and Llama-3.2-3B-Instruct models on the LongBench benchmark suite, demonstrating improved memory usage with better accuracy than baselines on long context tasks.

Large Language Models (LLMs), despite their impressive performance on a wide range of tasks, require significant GPU memory and consume substantial computational resources. In addition to model weights, the memory occupied by KV cache increases linearly with sequence length, becoming a main bottleneck for inference. In this paper, we introduce a novel approach for optimizing the KV cache which significantly reduces its memory footprint. Through a comprehensive investigation, we find that on LLaMA2 series models, (i) the similarity between adjacent tokens' query vectors is remarkably high, and (ii) current query's attention calculation can rely solely on the attention information of a small portion of the preceding queries. Based on these observations, we propose CORM, a KV cache eviction policy that dynamically retains important key-value pairs for inference without finetuning the model. We validate that CORM reduces the inference memory usage of KV cache by up to 70% without noticeable performance degradation across six tasks in LongBench.

Real-world applications require the classification model to adapt to new classes without forgetting old ones. Correspondingly, Class-Incremental Learning (CIL) aims to train a model with limited memory size to meet this requirement. Typical CIL methods tend to save representative exemplars from former classes to resist forgetting, while recent works find that storing models from history can substantially boost the performance. However, the stored models are not counted into the memory budget, which implicitly results in unfair comparisons. We find that when counting the model size into the total budget and comparing methods with aligned memory size, saving models do not consistently work, especially for the case with limited memory budgets. As a result, we need to holistically evaluate different CIL methods at different memory scales and simultaneously consider accuracy and memory size for measurement. On the other hand, we dive deeply into the construction of the memory buffer for memory efficiency. By analyzing the effect of different layers in the network, we find that shallow and deep layers have different characteristics in CIL. Motivated by this, we propose a simple yet effective baseline, denoted as MEMO for Memory-efficient Expandable MOdel. MEMO extends specialized layers based on the shared generalized representations, efficiently extracting diverse representations with modest cost and maintaining representative exemplars. Extensive experiments on benchmark datasets validate MEMO's competitive performance. Code is available at: https://github.com/wangkiw/ICLR23-MEMO

In this study, we introduce adaptive KV cache compression, a plug-and-play method that reduces the memory footprint of generative inference for Large Language Models (LLMs). Different from the conventional KV cache that retains key and value vectors for all context tokens, we conduct targeted profiling to discern the intrinsic structure of attention modules. Based on the recognized structure, we then construct the KV cache in an adaptive manner: evicting long-range contexts on attention heads emphasizing local contexts, discarding non-special tokens on attention heads centered on special tokens, and only employing the standard KV cache for attention heads that broadly attend to all tokens. Moreover, with the lightweight attention profiling used to guide the construction of the adaptive KV cache, FastGen can be deployed without resource-intensive fine-tuning or re-training. In our experiments across various asks, FastGen demonstrates substantial reduction on GPU memory consumption with negligible generation quality loss. We will release our code and the compatible CUDA kernel for reproducibility.

Memory plays a pivotal role in enabling large language model~(LLM)-based agents to engage in complex and long-term interactions, such as question answering (QA) and dialogue systems. While various memory modules have been proposed for these tasks, the impact of different memory structures across tasks remains insufficiently explored. This paper investigates how memory structures and memory retrieval methods affect the performance of LLM-based agents. Specifically, we evaluate four types of memory structures, including chunks, knowledge triples, atomic facts, and summaries, along with mixed memory that combines these components. In addition, we evaluate three widely used memory retrieval methods: single-step retrieval, reranking, and iterative retrieval. Extensive experiments conducted across four tasks and six datasets yield the following key insights: (1) Different memory structures offer distinct advantages, enabling them to be tailored to specific tasks; (2) Mixed memory structures demonstrate remarkable resilience in noisy environments; (3) Iterative retrieval consistently outperforms other methods across various scenarios. Our investigation aims to inspire further research into the design of memory systems for LLM-based agents.

While Mixture-of-Experts (MoE) scales capacity via conditional computation, Transformers lack a native primitive for knowledge lookup, forcing them to inefficiently simulate retrieval through computation. To address this, we introduce conditional memory as a complementary sparsity axis, instantiated via Engram, a module that modernizes classic N-gram embedding for O(1) lookup. By formulating the Sparsity Allocation problem, we uncover a U-shaped scaling law that optimizes the trade-off between neural computation (MoE) and static memory (Engram). Guided by this law, we scale Engram to 27B parameters, achieving superior performance over a strictly iso-parameter and iso-FLOPs MoE baseline. Most notably, while the memory module is expected to aid knowledge retrieval (e.g., MMLU +3.4; CMMLU +4.0), we observe even larger gains in general reasoning (e.g., BBH +5.0; ARC-Challenge +3.7) and code/math domains~(HumanEval +3.0; MATH +2.4). Mechanistic analyses reveal that Engram relieves the backbone's early layers from static reconstruction, effectively deepening the network for complex reasoning. Furthermore, by delegating local dependencies to lookups, it frees up attention capacity for global context, substantially boosting long-context retrieval (e.g., Multi-Query NIAH: 84.2 to 97.0). Finally, Engram establishes infrastructure-aware efficiency: its deterministic addressing enables runtime prefetching from host memory, incurring negligible overhead. We envision conditional memory as an indispensable modeling primitive for next-generation sparse models.

Transformer models have revolutionized natural language processing, achieving state-of-the-art performance and demonstrating remarkable scalability. However, their memory demands, particularly due to maintaining full context in memory, pose significant challenges for inference. In this paper, we present FlashEVA, an efficient implementation of EVA (Efficient Attention via Control Variates), and demonstrate how to finetune transformers to adapt to FlashEVA attention. Our method enables fine-tuning of Transformer models with as few as 1.5B tokens while preserving effectiveness across various downstream tasks. Notably, FlashEVA achieves up to 6.7x higher throughput and 5x lower peak GPU memory usage during inference compared to standard Transformer implementations. Despite these improvements, we observe limitations in retrieval-focused tasks. Our implementation offers control over the trade-off between throughput and accuracy through adjustable hyperparameters, providing flexibility for diverse use cases. This work represents a significant step towards more efficient and adaptable Transformer-based models for inference.

Large language models (LLMs) are central to modern natural language processing, delivering exceptional performance in various tasks. However, their intensive computational and memory requirements present challenges, especially for devices with limited DRAM capacity. This paper tackles the challenge of efficiently running LLMs that exceed the available DRAM capacity by storing the model parameters on flash memory but bringing them on demand to DRAM. Our method involves constructing an inference cost model that harmonizes with the flash memory behavior, guiding us to optimize in two critical areas: reducing the volume of data transferred from flash and reading data in larger, more contiguous chunks. Within this flash memory-informed framework, we introduce two principal techniques. First, "windowing'" strategically reduces data transfer by reusing previously activated neurons, and second, "row-column bundling", tailored to the sequential data access strengths of flash memory, increases the size of data chunks read from flash memory. These methods collectively enable running models up to twice the size of the available DRAM, with a 4-5x and 20-25x increase in inference speed compared to naive loading approaches in CPU and GPU, respectively. Our integration of sparsity awareness, context-adaptive loading, and a hardware-oriented design paves the way for effective inference of LLMs on devices with limited memory.

With the explosive growth of data, long-sequence modeling has become increasingly important in tasks such as natural language processing and bioinformatics. However, existing methods face inherent trade-offs between efficiency and memory. Recurrent neural networks suffer from gradient vanishing and explosion, making them hard to scale. Transformers can model global dependencies but are constrained by quadratic complexity. Recently, selective state-space models such as Mamba have demonstrated high efficiency with O(n) time and O(1) recurrent inference, yet their long-range memory decays exponentially. In this work, we conduct mathematical derivations and information-theoretic analysis to systematically uncover the memory decay mechanism of Mamba, answering a fundamental question: what is the nature of Mamba's long-range memory and how does it retain information? To quantify key information loss, we further introduce horizontal-vertical memory fidelity metrics that capture degradation both within and across layers. Inspired by how humans distill and retain salient information when reading long documents, we propose MemMamba, a novel architectural framework that integrates state summarization mechanism together with cross-layer and cross-token attention, which alleviates long-range forgetting while preserving linear complexity. MemMamba achieves significant improvements over existing Mamba variants and Transformers on long-sequence benchmarks such as PG19 and Passkey Retrieval, while delivering a 48% speedup in inference efficiency. Both theoretical analysis and empirical results demonstrate that MemMamba achieves a breakthrough in the complexity-memory trade-off, offering a new paradigm for ultra-long sequence modeling.

Training and serving long-context large language models (LLMs) incurs substantial overhead. To address this, two critical steps are often required: a pretrained LLM typically undergoes a separate stage for context length extension by training on long-context data, followed by architectural modifications to reduce the overhead of KV cache during serving. This paper argues that integrating length extension with a GPU-friendly KV cache reduction architecture not only reduces training overhead during length extension, but also achieves better long-context performance. This leads to our proposed LongGen, which finetunes a pretrained LLM into an efficient architecture during length extension. LongGen builds on three key insights: (1) Sparse attention patterns, such as window attention (attending to recent tokens), attention sink (initial ones), and blockwise sparse attention (strided token blocks) are well-suited for building efficient long-context models, primarily due to their GPU-friendly memory access patterns, enabling efficiency gains not just theoretically but in practice as well. (2) It is essential for the model to have direct access to all tokens. A hybrid architecture with 1/3 full attention layers and 2/3 efficient ones achieves a balanced trade-off between efficiency and long-context performance. (3) Lightweight training on 5B long-context data is sufficient to extend the hybrid model's context length from 4K to 128K. We evaluate LongGen on both Llama-2 7B and Llama-2 70B, demonstrating its effectiveness across different scales. During training with 128K-long contexts, LongGen achieves 1.55x training speedup and reduces wall-clock time by 36%, compared to a full-attention baseline. During inference, LongGen reduces KV cache memory by 62%, achieving 1.67x prefilling speedup and 1.41x decoding speedup.

