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README.md

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+<!-- markdownlint-disable first-line-h1 -->
+<!-- markdownlint-disable html -->
+<!-- markdownlint-disable no-duplicate-header -->
+
+<div align="center">
+  <img src="https://github.com/deepseek-ai/DeepSeek-V2/blob/main/figures/logo.svg?raw=true" width="60%" alt="DeepSeek-V3" />
+</div>
+<hr>
+<div align="center" style="line-height: 1;">
+  <a href="https://www.deepseek.com/" target="_blank" style="margin: 2px;">
+    <img alt="Homepage" src="https://github.com/deepseek-ai/DeepSeek-V2/blob/main/figures/badge.svg?raw=true" style="display: inline-block; vertical-align: middle;"/>
+  </a>
+  <a href="https://chat.deepseek.com/" target="_blank" style="margin: 2px;">
+    <img alt="Chat" src="https://img.shields.io/badge/🤖%20Chat-DeepSeek%20V3-536af5?color=536af5&logoColor=white" style="display: inline-block; vertical-align: middle;"/>
+  </a>
+  <a href="https://huggingface.co/deepseek-ai" target="_blank" style="margin: 2px;">
+    <img alt="Hugging Face" src="https://img.shields.io/badge/%F0%9F%A4%97%20Hugging%20Face-DeepSeek%20AI-ffc107?color=ffc107&logoColor=white" style="display: inline-block; vertical-align: middle;"/>
+  </a>
+</div>
+
+<div align="center" style="line-height: 1;">
+  <a href="https://discord.gg/Tc7c45Zzu5" target="_blank" style="margin: 2px;">
+    <img alt="Discord" src="https://img.shields.io/badge/Discord-DeepSeek%20AI-7289da?logo=discord&logoColor=white&color=7289da" style="display: inline-block; vertical-align: middle;"/>
+  </a>
+  <a href="https://github.com/deepseek-ai/DeepSeek-V2/blob/main/figures/qr.jpeg?raw=true" target="_blank" style="margin: 2px;">
+    <img alt="Wechat" src="https://img.shields.io/badge/WeChat-DeepSeek%20AI-brightgreen?logo=wechat&logoColor=white" style="display: inline-block; vertical-align: middle;"/>
+  </a>
+  <a href="https://twitter.com/deepseek_ai" target="_blank" style="margin: 2px;">
+    <img alt="Twitter Follow" src="https://img.shields.io/badge/Twitter-deepseek_ai-white?logo=x&logoColor=white" style="display: inline-block; vertical-align: middle;"/>
+  </a>
+</div>
+
+<div align="center" style="line-height: 1;">
+  <a href="https://github.com/deepseek-ai/DeepSeek-V3/blob/main/LICENSE-CODE" style="margin: 2px;">
+    <img alt="Code License" src="https://img.shields.io/badge/Code_License-MIT-f5de53?&color=f5de53" style="display: inline-block; vertical-align: middle;"/>
+  </a>
+  <a href="https://github.com/deepseek-ai/DeepSeek-V3/blob/main/LICENSE-MODEL" style="margin: 2px;">
+    <img alt="Model License" src="https://img.shields.io/badge/Model_License-Model_Agreement-f5de53?&color=f5de53" style="display: inline-block; vertical-align: middle;"/>
+  </a>
+</div>
+
+## 1. Introduction
+
+We introduce DeepSeek-Prover-V2, an open-source large language model designed for formal theorem proving in Lean 4, with initialization data collected through a recursive theorem proving pipeline powered by DeepSeek-V3. The cold-start training procedure begins by prompting DeepSeek-V3 to decompose complex problems into a series of subgoals. The proofs of resolved subgoals are synthesized into a chain-of-thought process, combined with DeepSeek-V3's step-by-step reasoning, to create an initial cold start for reinforcement learning. This process enables us to integrate both informal and formal mathematical reasoning into a unified model.
+
+<p align="center">
+  <img width="100%" src="https://github.com/deepseek-ai/DeepSeek-Prover-V2/blob/main/figures/performance.png?raw=true">
+</p>
+
+## 2. Model Summary
+
+---
+
+**Synthesize Cold-Start Reasoning Data through Recursive Proof Search**
+
+- To construct the cold-start dataset, we develop a simple yet effective pipeline for recursive theorem proving, utilizing DeepSeek-V3 as a unified tool for both subgoal decomposition and formalization. We prompt DeepSeek-V3 to decompose theorems into high-level proof sketches while simultaneously formalizing these proof steps in Lean 4, resulting in a sequence of subgoals.
+
+- We use a smaller 7B model to handle the proof search for each subgoal, thereby reducing the associated computational burden. Once the decomposed steps of a challenging problem are resolved, we pair the complete step-by-step formal proof with the corresponding chain-of-thought from DeepSeek-V3 to create cold-start reasoning data.
+
+---
+
+**Reinforcement Learning with Synthetic Cold-Start Data**
+
+- We curate a subset of challenging problems that remain unsolved by the 7B prover model in an end-to-end manner, but for which all decomposed subgoals have been successfully resolved. By composing the proofs of all subgoals, we construct a complete formal proof for the original problem. This proof is then appended to DeepSeek-V3's chain-of-thought, which outlines the corresponding lemma decomposition, thereby producing a cohesive synthesis of informal reasoning and subsequent formalization.
+