The emergence of long-context large language models (LLMs) offers a promising alternative to traditional retrieval-augmented generation (RAG) for processing extensive documents. However, the computational overhead of long-context inference, particularly in managing key-value (KV) caches, presents significant efficiency challenges. While Speculative Decoding (SD) traditionally accelerates inference using smaller draft models, its effectiveness diminishes substantially in long-context scenarios due to memory-bound KV cache operations. We present Retrieval-Augmented Speculative Decoding (RAPID), which leverages RAG for both accelerating and enhancing generation quality in long-context inference. RAPID introduces the RAG drafter-a draft LLM operating on shortened retrieval contexts-to speculate on the generation of long-context target LLMs. Our approach enables a new paradigm where same-scale or even larger LLMs can serve as RAG drafters while maintaining computational efficiency. To fully leverage the potentially superior capabilities from stronger RAG drafters, we develop an inference-time knowledge transfer dynamic that enriches the target distribution by RAG. Extensive experiments on the LLaMA-3.1 and Qwen2.5 backbones demonstrate that RAPID effectively integrates the strengths of both approaches, achieving significant performance improvements (e.g., from 39.33 to 42.83 on InfiniteBench for LLaMA-3.1-8B) with more than 2x speedups. Our analyses reveal that RAPID achieves robust acceleration beyond 32K context length and demonstrates superior generation quality in real-world applications.

We study the efficiency of multi-vector retrieval methods like ColBERT and its recent variant XTR. We introduce WARP, a retrieval engine that drastically improves the efficiency of XTR-based ColBERT retrievers through three key innovations: (1) WARP_SELECT for dynamic similarity imputation, (2) implicit decompression to bypass costly vector reconstruction, and (3) a two-stage reduction process for efficient scoring. Combined with optimized C++ kernels and specialized inference runtimes, WARP reduces end-to-end latency by 41x compared to XTR's reference implementation and thereby achieves a 3x speedup over PLAID from the the official ColBERT implementation. We study the efficiency of multi-vector retrieval methods like ColBERT and its recent variant XTR. We introduce WARP, a retrieval engine that drastically improves the efficiency of XTR-based ColBERT retrievers through three key innovations: (1) WARP_SELECT for dynamic similarity imputation, (2) implicit decompression during retrieval, and (3) a two-stage reduction process for efficient scoring. Thanks also to highly-optimized C++ kernels and to the adoption of specialized inference runtimes, WARP can reduce end-to-end query latency relative to XTR's reference implementation by 41x. And it thereby achieves a 3x speedup over the official ColBERTv2 PLAID engine, while preserving retrieval quality.

The training and inference of large language models (LLMs) are together a costly process that transports knowledge from raw data to meaningful computation. Inspired by the memory hierarchy of the human brain, we reduce this cost by equipping LLMs with explicit memory, a memory format cheaper than model parameters and text retrieval-augmented generation (RAG). Conceptually, with most of its knowledge externalized to explicit memories, the LLM can enjoy a smaller parameter size, training cost, and inference cost, all proportional to the amount of remaining "abstract knowledge". As a preliminary proof of concept, we train from scratch a 2.4B LLM, which achieves better performance than much larger LLMs as well as RAG models, and maintains higher decoding speed than RAG. The model is named Memory^3, since explicit memory is the third form of memory in LLMs after implicit memory (model parameters) and working memory (context key-values). We introduce a memory circuitry theory to support the externalization of knowledge, and present novel techniques including a memory sparsification mechanism that makes storage tractable and a two-stage pretraining scheme that facilitates memory formation.

Generating texts with a large language model (LLM) consumes massive amounts of memory. Apart from the already-large model parameters, the key/value (KV) cache that holds information about previous tokens in a sequence can grow to be even larger than the model itself. This problem is exacerbated in one of the current LLM serving frameworks which reserves the maximum sequence length of memory for the KV cache to guarantee generating a complete sequence as they do not know the output sequence length. This restricts us to use a smaller batch size leading to lower GPU utilization and above all, lower throughput. We argue that designing a system with a priori knowledge of the output sequence can mitigate this problem. To this end, we propose S^{3}, which predicts the output sequence length, schedules generation queries based on the prediction to increase device resource utilization and throughput, and handle mispredictions. Our proposed method achieves 6.49times throughput over those systems that assume the worst case for the output sequence length.

Long-context LLMs have enabled numerous downstream applications but also introduced significant challenges related to computational and memory efficiency. To address these challenges, optimizations for long-context inference have been developed, centered around the KV cache. However, existing benchmarks often evaluate in single-request, neglecting the full lifecycle of the KV cache in real-world use. This oversight is particularly critical, as KV cache reuse has become widely adopted in LLMs inference frameworks, such as vLLM and SGLang, as well as by LLM providers, including OpenAI, Microsoft, Google, and Anthropic. To address this gap, we introduce SCBench(SharedContextBench), a comprehensive benchmark for evaluating long-context methods from a KV cachecentric perspective: 1) KV cache generation, 2) KV cache compression, 3) KV cache retrieval, 4) KV cache loading. Specifically, SCBench uses test examples with shared context, ranging 12 tasks with two shared context modes, covering four categories of long-context capabilities: string retrieval, semantic retrieval, global information, and multi-task. With it, we provide an extensive KV cache-centric analysis of eight categories long-context solutions, including Gated Linear RNNs, Mamba-Attention hybrids, and efficient methods such as sparse attention, KV cache dropping, quantization, retrieval, loading, and prompt compression. The evaluation is conducted on 8 long-context LLMs. Our findings show that sub-O(n) memory methods suffer in multi-turn scenarios, while sparse encoding with O(n) memory and sub-O(n^2) pre-filling computation perform robustly. Dynamic sparsity yields more expressive KV caches than static patterns, and layer-level sparsity in hybrid architectures reduces memory usage with strong performance. Additionally, we identify attention distribution shift issues in long-generation scenarios. https://aka.ms/SCBench.

While fine-tuning large language models (LLMs) for specific tasks often yields impressive results, it comes at the cost of memory inefficiency due to back-propagation in gradient-based training. Memory-efficient Zeroth-order (MeZO) optimizers, recently proposed to address this issue, only require forward passes during training, making them more memory-friendly. However, the quality of gradient estimates in zeroth order optimization often depends on the data dimensionality, potentially explaining why MeZO still exhibits significant performance drops compared to standard fine-tuning across various tasks. Inspired by the success of Parameter-Efficient Fine-Tuning (PEFT), this paper introduces Sparse MeZO, a novel memory-efficient zeroth-order optimization approach that applies ZO only to a carefully chosen subset of parameters. We propose a simple yet effective parameter selection scheme that yields significant performance gains with Sparse-MeZO. Additionally, we develop a memory-optimized implementation for sparse masking, ensuring the algorithm requires only inference-level memory consumption, allowing Sparse-MeZO to fine-tune LLaMA-30b on a single A100 GPU. Experimental results illustrate that Sparse-MeZO consistently improves both performance and convergence speed over MeZO without any overhead. For example, it achieves a 9\% absolute accuracy improvement and 3.5x speedup over MeZO on the RTE task.

The rapid growth of Large Language Models (LLMs) has been a driving force in transforming various domains, reshaping the artificial general intelligence landscape. However, the increasing computational and memory demands of these models present substantial challenges, hindering both academic research and practical applications. To address these issues, a wide array of methods, including both algorithmic and hardware solutions, have been developed to enhance the efficiency of LLMs. This survey delivers a comprehensive review of algorithmic advancements aimed at improving LLM efficiency. Unlike other surveys that typically focus on specific areas such as training or model compression, this paper examines the multi-faceted dimensions of efficiency essential for the end-to-end algorithmic development of LLMs. Specifically, it covers various topics related to efficiency, including scaling laws, data utilization, architectural innovations, training and tuning strategies, and inference techniques. This paper aims to serve as a valuable resource for researchers and practitioners, laying the groundwork for future innovations in this critical research area. Our repository of relevant references is maintained at url{https://github.com/tding1/Efficient-LLM-Survey}.

Memory plays a key role in enhancing LLMs' performance when deployed to real-world applications. Existing solutions face trade-offs: explicit memory designs based on external storage require complex management and incur storage overhead, while implicit memory designs that store information via parameters struggle with reliable retrieval. In this paper, we propose R^3Mem, a memory network that optimizes both information Retention and Retrieval through Reversible context compression. Specifically, R^3Mem employs virtual memory tokens to compress and encode infinitely long histories, further enhanced by a hierarchical compression strategy that refines information from document- to entity-level for improved assimilation across granularities. For retrieval, R^3Mem employs a reversible architecture, reconstructing raw data by invoking the model backward with compressed information. Implemented via parameter-efficient fine-tuning, it can integrate seamlessly with any Transformer-based model. Experiments demonstrate that our memory design achieves state-of-the-art performance in long-context language modeling and retrieval-augmented generation tasks. It also significantly outperforms conventional memory modules in long-horizon interaction tasks like conversational agents, showcasing its potential for next-generation retrieval systems.

We introduce Llamba, a family of efficient recurrent language models distilled from Llama-3.x into the Mamba architecture. The series includes Llamba-1B, Llamba-3B, and Llamba-8B, which achieve higher inference throughput and handle significantly larger batch sizes than Transformer-based models while maintaining comparable benchmark performance. Furthermore, Llamba demonstrates the effectiveness of cross-architecture distillation using MOHAWK (Bick et al., 2024), achieving these results with less than 0.1% of the training data typically used for models of similar size. To take full advantage of their efficiency, we provide an optimized implementation of Llamba for resource-constrained devices such as smartphones and edge platforms, offering a practical and memory-efficient alternative to Transformers. Overall, Llamba improves the tradeoff between speed, memory efficiency, and performance, making high-quality language models more accessible.

Retrieval-Augmented Language Modeling (RALM) by integrating large language models (LLM) with relevant documents from an external corpus is a proven method for enabling the LLM to generate information beyond the scope of its pre-training corpus. Previous work using utilizing retrieved content by simply prepending retrieved contents to the input poses a high runtime issue, which degrades the inference efficiency of the LLMs because they fail to use the Key-Value (KV) cache efficiently. In this paper, we propose FlashBack, a modular RALM designed to improve the inference efficiency of RALM with appending context pattern while maintaining decent performance after specific fine-tuning without heavily destruct the knowledge integrity of the LLM. FlashBack appends retrieved documents at the end of the context for efficiently utilizing the KV cache instead of prepending them. Our experiment shows that the inference speed of FlashBack is up to 4times faster than the prepending method on a 7B LLM (Llama 2). Via bypassing unnecessary re-computation, it demonstrates an advancement by achieving significantly faster inference speed, and this heightened efficiency will substantially reduce inferential cost. Our code will be publicly available.

Large Language Models (LLMs) have made remarkable progress in processing extensive contexts, with the Key-Value (KV) cache playing a vital role in enhancing their performance. However, the growth of the KV cache in response to increasing input length poses challenges to memory and time efficiency. To address this problem, this paper introduces SnapKV, an innovative and fine-tuning-free approach that efficiently minimizes KV cache size while still delivering comparable performance in real-world applications. We discover that each attention head in the model consistently focuses on specific prompt attention features during generation. Meanwhile, this robust pattern can be obtained from an `observation' window located at the end of the prompts. Drawing on this insight, SnapKV automatically compresses KV caches by selecting clustered important KV positions for each attention head. Our approach significantly reduces the growing computational overhead and memory footprint when processing long input sequences. Specifically, SnapKV achieves a consistent decoding speed with a 3.6x increase in generation speed and an 8.2x enhancement in memory efficiency compared to baseline when processing inputs of 16K tokens. At the same time, it maintains comparable performance to baseline models across 16 long sequence datasets. Moreover, SnapKV can process up to 380K context tokens on a single A100-80GB GPU using HuggingFace implementation with minor changes, exhibiting only a negligible accuracy drop in the Needle-in-a-Haystack test. Further comprehensive studies suggest SnapKV's potential for practical applications.

Transformer-based large language models (LLMs) have already achieved remarkable results on long-text tasks, but the limited GPU memory (VRAM) resources struggle to accommodate the linearly growing demand for key-value (KV) cache as the sequence length increases, which has become a bottleneck for the application of LLMs on long sequences. Existing KV cache compression methods include eviction, merging, or quantization of the KV cache to reduce its size. However, compression results in irreversible information forgetting, potentially affecting the accuracy of subsequent decoding. In this paper, we propose SpeCache, which takes full advantage of the large and easily expandable CPU memory to offload the complete KV cache, and dynamically fetches KV pairs back in each decoding step based on their importance measured by low-bit KV cache copy in VRAM. To avoid inference latency caused by CPU-GPU communication, SpeCache speculatively predicts the KV pairs that the next token might attend to, allowing us to prefetch them before the next decoding step which enables parallelization of prefetching and computation. Experiments on LongBench and Needle-in-a-Haystack benchmarks verify that SpeCache effectively reduces VRAM usage while avoiding information forgetting for long sequences without re-training, even with a 10x high KV cache compression ratio.

Long sequence modeling has gained broad interest as large language models (LLMs) continue to advance. Recent research has identified that a large portion of hidden states within the key-value caches of Transformer models can be discarded (also termed evicted) without affecting the perplexity performance in generating long sequences. However, we show that these methods, despite preserving perplexity performance, often drop information that is important for solving downstream tasks, a problem which we call information neglect. To address this issue, we introduce Chunked Instruction-aware State Eviction (CItruS), a novel modeling technique that integrates the attention preferences useful for a downstream task into the eviction process of hidden states. In addition, we design a method for chunked sequence processing to further improve efficiency. Our training-free method exhibits superior performance on long sequence comprehension and retrieval tasks over several strong baselines under the same memory budget, while preserving language modeling perplexity.

There has recently been considerable interest in incorporating information retrieval into large language models (LLMs). Retrieval from a dynamically expanding external corpus of text allows a model to incorporate current events and can be viewed as a form of episodic memory. Here we demonstrate that pre-processing the external corpus into semi-structured ''atomic facts'' makes retrieval more efficient. More specifically, we demonstrate that our particular form of atomic facts improves performance on various question answering tasks when the amount of retrieved text is limited. Limiting the amount of retrieval reduces the size of the context and improves inference efficiency.

This paper introduces a structured memory which can be easily integrated into a neural network. The memory is very large by design and significantly increases the capacity of the architecture, by up to a billion parameters with a negligible computational overhead. Its design and access pattern is based on product keys, which enable fast and exact nearest neighbor search. The ability to increase the number of parameters while keeping the same computational budget lets the overall system strike a better trade-off between prediction accuracy and computation efficiency both at training and test time. This memory layer allows us to tackle very large scale language modeling tasks. In our experiments we consider a dataset with up to 30 billion words, and we plug our memory layer in a state-of-the-art transformer-based architecture. In particular, we found that a memory augmented model with only 12 layers outperforms a baseline transformer model with 24 layers, while being twice faster at inference time. We release our code for reproducibility purposes.

Key-Value (KV) Caching has become an essential technique for accelerating the inference speed and throughput of generative Large Language Models~(LLMs). However, the memory footprint of the KV cache poses a critical bottleneck in LLM deployment as the cache size grows with batch size and sequence length, often surpassing even the size of the model itself. Although recent methods were proposed to select and evict unimportant KV pairs from the cache to reduce memory consumption, the potential ramifications of eviction on the generative process are yet to be thoroughly examined. In this paper, we examine the detrimental impact of cache eviction and observe that unforeseen risks arise as the information contained in the KV pairs is exhaustively discarded, resulting in safety breaches, hallucinations, and context loss. Surprisingly, we find that preserving even a small amount of information contained in the evicted KV pairs via reduced precision quantization substantially recovers the incurred degradation. On the other hand, we observe that the important KV pairs must be kept at a relatively higher precision to safeguard the generation quality. Motivated by these observations, we propose Mixed-precision KV cache~(MiKV), a reliable cache compression method that simultaneously preserves the context details by retaining the evicted KV pairs in low-precision and ensure generation quality by keeping the important KV pairs in high-precision. Experiments on diverse benchmarks and LLM backbones show that our proposed method offers a state-of-the-art trade-off between compression ratio and performance, compared to other baselines.

Existing works increasingly adopt memory-centric mechanisms to process long contexts in a segment manner, and effective memory management is one of the key capabilities that enables large language models to effectively propagate information across the entire sequence. Therefore, leveraging reward models (RMs) to automatically and reliably evaluate memory quality is critical. In this work, we introduce MemoryRewardBench, the first benchmark to systematically study the ability of RMs to evaluate long-term memory management processes. MemoryRewardBench covers both long-context comprehension and long-form generation tasks, featuring 10 distinct settings with different memory management patterns, with context length ranging from 8K to 128K tokens. Evaluations on 13 cutting-edge RMs indicate a diminishing performance gap between open-source and proprietary models, with newer-generation models consistently outperforming their predecessors regardless of parameter count. We further expose the capabilities and fundamental limitations of current RMs in evaluating LLM memory management across diverse settings.

Large Language Model (LLM)-based search agents have shown remarkable capabilities in solving complex tasks by dynamically decomposing problems and addressing them through interleaved reasoning and retrieval. However, this interleaved paradigm introduces substantial efficiency bottlenecks. First, we observe that both highly accurate and overly approximate retrieval methods degrade system efficiency: exact search incurs significant retrieval overhead, while coarse retrieval requires additional reasoning steps during generation. Second, we identify inefficiencies in system design, including improper scheduling and frequent retrieval stalls, which lead to cascading latency -- where even minor delays in retrieval amplify end-to-end inference time. To address these challenges, we introduce SearchAgent-X, a high-efficiency inference framework for LLM-based search agents. SearchAgent-X leverages high-recall approximate retrieval and incorporates two key techniques: priority-aware scheduling and non-stall retrieval. Extensive experiments demonstrate that SearchAgent-X consistently outperforms state-of-the-art systems such as vLLM and HNSW-based retrieval across diverse tasks, achieving up to 3.4times higher throughput and 5times lower latency, without compromising generation quality. SearchAgent-X is available at https://github.com/tiannuo-yang/SearchAgent-X.

As large language models increasingly gain popularity in real-world applications, processing extremely long contexts, often exceeding the model's pre-trained context limits, has emerged as a critical challenge. While existing approaches to efficient long-context processing show promise, recurrent compression-based methods struggle with information preservation, whereas random access approaches require substantial memory resources. We introduce REFORM, a novel inference framework that efficiently handles long contexts through a two-phase approach. First, it incrementally processes input chunks while maintaining a compressed KV cache, constructs cross-layer context embeddings, and utilizes early exit strategy for improved efficiency. Second, it identifies and gathers essential tokens via similarity matching and selectively recomputes the KV cache. Compared to baselines, REFORM achieves over 50% and 27% performance gains on RULER and BABILong respectively at 1M context length. It also outperforms baselines on Infinite-Bench and MM-NIAH, demonstrating flexibility across diverse tasks and domains. Additionally, REFORM reduces inference time by 30% and peak memory usage by 5%, achieving both efficiency and superior performance.

Fueled by their remarkable ability to tackle diverse tasks across multiple domains, large language models (LLMs) have grown at an unprecedented rate, with some recent models containing trillions of parameters. This growth is accompanied by substantial computational challenges, particularly regarding the memory and compute resources required for training and fine-tuning. Numerous approaches have been explored to address these issues, such as LoRA. While these methods are effective for fine-tuning, their application to pre-training is significantly more challenging due to the need to learn vast datasets. Motivated by this issue, we aim to address the following questions: Can parameter- or memory-efficient methods enhance pre-training efficiency while achieving performance comparable to full-model training? How can the performance gap be narrowed? To this end, the contributions of this work are the following. (1) We begin by conducting a comprehensive survey that summarizes state-of-the-art methods for efficient pre-training. (2) We perform a benchmark evaluation of several representative memory efficient pre-training approaches to comprehensively evaluate their performance across model sizes. We observe that with a proper choice of optimizer and hyperparameters, full-rank training delivers the best performance, as expected. We also notice that incorporating high-rank updates in low-rank approaches is the key to improving their performance. (3) Finally, we propose two practical techniques, namely weight refactorization and momentum reset, to enhance the performance of efficient pre-training methods. We observe that applying these techniques to the low-rank method (on a 1B model) can achieve a lower perplexity than popular memory efficient algorithms such as GaLore and Fira, while simultaneously using about 25% less memory.