+- After fine-tuning the prover model on the synthetic cold-start data, we perform a reinforcement learning stage to further enhance its ability to bridge informal reasoning with formal proof construction. Following the standard training objective for reasoning models, we use binary correct-or-incorrect feedback as the primary form of reward supervision.
+- The resulting model, DeepSeek-Prover-V2-671B, achieves state-of-the-art performance in neural theorem proving, reaching $88.9$% pass ratio on the MiniF2F-test and solving 49 out of 658 problems from PutnamBench. The proofs generated by DeepSeek-Prover-V2 for the miniF2F dataset are available for download as a [ZIP archive](https://github.com/deepseek-ai/DeepSeek-Prover-V2/blob/master/minif2f-solutions.zip).
+
+---
+
+## 3. ProverBench: Formalization of AIME and Textbook Problems
+
+we introduce ProverBench, a benchmark dataset comprising 325 problems. Of these, 15 are formalized from number theory and algebra questions featured in the recent AIME competitions (AIME 24 and 25), offering authentic high-school competition-level challenges. The remaining 310 problems are drawn from curated textbook examples and educational tutorials, contributing a diverse and pedagogically grounded collection of formalized mathematical problems. This benchmark is designed to enable more comprehensive evaluation across both high-school competition problems and undergraduate-level mathematics.
+
+<div align="center">
+
+| Area                | Count |
+| :---------------------: | :-------: |
+| AIME 24&25          | 15    |
+| Number Theory       | 40    |
+| Elementary Algebra  | 30    |
+| Linear Algebra      | 50    |
+| Abstract Algebra    | 40    |
+| Calculus            | 90    |
+| Real Analysis       | 30    |
+| Complex Analysis    | 10    |
+| Functional Analysis | 10    |
+| Probability         | 10    |
+| Total               | 325   |
+
+</div>
+
+## 4. Model & Dataset Downloads
+
+We release DeepSeek-Prover-V2 in two model sizes: 7B and 671B parameters. DeepSeek-Prover-V2-671B is trained on top of DeepSeek-V3-Base. DeepSeek-Prover-V2-7B is built upon DeepSeek-Prover-V1.5-Base and features an extended context length of up to 32K tokens.
+
+<div align="center">
+
+|            **Model**            |                          **Download**                         |
+| :-----------------------------: | :----------------------------------------------------------: |
+|   DeepSeek-Prover-V2-7B   | [🤗 HuggingFace](https://huggingface.co/deepseek-ai/DeepSeek-Prover-V2-7B) |
+|   DeepSeek-Prover-V2-671B   | [🤗 HuggingFace](https://huggingface.co/deepseek-ai/DeepSeek-Prover-V2-671B) |
+
+</div>
+
+<div align="center">
+
+|            **Dataset**            |                          **Download**                         |
+| :-----------------------------: | :----------------------------------------------------------: |
+|   DeepSeek-ProverBench   | [🤗 HuggingFace](https://huggingface.co/datasets/deepseek-ai/DeepSeek-ProverBench) |
+
+</div>
+
+## 5. Quick Start
+
+You can directly use [Huggingface's Transformers](https://github.com/huggingface/transformers) for model inference. DeepSeek-Prover-V2-671B shares the same architecture as DeepSeek-V3. For detailed information and supported features, please refer to [the DeepSeek-V3 documentation on Hugging Face](https://github.com/huggingface/transformers/blob/main/docs/source/en/model_doc/deepseek_v3.md).
+
+The following is a basic example of generating a proof for a problem from the miniF2F dataset:
+````python
+from transformers import AutoModelForCausalLM, AutoTokenizer
+import torch
+torch.manual_seed(30)
+
+model_id = "DeepSeek-Prover-V2-7B"  # or DeepSeek-Prover-V2-671B
+tokenizer = AutoTokenizer.from_pretrained(model_id)
+
+formal_statement = """
+import Mathlib
+import Aesop
+
+set_option maxHeartbeats 0
+
+open BigOperators Real Nat Topology Rat
+
+/-- What is the positive difference between $120\%$ of 30 and $130\%$ of 20? Show that it is 10.-/
+theorem mathd_algebra_10 : abs ((120 : ℝ) / 100 * 30 - 130 / 100 * 20) = 10 := by
+  sorry
+""".strip()
+
+prompt = """
+Complete the following Lean 4 code:
+
+```lean4
+{}
+```
+
+Before producing the Lean 4 code to formally prove the given theorem, provide a detailed proof plan outlining the main proof steps and strategies.
+The plan should highlight key ideas, intermediate lemmas, and proof structures that will guide the construction of the final formal proof.
+""".strip()
+
+chat = [
+  {"role": "user", "content": prompt.format(formal_statement)},
+]
+
+model = AutoModelForCausalLM.from_pretrained(model_id, device_map="auto", torch_dtype=torch.bfloat16, trust_remote_code=True)
+inputs = tokenizer.apply_chat_template(chat, tokenize=True, add_generation_prompt=True, return_tensors="pt").to(model.device)
+
+import time
+start = time.time()
+outputs = model.generate(inputs, max_new_tokens=8192)
+print(tokenizer.batch_decode(outputs))
+print(time.time() - start)
+````
+
+## 6. License
+The use of DeepSeek-Prover-V2 models is subject to [the Model License](LICENSE-MODEL).
+
+## 7. Contact
+
+If you have any questions, please raise an issue or contact us at [[email protected]](mailto:[email protected]).