Recent advances in large language models (LLMs) have significantly boosted long-context processing. However, the increasing key-value (KV) cache size poses critical challenges to memory and execution efficiency. Most KV cache compression methods rely on heuristic token eviction using all attention heads in Grouped Query Attention (GQA)-based LLMs. This method ignores the different functionalities of attention heads, leading to the eviction of critical tokens and thus degrades the performance of LLMs. To address the issue above, instead of using all the attention heads in GQA-based LLMs to determine important tokens as in the previous work, we first identify the attention heads in each layer that are not only capable of retrieving the initial and final tokens of a prompt, but also capable of retrieving important tokens within the text and attending to their surrounding semantic context. Afterwards, we exploit such heads to determine the important tokens and retain their corresponding KV cache pairs. Furthermore, we analyze the cache eviction error of each layer individually and introduce a layer-adaptive KV cache allocation strategy. Experimental results demonstrate the proposed CompressKV consistently outperforms state-of-the-art approaches under various memory budgets on LongBench and Needle-in-a-Haystack benchmarks. Our code is publicly available at: https://github.com/TUDa-HWAI/CompressKV.git.

Large Language Models (LLMs) have been widely deployed in a variety of applications, and the context length is rapidly increasing to handle tasks such as long-document QA and complex logical reasoning. However, long context poses significant challenges for inference efficiency, including high memory costs of key-value (KV) cache and increased latency due to extensive memory accesses. Recent works have proposed compressing KV cache to approximate computation, but these methods either evict tokens permanently, never recalling them for later inference, or recall previous tokens at the granularity of pages divided by textual positions. Both approaches degrade the model accuracy and output quality. To achieve efficient and accurate recallable KV cache compression, we introduce ClusterKV, which recalls tokens at the granularity of semantic clusters. We design and implement efficient algorithms and systems for clustering, selection, indexing and caching. Experiment results show that ClusterKV attains negligible accuracy loss across various tasks with 32k context lengths, using only a 1k to 2k KV cache budget, and achieves up to a 2times speedup in latency and a 2.5times improvement in decoding throughput. Compared to SoTA recallable KV compression methods, ClusterKV demonstrates higher model accuracy and output quality, while maintaining or exceeding inference efficiency.

While Key-Value (KV) cache succeeds in reducing redundant computations in auto-regressive models, it introduces significant memory overhead, limiting its practical deployment in long-sequence scenarios. Existing KV retrieval methods mitigate this by dynamically retaining only a subset of KV entries on the GPU. However, they still suffer from notable efficiency and accuracy bottlenecks due to per-token retrieval and coarse-grained page-level KV management, especially in long-output reasoning scenarios. With the emergence of large reasoning models, efficiently handling such scenarios has become increasingly important. To address this issue, we present two key observations: (1) critical KVs exhibit strong temporal locality during decoding, and (2) these KVs exhibit distinct distribution patterns across the input prompt and generated output. Building on these observations, we propose LouisKV, an efficient KV cache retrieval framework designed for various long-sequence scenarios. Specifically, LouisKV introduces a semantic-aware retrieval strategy leveraging temporal locality to trigger retrieval only at semantic boundaries, drastically reducing computation and data transfer overhead. LouisKV also designs a decoupled, fine-grained management scheme that tailors differentiated strategies for input and output sequences to create retrieval units that better match the model's attention patterns, enabling precise identification of critical KVs. Furthermore, to boost efficiency, LouisKV incorporates several kernel-level optimizations, including custom Triton and CUDA kernels to accelerate the KV clustering and retrieval. Evaluations show that LouisKV achieves up to 4.7times speedup over state-of-the-art KV retrieval methods while maintaining near-lossless accuracy across diverse long-sequence tasks, including long-input short-output, short-input long-output, and long-input long-output scenarios.

Memory is a fundamental component of AI systems, underpinning large language models (LLMs) based agents. While prior surveys have focused on memory applications with LLMs, they often overlook the atomic operations that underlie memory dynamics. In this survey, we first categorize memory representations into parametric, contextual structured, and contextual unstructured and then introduce six fundamental memory operations: Consolidation, Updating, Indexing, Forgetting, Retrieval, and Compression. We systematically map these operations to the most relevant research topics across long-term, long-context, parametric modification, and multi-source memory. By reframing memory systems through the lens of atomic operations and representation types, this survey provides a structured and dynamic perspective on research, benchmark datasets, and tools related to memory in AI, clarifying the functional interplay in LLMs based agents while outlining promising directions for future researchThe paper list, datasets, methods and tools are available at \href{https://github.com/Elvin-Yiming-Du/Survey_Memory_in_AI{https://github.com/Elvin-Yiming-Du/Survey\_Memory\_in\_AI}.}.

Large Language Models (LLMs) have become an essential infrastructure for Artificial General Intelligence (AGI), yet their lack of well-defined memory management systems hinders the development of long-context reasoning, continual personalization, and knowledge consistency.Existing models mainly rely on static parameters and short-lived contextual states, limiting their ability to track user preferences or update knowledge over extended periods.While Retrieval-Augmented Generation (RAG) introduces external knowledge in plain text, it remains a stateless workaround without lifecycle control or integration with persistent representations.Recent work has modeled the training and inference cost of LLMs from a memory hierarchy perspective, showing that introducing an explicit memory layer between parameter memory and external retrieval can substantially reduce these costs by externalizing specific knowledge. Beyond computational efficiency, LLMs face broader challenges arising from how information is distributed over time and context, requiring systems capable of managing heterogeneous knowledge spanning different temporal scales and sources. To address this challenge, we propose MemOS, a memory operating system that treats memory as a manageable system resource. It unifies the representation, scheduling, and evolution of plaintext, activation-based, and parameter-level memories, enabling cost-efficient storage and retrieval. As the basic unit, a MemCube encapsulates both memory content and metadata such as provenance and versioning. MemCubes can be composed, migrated, and fused over time, enabling flexible transitions between memory types and bridging retrieval with parameter-based learning. MemOS establishes a memory-centric system framework that brings controllability, plasticity, and evolvability to LLMs, laying the foundation for continual learning and personalized modeling.

Distribution shift (e.g., task or domain shift) in continual learning (CL) usually results in catastrophic forgetting of neural networks. Although it can be alleviated by repeatedly replaying buffered data, the every-step replay is time-consuming. In this paper, we study which modules in neural networks are more prone to forgetting by investigating their training dynamics during CL. Our proposed metrics show that only a few modules are more task-specific and sensitively alter between tasks, while others can be shared across tasks as common knowledge. Hence, we attribute forgetting mainly to the former and find that finetuning them only on a small buffer at the end of any CL method can bring non-trivial improvement. Due to the small number of finetuned parameters, such ``Forgetting Prioritized Finetuning (FPF)'' is efficient in computation. We further propose a more efficient and simpler method that entirely removes the every-step replay and replaces them by only k-times of FPF periodically triggered during CL. Surprisingly, this ``k-FPF'' performs comparably to FPF and outperforms the SOTA CL methods but significantly reduces their computational overhead and cost. In experiments on several benchmarks of class- and domain-incremental CL, FPF consistently improves existing CL methods by a large margin, and k-FPF further excels in efficiency without degrading the accuracy. We also empirically studied the impact of buffer size, epochs per task, and finetuning modules on the cost and accuracy of our methods.

Sequence modeling layers in modern language models typically face a trade-off between storage capacity and computational efficiency. While Softmax attention offers unbounded storage at prohibitive quadratic costs, linear variants provide efficiency but suffer from limited, fixed-size storage. We propose Fast-weight Product Key Memory (FwPKM), a novel architecture that resolves this tension by transforming the sparse Product Key Memory (PKM) from a static module into a dynamic, "fast-weight" episodic memory. Unlike PKM, FwPKM updates its parameters dynamically at both training and inference time via local chunk-level gradient descent, allowing the model to rapidly memorize and retrieve new key-value pairs from input sequences. Experiments reveal that FwPKM functions as an effective episodic memory that complements the semantic memory of standard modules, yielding significant perplexity reductions on long-context datasets. Notably, in Needle in a Haystack evaluations, FwPKM generalizes to 128K-token contexts despite being trained on only 4K-token sequences.

Retrieval augmentation is a powerful but expensive method to make language models more knowledgeable about the world. Memory-based methods like LUMEN pre-compute token representations for retrieved passages to drastically speed up inference. However, memory also leads to much greater storage requirements from storing pre-computed representations. We propose MEMORY-VQ, a new method to reduce storage requirements of memory-augmented models without sacrificing performance. Our method uses a vector quantization variational autoencoder (VQ-VAE) to compress token representations. We apply MEMORY-VQ to the LUMEN model to obtain LUMEN-VQ, a memory model that achieves a 16x compression rate with comparable performance on the KILT benchmark. LUMEN-VQ enables practical retrieval augmentation even for extremely large retrieval corpora.

Large language models (LLMs) power many state-of-the-art systems in natural language processing. However, these models are extremely computationally expensive, even at inference time, raising the natural question: when is the extra cost of deploying a larger model worth the anticipated boost in capabilities? Better understanding this tradeoff fundamentally could benefit from an inference efficiency metric that is both (i) easily comparable across models from different providers, and (ii) representative of the true cost of running queries in an isolated performance environment. Unfortunately, access to LLMs today is largely restricted to black-box text generation APIs and raw runtimes measured through this interface do not satisfy these desiderata: model providers can apply various software and hardware optimizations orthogonal to the model, and models served on shared infrastructure are susceptible to performance contention. To circumvent these problems, we propose a new metric for comparing inference efficiency across models. This metric puts models on equal footing as though they were served (i) on uniform hardware and software, and (ii) without performance contention. We call this metric the idealized runtime, and we propose a methodology to efficiently estimate this metric for autoregressive Transformer models. We also propose cost-aware variants that incorporate the number of accelerators needed to serve the model. Using these metrics, we compare ten state-of-the-art LLMs to provide the first analysis of inference efficiency-capability tradeoffs; we make several observations from this analysis, including the fact that the superior inference runtime performance of certain APIs is often a byproduct of optimizations within the API rather than the underlying model. Our methodology also facilitates the efficient comparison of different software and hardware stacks.

The increasing context window size in Large Language Models (LLMs), such as the GPT and LLaMA series, has improved their ability to tackle complex, long-text tasks, but at the cost of inference efficiency, particularly regarding memory and computational complexity. Existing methods, including selective token retention and window-based attention, improve efficiency but risk discarding important tokens needed for future text generation. In this paper, we propose an approach that enhances LLM efficiency without token loss by reducing the memory and computational load of less important tokens, rather than discarding them.We address two challenges: 1) investigating the distribution of important tokens in the context, discovering recent tokens are more important than distant tokens in context, and 2) optimizing resources for distant tokens by sharing attention scores across layers. The experiments show that our method saves 35% KV cache without compromising the performance.