config.json

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+{
+    "architectures": [
+        "LlamaForCausalLM"
+    ],
+    "attention_bias": false,
+    "attention_dropout": 0.0,
+    "bos_token_id": 100000,
+    "eos_token_id": 100001,
+    "head_dim": 128,
+    "hidden_act": "silu",
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+    "model_type": "llama",
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+        "beta_slow": 1,
+        "factor": 16,
+        "mscale": true,
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+        "rope_type": "yarn",
+        "type": "yarn"
+    },
+    "rope_theta": 10000,
+    "tie_word_embeddings": false,
+    "torch_dtype": "bfloat16",
+    "transformers_version": "4.51.3",
+    "use_cache": true,
+    "vocab_size": 102400,
+    "quantization_config": {
+        "ignore": [
+            "lm_head"
+        ],
+        "quant_algo": "NVFP4",
+        "kv_cache_scheme": "FP8",
+        "producer": {
+            "name": "modelopt",
+            "version": "0.31.0"
+        }
+    }
+}

generation_config.json

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+{
+  "_from_model_config": true,
+  "bos_token_id": 100000,
+  "eos_token_id": 100001,
+  "transformers_version": "4.51.3"
+}

hf_quant_config.json

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+    "producer": {
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+        "version": "0.31.0"
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+    "quantization": {
+        "quant_algo": "NVFP4",
+        "kv_cache_quant_algo": "FP8",
+        "group_size": 16,
+        "exclude_modules": [
+            "lm_head"
+        ]
+    }
+}