Linear sequence modeling methods, such as linear attention, state space modeling, and linear RNNs, offer significant efficiency improvements by reducing the complexity of training and inference. However, these methods typically compress the entire input sequence into a single fixed-size memory state, which leads to suboptimal performance on recall-intensive downstream tasks. Drawing inspiration from neuroscience, particularly the brain's ability to maintain robust long-term memory while mitigating "memory interference", we introduce a novel architecture called Mixture-of-Memories (MoM). MoM utilizes multiple independent memory states, with a router network directing input tokens to specific memory states. This approach greatly enhances the overall memory capacity while minimizing memory interference. As a result, MoM performs exceptionally well on recall-intensive tasks, surpassing existing linear sequence modeling techniques. Despite incorporating multiple memory states, the computation of each memory state remains linear in complexity, allowing MoM to retain the linear-complexity advantage during training, while constant-complexity during inference. Our experimental results show that MoM significantly outperforms current linear sequence models on downstream language tasks, particularly recall-intensive tasks, and even achieves performance comparable to Transformer models. The code is released at https://github.com/OpenSparseLLMs/MoM and is also released as a part of https://github.com/OpenSparseLLMs/Linear-MoE.

Large Language Models (LLMs) exhibit enhanced reasoning capabilities by employing Chain-of-Thought (CoT). However, the extended reasoning sequences introduce significant GPU memory overhead due to increased key-value (KV) cache size, particularly in tasks requiring long reasoning sequences, such as mathematics and programming. Existing KV cache compression methods mitigate memory bottlenecks but struggle in long reasoning tasks. In this paper, we analyze attention patterns in reasoning tasks and reveal a Token Importance Recurrence phenomenon: a large proportion of tokens receive renewed attention after multiple decoding steps, which is failed to capture by existing works and may lead to unpredictable eviction on such periodically critical tokens. To address this, we propose LazyEviction, a lagged KV eviction framework designed to maintain reasoning performance while reducing KV memory. LazyEviction is an Observation Window-based Lagged Eviction Mechanism retaining latent recurring tokens by performing lagged evictions across decoding steps, which contains two key components: (1) Recurrence Interval Tracking for capturing temporal variations in token importance, and (2) an Maximum Recurrence Interval-Centric Eviction Policy that prioritizes eviction based on tokens' recurrence patterns. Extensive experiments demonstrate that LazyEviction reduces KV cache size by 50% while maintaining comparable accuracy on mathematics reasoning datasets, outperforming state-of-the-art methods. Our findings highlight the importance of preserving recurring tokens, which are critical for maintaining knowledge continuity in multi-step reasoning tasks.

Long-range tasks require reasoning over long inputs. Existing solutions either need large compute budgets, training data, access to model weights, or use complex, task-specific approaches. We present PRISM, which alleviates these concerns by processing information as a stream of chunks, maintaining a structured in-context memory specified by a typed hierarchy schema. This approach demonstrates superior performance to baselines on diverse tasks while using at least 4x smaller contexts than long-context models. Moreover, PRISM is token-efficient. By producing short outputs and efficiently leveraging key-value (KV) caches, it achieves up to 54% cost reduction when compared to alternative short-context approaches. The method also scales down to tiny information chunks (e.g., 500 tokens) without increasing the number of tokens encoded or sacrificing quality. Furthermore, we show that it is possible to generate schemas to generalize our approach to new tasks with minimal effort.

Efficient use of GPU memory is essential for high throughput LLM inference. Prior systems reserved memory for the KV-cache ahead-of-time, resulting in wasted capacity due to internal fragmentation. Inspired by OS-based virtual memory systems, vLLM proposed PagedAttention to enable dynamic memory allocation for KV-cache. This approach eliminates fragmentation, enabling high-throughput LLM serving with larger batch sizes. However, to be able to allocate physical memory dynamically, PagedAttention changes the layout of KV-cache from contiguous virtual memory to non-contiguous virtual memory. This change requires attention kernels to be rewritten to support paging, and serving framework to implement a memory manager. Thus, the PagedAttention model leads to software complexity, portability issues, redundancy and inefficiency. In this paper, we propose vAttention for dynamic KV-cache memory management. In contrast to PagedAttention, vAttention retains KV-cache in contiguous virtual memory and leverages low-level system support for demand paging, that already exists, to enable on-demand physical memory allocation. Thus, vAttention unburdens the attention kernel developer from having to explicitly support paging and avoids re-implementation of memory management in the serving framework. We show that vAttention enables seamless dynamic memory management for unchanged implementations of various attention kernels. vAttention also generates tokens up to 1.97x faster than vLLM, while processing input prompts up to 3.92x and 1.45x faster than the PagedAttention variants of FlashAttention and FlashInfer.

To support reliable long-term interaction in complex environments, LLM agents require memory systems that efficiently manage historical experiences. Existing approaches either retain full interaction histories via passive context extension, leading to substantial redundancy, or rely on iterative reasoning to filter noise, incurring high token costs. To address this challenge, we introduce SimpleMem, an efficient memory framework based on semantic lossless compression. We propose a three-stage pipeline designed to maximize information density and token utilization: (1) Semantic Structured Compression, which applies entropy-aware filtering to distill unstructured interactions into compact, multi-view indexed memory units; (2) Recursive Memory Consolidation, an asynchronous process that integrates related units into higher-level abstract representations to reduce redundancy; and (3) Adaptive Query-Aware Retrieval, which dynamically adjusts retrieval scope based on query complexity to construct precise context efficiently. Experiments on benchmark datasets show that our method consistently outperforms baseline approaches in accuracy, retrieval efficiency, and inference cost, achieving an average F1 improvement of 26.4% while reducing inference-time token consumption by up to 30-fold, demonstrating a superior balance between performance and efficiency. Code is available at https://github.com/aiming-lab/SimpleMem.

Large language model (LLM) inference is computation and memory intensive, so we adapt lexical shortlisting to it hoping to improve both. While lexical shortlisting is well-explored in tasks like machine translation, it requires modifications before being suitable for LLMs as the intended applications vary significantly. Our work studies two heuristics to shortlist sub-vocabulary at LLM inference time: Unicode-based script filtering and corpus-based selection. We explore different LLM families and sizes, and we find that lexical shortlisting can reduce the memory usage of some models by nearly 50\% and has an upper bound of 25\% improvement in generation speed. In this pilot study, we also identify the drawbacks of such vocabulary selection methods and propose avenues for future research.

The escalating demand for long-context applications has intensified the necessity of extending the LLM context windows. Despite recent fine-tuning approaches successfully expanding context lengths, their high memory footprints, especially for activations, present a critical practical limitation. Current parameter-efficient fine-tuning methods prioritize reducing parameter update overhead over addressing activation memory constraints. Similarly, existing sparsity mechanisms improve computational efficiency but overlook activation memory optimization due to the phenomenon of Shadowy Activation. In this paper, we propose LeMo, the first LLM fine-tuning system that explores and exploits a new token-level sparsity mechanism inherent in long-context scenarios, termed Contextual Token Sparsity. LeMo minimizes redundant token involvement by assessing the informativeness of token embeddings while preserving model accuracy. Specifically, LeMo introduces three key techniques: (1) Token Elimination, dynamically identifying and excluding redundant tokens across varying inputs and layers. (2) Pattern Prediction, utilizing well-trained predictors to approximate token sparsity patterns with minimal overhead. (3) Kernel Optimization, employing permutation-free and segment-based strategies to boost system performance. We implement LeMo as an end-to-end fine-tuning system compatible with various LLM architectures and other optimization techniques. Comprehensive evaluations demonstrate that LeMo reduces memory consumption by up to 1.93x and achieves up to 1.36x speedups, outperforming state-of-the-art fine-tuning systems.

Adaptive gradient methods, such as Adam and LAMB, have demonstrated excellent performance in the training of large language models. Nevertheless, the need for adaptivity requires maintaining second-moment estimates of the per-parameter gradients, which entails a high cost of extra memory overheads. To solve this problem, several memory-efficient optimizers (e.g., Adafactor) have been proposed to obtain a drastic reduction in auxiliary memory usage, but with a performance penalty. In this paper, we first study a confidence-guided strategy to reduce the instability of existing memory efficient optimizers. Based on this strategy, we propose CAME to simultaneously achieve two goals: fast convergence as in traditional adaptive methods, and low memory usage as in memory-efficient methods. Extensive experiments demonstrate the training stability and superior performance of CAME across various NLP tasks such as BERT and GPT-2 training. Notably, for BERT pre-training on the large batch size of 32,768, our proposed optimizer attains faster convergence and higher accuracy compared with the Adam optimizer. The implementation of CAME is publicly available.

Efficient attentions have greatly improved the computational efficiency of Transformers. However, most existing linear attention mechanisms suffer from an efficiency degradation problem, leading to inefficiencies in causal language modeling and hindering their application in long-range language models. This problem is more pronounced under language modeling with unbounded contexts. In this paper, we propose Linear Attention Via Orthogonal memory~(\shortname) to address these limitations, achieving strong performance while maintaining linear complexity. \shortname employs orthogonal decomposition to compress a context into a fixed-size orthogonal memory while effectively minimizing redundancy within the context. Given that orthogonal memory compresses global information, we further dissect the context to amplify fine-grained local information. Additionally, we embed the relative position encoding into \shortname to improve the extrapolation ability. Experimental results show that \shortname greatly improves the efficiency of the causal language model with the best extrapolation performance and outperforms other efficient baselines. Further, we endeavor to employ \shortname for unbounded language modeling and successfully scale the context length to 128K.

Transformers have reached remarkable success in sequence modeling. However, these models have efficiency issues as they need to store all the history token-level representations as memory. We present Memformer, an efficient neural network for sequence modeling, that utilizes an external dynamic memory to encode and retrieve past information. Our model achieves linear time complexity and constant memory space complexity when processing long sequences. We also propose a new optimization scheme, memory replay back-propagation (MRBP), which promotes long-range back-propagation through time with a significantly reduced memory requirement. Experimental results show that Memformer has achieved comparable performance compared to the baselines by using 8.1x less memory space and 3.2x faster on inference. Analysis of the attention pattern shows that our external memory slots can encode and retain important information through timesteps.

This paper examines memory mechanisms in Large Language Models (LLMs), emphasizing their importance for context-rich responses, reduced hallucinations, and improved efficiency. It categorizes memory into sensory, short-term, and long-term, with sensory memory corresponding to input prompts, short-term memory processing immediate context, and long-term memory implemented via external databases or structures. The text-based memory section covers acquisition (selection and summarization), management (updating, accessing, storing, and resolving conflicts), and utilization (full-text search, SQL queries, semantic search). The KV cache-based memory section discusses selection methods (regularity-based summarization, score-based approaches, special token embeddings) and compression techniques (low-rank compression, KV merging, multimodal compression), along with management strategies like offloading and shared attention mechanisms. Parameter-based memory methods (LoRA, TTT, MoE) transform memories into model parameters to enhance efficiency, while hidden-state-based memory approaches (chunk mechanisms, recurrent transformers, Mamba model) improve long-text processing by combining RNN hidden states with current methods. Overall, the paper offers a comprehensive analysis of LLM memory mechanisms, highlighting their significance and future research directions.

Retrieval-Augmented Generation (RAG) is often used with Large Language Models (LLMs) to infuse domain knowledge or user-specific information. In RAG, given a user query, a retriever extracts chunks of relevant text from a knowledge base. These chunks are sent to an LLM as part of the input prompt. Typically, any given chunk is repeatedly retrieved across user questions. However, currently, for every question, attention-layers in LLMs fully compute the key values (KVs) repeatedly for the input chunks, as state-of-the-art methods cannot reuse KV-caches when chunks appear at arbitrary locations with arbitrary contexts. Naive reuse leads to output quality degradation. This leads to potentially redundant computations on expensive GPUs and increases latency. In this work, we propose Cache-Craft, a system for managing and reusing precomputed KVs corresponding to the text chunks (we call chunk-caches) in RAG-based systems. We present how to identify chunk-caches that are reusable, how to efficiently perform a small fraction of recomputation to fix the cache to maintain output quality, and how to efficiently store and evict chunk-caches in the hardware for maximizing reuse while masking any overheads. With real production workloads as well as synthetic datasets, we show that Cache-Craft reduces redundant computation by 51% over SOTA prefix-caching and 75% over full recomputation. Additionally, with continuous batching on a real production workload, we get a 1.6X speed up in throughput and a 2X reduction in end-to-end response latency over prefix-caching while maintaining quality, for both the LLaMA-3-8B and LLaMA-3-70B models.

Large Language Models (LLMs) are difficult to fully fine-tune (e.g., with instructions or human feedback) due to their sheer number of parameters. A family of parameter-efficient sparse fine-tuning (SFT) methods have proven promising in terms of performance but their memory requirements increase proportionally to the size of the LLMs. In this work, we scale sparse fine-tuning to state-of-the-art LLMs like LLaMA 2 7B and 13B. At any given time, for a desired density level, we maintain an array of parameter indices and the deltas of these parameters relative to their pretrained values. We iterate among: (a) updating the active deltas, (b) pruning indices (based on the change of magnitude of their deltas) and (c) regrowth of indices. For regrowth, we explore two criteria based on either the accumulated gradients of a few candidate parameters or their approximate momenta estimated using the efficient SM3 optimizer. We experiment with instruction-tuning of LLMs on standard dataset mixtures, finding that SFT is often superior to popular parameter-efficient fine-tuning methods like LoRA (low-rank adaptation) in terms of performance and comparable in terms of run time. We additionally show that SFT is compatible with both quantization and efficient optimizers, to facilitate scaling to ever-larger model sizes. We release the code for SFT at https://github.com/AlanAnsell/peft and for the instruction-tuning experiments at https://github.com/ducdauge/sft-llm.

Over more than a decade there has been an extensive research effort on how to effectively utilize recurrent models and attention. While recurrent models aim to compress the data into a fixed-size memory (called hidden state), attention allows attending to the entire context window, capturing the direct dependencies of all tokens. This more accurate modeling of dependencies, however, comes with a quadratic cost, limiting the model to a fixed-length context. We present a new neural long-term memory module that learns to memorize historical context and helps attention to attend to the current context while utilizing long past information. We show that this neural memory has the advantage of fast parallelizable training while maintaining a fast inference. From a memory perspective, we argue that attention due to its limited context but accurate dependency modeling performs as a short-term memory, while neural memory due to its ability to memorize the data, acts as a long-term, more persistent, memory. Based on these two modules, we introduce a new family of architectures, called Titans, and present three variants to address how one can effectively incorporate memory into this architecture. Our experimental results on language modeling, common-sense reasoning, genomics, and time series tasks show that Titans are more effective than Transformers and recent modern linear recurrent models. They further can effectively scale to larger than 2M context window size with higher accuracy in needle-in-haystack tasks compared to baselines.

Nearly all real world tasks are inherently partially observable, necessitating the use of memory in Reinforcement Learning (RL). Most model-free approaches summarize the trajectory into a latent Markov state using memory models borrowed from Supervised Learning (SL), even though RL tends to exhibit different training and efficiency characteristics. Addressing this discrepancy, we introduce Fast and Forgetful Memory, an algorithm-agnostic memory model designed specifically for RL. Our approach constrains the model search space via strong structural priors inspired by computational psychology. It is a drop-in replacement for recurrent neural networks (RNNs) in recurrent RL algorithms, achieving greater reward than RNNs across various recurrent benchmarks and algorithms without changing any hyperparameters. Moreover, Fast and Forgetful Memory exhibits training speeds two orders of magnitude faster than RNNs, attributed to its logarithmic time and linear space complexity. Our implementation is available at https://github.com/proroklab/ffm.

Recently, large vision-language models (LVLMs) have rapidly gained popularity for their strong generation and reasoning capabilities given diverse multimodal inputs. However, these models incur significant computational and memory overhead during inference, which greatly hinders the efficient deployment in practical scenarios. The extensive key-value (KV) cache, necessitated by the lengthy input and output sequences, notably contributes to the high inference cost. Based on this, recent works have investigated ways to reduce the KV cache size for higher efficiency. Although effective, they generally overlook the distinct importance distributions of KV vectors across layers and maintain the same cache size for each layer during the next token prediction. This results in the significant contextual information loss for certain layers, leading to notable performance decline. To address this, we present PrefixKV. It reframes the challenge of determining KV cache sizes for all layers into the task of searching for the optimal global prefix configuration. With an adaptive layer-wise KV retention recipe based on binary search, the maximum contextual information can thus be preserved in each layer, facilitating the generation. Extensive experiments demonstrate that our method achieves the state-of-the-art performance compared with others. It exhibits superior inference efficiency and generation quality trade-offs, showing promising potential for practical applications. Code is available at https://github.com/THU-MIG/PrefixKV.

Scaling the context length of large language models (LLMs) offers significant benefits but is computationally expensive. This expense stems primarily from the self-attention mechanism, whose O(N^2) complexity with respect to sequence length presents a major bottleneck for both memory and latency. Fortunately, the attention matrix is often sparse, particularly for long sequences, suggesting an opportunity for optimization. Block-sparse attention has emerged as a promising solution that partitions sequences into blocks and skips computation for a subset of these blocks. However, the effectiveness of this method is highly dependent on the underlying attention patterns, which can lead to sub-optimal block-level sparsity. For instance, important key tokens for queries within a single block may be scattered across numerous other blocks, leading to computational redundancy. In this work, we propose Permuted Block-Sparse Attention (PBS-Attn), a plug-and-play method that leverages the permutation properties of attention to increase block-level sparsity and enhance the computational efficiency of LLM prefilling. We conduct comprehensive experiments on challenging real-world long-context datasets, demonstrating that PBS-Attn consistently outperforms existing block-sparse attention methods in model accuracy and closely matches the full attention baseline. Powered by our custom permuted-FlashAttention kernels, PBS-Attn achieves an end-to-end speedup of up to 2.75times in long-context prefilling, confirming its practical viability. Code available at https://github.com/xinghaow99/pbs-attn

As the demand for long-context large language models (LLMs) increases, models with context windows of up to 128K or 1M tokens are becoming increasingly prevalent. However, long-context LLM inference is challenging since the inference speed decreases significantly as the sequence length grows. This slowdown is primarily caused by loading a large KV cache during self-attention. Previous works have shown that a small portion of critical tokens will dominate the attention outcomes. However, we observe the criticality of a token highly depends on the query. To this end, we propose Quest, a query-aware KV cache selection algorithm. Quest keeps track of the minimal and maximal Key values in KV cache pages and estimates the criticality of a given page using Query vectors. By only loading the Top-K critical KV cache pages for attention, Quest significantly speeds up self-attention without sacrificing accuracy. We show that Quest can achieve up to 2.23x self-attention speedup, which reduces inference latency by 7.03x while performing well on tasks with long dependencies with negligible accuracy loss. Code is available at http://github.com/mit-han-lab/Quest .

Key-Value (KV) cache has become a bottleneck of LLMs for long-context generation. Despite the numerous efforts in this area, the optimization for the decoding phase is generally ignored. However, we believe such optimization is crucial, especially for long-output generation tasks based on the following two observations: (i) Excessive compression during the prefill phase, which requires specific full context impairs the comprehension of the reasoning task; (ii) Deviation of heavy hitters occurs in the reasoning tasks with long outputs. Therefore, SCOPE, a simple yet efficient framework that separately performs KV cache optimization during the prefill and decoding phases, is introduced. Specifically, the KV cache during the prefill phase is preserved to maintain the essential information, while a novel strategy based on sliding is proposed to select essential heavy hitters for the decoding phase. Memory usage and memory transfer are further optimized using adaptive and discontinuous strategies. Extensive experiments on LongGenBench show the effectiveness and generalization of SCOPE and its compatibility as a plug-in to other prefill-only KV compression methods.

Memory layers use a trainable key-value lookup mechanism to add extra parameters to a model without increasing FLOPs. Conceptually, sparsely activated memory layers complement compute-heavy dense feed-forward layers, providing dedicated capacity to store and retrieve information cheaply. This work takes memory layers beyond proof-of-concept, proving their utility at contemporary scale. On downstream tasks, language models augmented with our improved memory layer outperform dense models with more than twice the computation budget, as well as mixture-of-expert models when matched for both compute and parameters. We find gains are especially pronounced for factual tasks. We provide a fully parallelizable memory layer implementation, demonstrating scaling laws with up to 128B memory parameters, pretrained to 1 trillion tokens, comparing to base models with up to 8B parameters.