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+    "model.layers.9.self_attn.q_proj.input_scale": "model-00001-of-00002.safetensors",
+    "model.layers.9.self_attn.q_proj.weight": "model-00001-of-00002.safetensors",
+    "model.layers.9.self_attn.q_proj.weight_scale": "model-00001-of-00002.safetensors",
+    "model.layers.9.self_attn.q_proj.weight_scale_2": "model-00001-of-00002.safetensors",
+    "model.layers.9.self_attn.v_proj.input_scale": "model-00001-of-00002.safetensors",
+    "model.layers.9.self_attn.v_proj.v_scale": "model-00001-of-00002.safetensors",
+    "model.layers.9.self_attn.v_proj.weight": "model-00001-of-00002.safetensors",
+    "model.layers.9.self_attn.v_proj.weight_scale": "model-00001-of-00002.safetensors",
+    "model.layers.9.self_attn.v_proj.weight_scale_2": "model-00001-of-00002.safetensors",
+    "model.norm.weight": "model-00001-of-00002.safetensors"
+  }
+}

special_tokens_map.json

@@ -0,0 +1,17 @@
+{
+  "bos_token": {
+    "content": "<｜begin▁of▁sentence｜>",
+    "lstrip": false,
+    "normalized": true,
+    "rstrip": false,
+    "single_word": false
+  },
+  "eos_token": {
+    "content": "<｜end▁of▁sentence｜>",
+    "lstrip": false,
+    "normalized": true,
+    "rstrip": false,
+    "single_word": false
+  },
+  "pad_token": "<｜end▁of▁sentence｜>"
+}