Efficiency is a key property to foster inclusiveness and reduce environmental costs, especially in an era of LLMs. In this work, we provide a comprehensive evaluation of efficiency for MT evaluation metrics. Our approach involves replacing computation-intensive transformers with lighter alternatives and employing linear and quadratic approximations for alignment algorithms on top of LLM representations. We evaluate six (reference-free and reference-based) metrics across three MT datasets and examine 16 lightweight transformers. In addition, we look into the training efficiency of metrics like COMET by utilizing adapters. Our results indicate that (a) TinyBERT provides the optimal balance between quality and efficiency, (b) CPU speed-ups are more substantial than those on GPU; (c) WMD approximations yield no efficiency gains while reducing quality and (d) adapters enhance training efficiency (regarding backward pass speed and memory requirements) as well as, in some cases, metric quality. These findings can help to strike a balance between evaluation speed and quality, which is essential for effective NLG systems. Furthermore, our research contributes to the ongoing efforts to optimize NLG evaluation metrics with minimal impact on performance. To our knowledge, ours is the most comprehensive analysis of different aspects of efficiency for MT metrics conducted so far.

In this paper, we present an efficient method for storing fine-tuned models by leveraging the low-rank properties of weight residuals. Our key observation is that weight residuals in large overparameterized models exhibit even stronger low-rank characteristics. Based on this insight, we propose Efficient Residual Encoding (ERE), a novel approach that achieves efficient storage of fine-tuned model weights by approximating the low-rank weight residuals. Furthermore, we analyze the robustness of weight residuals and push the limit of storage efficiency by utilizing additional quantization and layer-wise rank allocation. Our experimental results demonstrate that our method significantly reduces memory footprint while preserving performance in various tasks and modalities. We release our code.

With the widespread deployment of long-context large language models (LLMs), there has been a growing demand for efficient support of high-throughput inference. However, as the key-value (KV) cache expands with the sequence length, the increasing memory footprint and the need to access it for each token generation both result in low throughput when serving long-context LLMs. While various dynamic sparse attention methods have been proposed to speed up inference while maintaining generation quality, they either fail to sufficiently reduce GPU memory consumption or introduce significant decoding latency by offloading the KV cache to the CPU. We present ShadowKV, a high-throughput long-context LLM inference system that stores the low-rank key cache and offloads the value cache to reduce the memory footprint for larger batch sizes and longer sequences. To minimize decoding latency, ShadowKV employs an accurate KV selection strategy that reconstructs minimal sparse KV pairs on-the-fly. By evaluating ShadowKV on a broad range of benchmarks, including RULER, LongBench, and Needle In A Haystack, and models like Llama-3.1-8B, Llama-3-8B-1M, GLM-4-9B-1M, Yi-9B-200K, Phi-3-Mini-128K, and Qwen2-7B-128K, we demonstrate that it can support up to 6times larger batch sizes and boost throughput by up to 3.04times on an A100 GPU without sacrificing accuracy, even surpassing the performance achievable with infinite batch size under the assumption of infinite GPU memory. The code is available at https://github.com/bytedance/ShadowKV.

Fine-tuning large language models (LLMs) with parameter-efficient techniques such as LoRA and QLoRA has enabled adaptation of foundation models on modest hardware. Yet the efficiency of such training on consumer-grade GPUs, especially under strict 8 GB VRAM limits, remains underexplored. We present a controlled profiling study of LoRA/QLoRA fine-tuning using the Qwen2.5-1.5B-Instruct model on a single NVIDIA RTX 4060. Across three representative configurations, we systematically vary batch size, sequence length, optimizer choice (AdamW vs. PagedAdamW), and precision (fp16 vs. bf16). We report throughput (tokens/s), time per 10k tokens, and VRAM footprint, alongside energy estimates derived from GPU board power limits. Our results show that paged optimizers improve throughput by up to 25% (628 tok/s vs. 500 tok/s baseline), while bf16 degrades efficiency relative to fp16. Despite 8 GB constraints, sequence lengths up to 2048 tokens were feasible using parameter-efficient strategies. To our knowledge, this is the first systematic case study of LLM fine- tuning efficiency on consumer GPUs, providing reproducible benchmarks and practical guidelines for resource-constrained researchers and practitioners.

We describe a family of architectures to support transductive inference by allowing memory to grow to a finite but a-priori unknown bound while making efficient use of finite resources for inference. Current architectures use such resources to represent data either eidetically over a finite span ("context" in Transformers), or fading over an infinite span (in State Space Models, or SSMs). Recent hybrid architectures have combined eidetic and fading memory, but with limitations that do not allow the designer or the learning process to seamlessly modulate the two, nor to extend the eidetic memory span. We leverage ideas from Stochastic Realization Theory to develop a class of models called B'MOJO to seamlessly combine eidetic and fading memory within an elementary composable module. The overall architecture can be used to implement models that can access short-term eidetic memory "in-context," permanent structural memory "in-weights," fading memory "in-state," and long-term eidetic memory "in-storage" by natively incorporating retrieval from an asynchronously updated memory. We show that Transformers, existing SSMs such as Mamba, and hybrid architectures such as Jamba are special cases of B'MOJO and describe a basic implementation, to be open sourced, that can be stacked and scaled efficiently in hardware. We test B'MOJO on transductive inference tasks, such as associative recall, where it outperforms existing SSMs and Hybrid models; as a baseline, we test ordinary language modeling where B'MOJO achieves perplexity comparable to similarly-sized Transformers and SSMs up to 1.4B parameters, while being up to 10% faster to train. Finally, we show that B'MOJO's ability to modulate eidetic and fading memory results in better inference on longer sequences tested up to 32K tokens, four-fold the length of the longest sequences seen during training.

The maximum supported context length is a critical bottleneck limiting the practical application of the Large Language Model (LLM). Although existing length extrapolation methods can extend the context of LLMs to millions of tokens, these methods all have an explicit upper bound. In this work, we propose LongCache, a training-free approach that enables LLM to support an infinite context with finite context scope, through full-context cache selection and training-free integration. This effectively frees LLMs from the length extrapolation issue. We validate LongCache on the LongBench and L-Eval and demonstrate its performance is on par with traditional full-attention mechanisms. Furthermore, we have applied LongCache on mainstream LLMs, including LLaMA3 and Mistral-v0.3, enabling them to support context lengths of at least 400K in Needle-In-A-Haystack tests. We will improve the efficiency of LongCache by GPU-aware optimization soon.

Nowadays, Large Language Models (LLMs) have been trained using extended context lengths to foster more creative applications. However, long context training poses great challenges considering the constraint of GPU memory. It not only leads to substantial activation memory consumption during training, but also incurs considerable memory fragmentation. To facilitate long context training, existing frameworks have adopted strategies such as recomputation and various forms of parallelisms. Nevertheless, these techniques rely on redundant computation or extensive communication, resulting in low Model FLOPS Utilization (MFU). In this paper, we propose MEMO, a novel LLM training framework designed for fine-grained activation memory management. Given the quadratic scaling of computation and linear scaling of memory with sequence lengths when using FlashAttention, we offload memory-consuming activations to CPU memory after each layer's forward pass and fetch them during the backward pass. To maximize the swapping of activations without hindering computation, and to avoid exhausting limited CPU memory, we implement a token-wise activation recomputation and swapping mechanism. Furthermore, we tackle the memory fragmentation issue by employing a bi-level Mixed Integer Programming (MIP) approach, optimizing the reuse of memory across transformer layers. Empirical results demonstrate that MEMO achieves an average of 2.42x and 2.26x MFU compared to Megatron-LM and DeepSpeed, respectively. This improvement is attributed to MEMO's ability to minimize memory fragmentation, reduce recomputation and intensive communication, and circumvent the delays associated with the memory reorganization process due to fragmentation. By leveraging fine-grained activation memory management, MEMO facilitates efficient training of 7B LLM with 1 million sequence length on just 8 A800 GPUs, achieving an MFU of 52.30%.

Recent advances in large language models (LLMs) have showcased exceptional performance in long-context tasks, while facing significant inference efficiency challenges with limited GPU memory. Existing solutions first proposed the sliding-window approach to accumulate a set of historical key-value (KV) pairs for reuse, then further improvements selectively retain its subsets at each step. However, due to the sparse attention distribution across a long context, it is hard to identify and recall relevant KV pairs, as the attention is distracted by massive candidate pairs. Additionally, we found it promising to select representative tokens as probe-Query in each sliding window to effectively represent the entire context, which is an approach overlooked by existing methods. Thus, we propose ActQKV, a training-free, Activation-aware approach that dynamically determines probe-Query and leverages it to retrieve the relevant KV pairs for inference. Specifically, ActQKV monitors a token-level indicator, Activation Bias, within each context window, enabling the proper construction of probe-Query for retrieval at pre-filling stage. To accurately recall the relevant KV pairs and minimize the irrelevant ones, we design a dynamic KV cut-off mechanism guided by information density across layers at the decoding stage. Experiments on the Long-Bench and infty Benchmarks demonstrate its state-of-the-art performance with competitive inference quality and resource efficiency.

While inference-time scaling enables LLMs to carry out increasingly long and capable reasoning traces, the patterns and insights uncovered during these traces are immediately discarded once the context window is reset for a new query. External memory is a natural way to persist these discoveries, and recent work has shown clear benefits for reasoning-intensive tasks. We see an opportunity to make such memories more broadly reusable and scalable by moving beyond instance-based memory entries (e.g. exact query/response pairs, or summaries tightly coupled with the original problem context) toward concept-level memory: reusable, modular abstractions distilled from solution traces and stored in natural language. For future queries, relevant concepts are selectively retrieved and integrated into the prompt, enabling test-time continual learning without weight updates. Our design introduces new strategies for abstracting takeaways from rollouts and retrieving entries for new queries, promoting reuse and allowing memory to expand with additional experiences. We evaluate on ARC-AGI, a benchmark that stresses compositional generalization and abstract reasoning, making it a natural fit for concept memory. Our method yields a 7.5% relative gain over a strong no-memory baseline with performance continuing to scale with inference compute. We find abstract concepts to be the most consistent memory design, outscoring the baseline at all tested inference compute scales. Moreover, dynamically updating memory during test-time outperforms fixed settings, supporting the hypothesis that accumulating and abstracting patterns enables further solutions in a form of self-improvement. Code is available at https://github.com/matt-seb-ho/arc_memo.

Most state-of-the-art open-domain question answering systems use a neural retrieval model to encode passages into continuous vectors and extract them from a knowledge source. However, such retrieval models often require large memory to run because of the massive size of their passage index. In this paper, we introduce Binary Passage Retriever (BPR), a memory-efficient neural retrieval model that integrates a learning-to-hash technique into the state-of-the-art Dense Passage Retriever (DPR) to represent the passage index using compact binary codes rather than continuous vectors. BPR is trained with a multi-task objective over two tasks: efficient candidate generation based on binary codes and accurate reranking based on continuous vectors. Compared with DPR, BPR substantially reduces the memory cost from 65GB to 2GB without a loss of accuracy on two standard open-domain question answering benchmarks: Natural Questions and TriviaQA. Our code and trained models are available at https://github.com/studio-ousia/bpr.

State-of-the-art video object detection methods maintain a memory structure, either a sliding window or a memory queue, to enhance the current frame using attention mechanisms. However, we argue that these memory structures are not efficient or sufficient because of two implied operations: (1) concatenating all features in memory for enhancement, leading to a heavy computational cost; (2) frame-wise memory updating, preventing the memory from capturing more temporal information. In this paper, we propose a multi-level aggregation architecture via memory bank called MAMBA. Specifically, our memory bank employs two novel operations to eliminate the disadvantages of existing methods: (1) light-weight key-set construction which can significantly reduce the computational cost; (2) fine-grained feature-wise updating strategy which enables our method to utilize knowledge from the whole video. To better enhance features from complementary levels, i.e., feature maps and proposals, we further propose a generalized enhancement operation (GEO) to aggregate multi-level features in a unified manner. We conduct extensive evaluations on the challenging ImageNetVID dataset. Compared with existing state-of-the-art methods, our method achieves superior performance in terms of both speed and accuracy. More remarkably, MAMBA achieves mAP of 83.7/84.6% at 12.6/9.1 FPS with ResNet-101. Code is available at https://github.com/guanxiongsun/video_feature_enhancement.

Pipeline parallelism has been widely explored, but most existing schedules lack a systematic methodology. In this paper, we propose a framework to decompose pipeline schedules as repeating a building block and we show that the lifespan of the building block decides the peak activation memory of the pipeline schedule. Guided by the observations, we find that almost all existing pipeline schedules, to the best of our knowledge, are memory inefficient. To address this, we introduce a family of memory efficient building blocks with controllable activation memory, which can reduce the peak activation memory to 1/2 of 1F1B without sacrificing efficiency, and even to 1/3 with comparable throughput. We can also achieve almost zero pipeline bubbles while maintaining the same activation memory as 1F1B. Our evaluations demonstrate that in pure pipeline parallelism settings, our methods outperform 1F1B by from 7% to 55% in terms of throughput. When employing a grid search over hybrid parallelism hyperparameters in practical scenarios, our proposed methods demonstrate a 16% throughput improvement over the 1F1B baseline for large language models.

Engineering efficient implementations of compact and succinct structures is a time-consuming and challenging task, since there is no standard library of easy-to- use, highly optimized, and composable components. One consequence is that measuring the practical impact of new theoretical proposals is a difficult task, since older base- line implementations may not rely on the same basic components, and reimplementing from scratch can be very time-consuming. In this paper we present a framework for experimentation with succinct data structures, providing a large set of configurable components, together with tests, benchmarks, and tools to analyze resource requirements. We demonstrate the functionality of the framework by recomposing succinct solutions for document retrieval.

This work explores the challenge of building ``Machines that Can Remember'', framing long-term memory as the problem of efficient ultra-long context modeling. We argue that this requires three key properties: sparsity, random-access flexibility, and length generalization. To address ultra-long-context modeling, we leverage Hierarchical Sparse Attention (HSA), a novel attention mechanism that satisfies all three properties. We integrate HSA into Transformers to build HSA-UltraLong, which is an 8B-parameter MoE model trained on over 8 trillion tokens and is rigorously evaluated on different tasks with in-domain and out-of-domain context lengths to demonstrate its capability in handling ultra-long contexts. Results show that our model performs comparably to full-attention baselines on in-domain lengths while achieving over 90\% accuracy on most in-context retrieval tasks with contexts up to 16M. This report outlines our experimental insights and open problems, contributing a foundation for future research in ultra-long context modeling.

Generating long sequences of tokens given a long-context input imposes a heavy computational burden for large language models (LLMs). One of the computational bottleneck comes from computing attention over a long sequence of input at each generation step. In this paper, we propose Recycled Attention, an inference-time method which alternates between full context attention and attention over a subset of input tokens. When performing partial attention, we recycle the attention pattern of a previous token that has performed full attention and attend only to the top K most attended tokens, reducing the cost of data movement and attention computation. Compared to previously proposed inference-time acceleration method which attends only to local context or tokens with high accumulative attention scores, our approach flexibly chooses tokens that are relevant to the current decoding step. We evaluate our methods on RULER, a suite of tasks designed to comprehensively evaluate long-context abilities, and long-context language modeling tasks. Applying our method to off-the-shelf LLMs achieves comparable speedup to baselines which only consider local context while improving the performance by 2x. We further explore two ideas to improve performance-efficiency trade-offs: (1) dynamically decide when to perform recycled or full attention step based on the query similarities and (2) continued pre-training the model with Recycled Attention.

Autoregressive Transformers rely on Key-Value (KV) caching to accelerate inference. However, the linear growth of the KV cache with context length leads to excessive memory consumption and bandwidth constraints. This bottleneck is particularly problematic in real-time applications -- such as chatbots and interactive assistants -- where low latency and high memory efficiency are critical. Existing methods drop distant tokens or compress states in a lossy manner, sacrificing accuracy by discarding vital context or introducing bias. We propose MorphKV, an inference-time technique that maintains a constant-sized KV cache while preserving accuracy. MorphKV balances long-range dependencies and local coherence during text generation. It eliminates early-token bias while retaining high-fidelity context by adaptively ranking tokens through correlation-aware selection. Unlike heuristic retention or lossy compression, MorphKV iteratively refines the KV cache via lightweight updates guided by attention patterns of recent tokens. This approach captures inter-token correlation with greater accuracy, crucial for tasks like content creation and code generation. Our studies on long-response tasks show 52.9% memory savings and 18.2% higher accuracy on average compared to state-of-the-art prior works, enabling efficient real-world deployment.

Large Language Models (LLMs) are powerful but often too slow and costly for real-world use during inference. Looped transformers save on parameters by reusing the same weights for multiple computational steps, or "loops." However, this approach has a major flaw: the loops run one after another, causing inference latency and memory requirements to increase with each added loop. This makes them impractical for fast applications. To solve this problem, we introduce the Parallel Loop Transformer (PLT). PLT is a new architecture that delivers the performance benefits of a deep, looped model but with the low latency of a standard, non-looped model. PLT works using two key techniques. First, Cross-Loop Parallelism (CLP) breaks the sequential dependency by computing different loops for different tokens at the same time, all within a single pass. Second, to prevent memory costs from growing, we use an Efficient Representation Enhancement strategy. This method shares the memory (KV cache) from the first loop with all other loops. It then uses a Gated Sliding-Window Attention (G-SWA) to combine this shared global information with local information, maintaining high accuracy. Our experiments show that PLT achieves the high accuracy of a traditional looped model but with almost no extra latency or memory cost compared to a standard transformer.

Large Language Models (LLMs) have shown exciting performance in listwise passage ranking. Due to the limited input length, existing methods often adopt the sliding window strategy. Such a strategy, though effective, is inefficient as it involves repetitive and serialized processing, which usually re-evaluates relevant passages multiple times. As a result, it incurs redundant API costs, which are proportional to the number of inference tokens. The development of long-context LLMs enables the full ranking of all passages within a single inference, avoiding redundant API costs. In this paper, we conduct a comprehensive study of long-context LLMs for ranking tasks in terms of efficiency and effectiveness. Surprisingly, our experiments reveal that full ranking with long-context LLMs can deliver superior performance in the supervised fine-tuning setting with a huge efficiency improvement. Furthermore, we identify two limitations of fine-tuning the full ranking model based on existing methods: (1) sliding window strategy fails to produce a full ranking list as a training label, and (2) the language modeling loss cannot emphasize top-ranked passage IDs in the label. To alleviate these issues, we propose a new complete listwise label construction approach and a novel importance-aware learning objective for full ranking. Experiments show the superior performance of our method over baselines. Our codes are available at https://github.com/8421BCD/fullrank.

Retrieval-augmented generation (RAG) extends large language models (LLMs) with external data sources to enhance factual correctness and domain coverage. Modern RAG pipelines rely on large datastores, leading to system challenges in latency-sensitive deployments, especially when limited GPU memory is available. To address these challenges, we propose TeleRAG, an efficient inference system that reduces RAG latency with minimal GPU memory requirements. The core innovation of TeleRAG is lookahead retrieval, a prefetching mechanism that anticipates required data and transfers it from CPU to GPU in parallel with LLM generation. By leveraging the modularity of RAG pipelines, the inverted file index (IVF) search algorithm and similarities between queries, TeleRAG optimally overlaps data movement and computation. Experimental results show that TeleRAG reduces end-to-end RAG inference latency by up to 1.72x on average compared to state-of-the-art systems, enabling faster, more memory-efficient deployments of advanced RAG applications.

Long context large language models (LLMs) pose significant challenges for efficient serving due to the large memory footprint and high access overhead of KV cache. Retrieval-based KV cache reduction methods can mitigate these challenges, typically by offloading the complete KV cache to CPU and retrieving necessary tokens on demand during inference. However, these methods still suffer from unsatisfactory accuracy degradation and extra retrieval overhead. To address these limitations, this paper proposes A^2ATS, a novel retrieval-based KV cache reduction method. A^2ATS aims to obtain an accurate approximation of attention scores by applying the vector quantization technique to key states, thereby enabling efficient and precise retrieval of the top-K tokens. First, we propose Windowed Rotary Position Embedding, which decouples the positional dependency from query and key states after position embedding. Then, we propose query-aware vector quantization that optimizes the objective of attention score approximation directly. Finally, we design the heterogeneous inference architecture for KV cache offloading, enabling long context serving with larger batch sizes. Experimental results demonstrate that A^2ATS can achieve a lower performance degradation with similar or lower overhead compared to existing methods, thereby increasing long context serving throughput by up to 2.7 times.