tokenizer_config.json

@@ -0,0 +1,163 @@
+{
+  "add_bos_token": true,
+  "add_eos_token": false,
+  "add_prefix_space": null,
+  "added_tokens_decoder": {
+    "100000": {
+      "content": "<｜begin▁of▁sentence｜>",
+      "lstrip": false,
+      "normalized": true,
+      "rstrip": false,
+      "single_word": false,
+      "special": true
+    },
+    "100001": {
+      "content": "<｜end▁of▁sentence｜>",
+      "lstrip": false,
+      "normalized": true,
+      "rstrip": false,
+      "single_word": false,
+      "special": true
+    },
+    "100002": {
+      "content": "<｜fim▁hole｜>",
+      "lstrip": false,
+      "normalized": true,
+      "rstrip": false,
+      "single_word": false,
+      "special": false
+    },
+    "100003": {
+      "content": "<｜fim▁begin｜>",
+      "lstrip": false,
+      "normalized": true,
+      "rstrip": false,
+      "single_word": false,
+      "special": false
+    },
+    "100004": {
+      "content": "<｜fim▁end｜>",
+      "lstrip": false,
+      "normalized": true,
+      "rstrip": false,
+      "single_word": false,
+      "special": false
+    },
+    "100005": {
+      "content": "<｜completion｜>",
+      "lstrip": false,
+      "normalized": true,
+      "rstrip": false,
+      "single_word": false,
+      "special": false
+    },
+    "100006": {
+      "content": "<｜User｜>",
+      "lstrip": false,
+      "normalized": true,
+      "rstrip": false,
+      "single_word": false,
+      "special": false
+    },
+    "100007": {
+      "content": "<｜Assistant｜>",
+      "lstrip": false,
+      "normalized": true,
+      "rstrip": false,
+      "single_word": false,
+      "special": false
+    },
+    "100008": {
+      "content": "<|EOT|>",
+      "lstrip": false,
+      "normalized": true,
+      "rstrip": false,
+      "single_word": false,
+      "special": true
+    },
+    "100009": {
+      "content": "<｜tool▁calls▁begin｜>",
+      "lstrip": false,
+      "normalized": true,
+      "rstrip": false,
+      "single_word": false,
+      "special": false
+    },
+    "100010": {
+      "content": "<｜tool▁calls▁end｜>",
+      "lstrip": false,
+      "normalized": true,
+      "rstrip": false,
+      "single_word": false,
+      "special": false
+    },
+    "100011": {
+      "content": "<｜tool▁call▁begin｜>",
+      "lstrip": false,
+      "normalized": true,
+      "rstrip": false,
+      "single_word": false,
+      "special": false
+    },
+    "100012": {
+      "content": "<｜tool▁call▁end｜>",
+      "lstrip": false,
+      "normalized": true,
+      "rstrip": false,
+      "single_word": false,
+      "special": false
+    },
+    "100013": {
+      "content": "<｜tool▁outputs▁begin｜>",
+      "lstrip": false,
+      "normalized": true,
+      "rstrip": false,
+      "single_word": false,
+      "special": false
+    },
+    "100014": {
+      "content": "<｜tool▁outputs▁end｜>",
+      "lstrip": false,
+      "normalized": true,
+      "rstrip": false,
+      "single_word": false,
+      "special": false
+    },
+    "100015": {
+      "content": "<｜tool▁output▁begin｜>",
+      "lstrip": false,
+      "normalized": true,
+      "rstrip": false,
+      "single_word": false,
+      "special": false
+    },
+    "100016": {
+      "content": "<｜tool▁output▁end｜>",
+      "lstrip": false,
+      "normalized": true,
+      "rstrip": false,
+      "single_word": false,
+      "special": false
+    },
+    "100017": {
+      "content": "<｜tool▁sep｜>",
+      "lstrip": false,
+      "normalized": true,
+      "rstrip": false,
+      "single_word": false,
+      "special": false
+    }
+  },
+  "bos_token": "<｜begin▁of▁sentence｜>",
+  "chat_template": "{% if not add_generation_prompt is defined %}{% set add_generation_prompt = false %}{% endif %}{% set ns = namespace(is_first=false, is_tool=false, is_output_first=true, system_prompt='', is_first_sp=true, is_last_user=false) %}{%- for message in messages %}{%- if message['role'] == 'system' %}{%- if ns.is_first_sp %}{% set ns.system_prompt = ns.system_prompt + message['content'] %}{% set ns.is_first_sp = false %}{%- else %}{% set ns.system_prompt = ns.system_prompt + '\n\n' + message['content'] %}{%- endif %}{%- endif %}{%- endfor %}{{ bos_token }}{{ ns.system_prompt }}{%- for message in messages %}{%- if message['role'] == 'user' %}{%- set ns.is_tool = false -%}{%- set ns.is_first = false -%}{%- set ns.is_last_user = true -%}{{'<｜User｜>' + message['content'] + '<｜Assistant｜>'}}{%- endif %}{%- if message['role'] == 'assistant' and message['tool_calls'] is defined and message['tool_calls'] is not none %}{%- set ns.is_last_user = false -%}{%- if ns.is_tool %}{{'<｜tool▁outputs▁end｜>'}}{%- endif %}{%- set ns.is_first = false %}{%- set ns.is_tool = false -%}{%- set ns.is_output_first = true %}{%- for tool in message['tool_calls'] %}{%- if not ns.is_first %}{%- if message['content'] is none %}{{'<｜tool▁calls▁begin｜><｜tool▁call▁begin｜>' + tool['type'] + '<｜tool▁sep｜>' + tool['function']['name'] + '\n' + '```json' + '\n' + tool['function']['arguments'] + '\n' + '```' + '<｜tool▁call▁end｜>'}}{%- else %}{{message['content'] + '<｜tool▁calls▁begin｜><｜tool▁call▁begin｜>' + tool['type'] + '<｜tool▁sep｜>' + tool['function']['name'] + '\n' + '```json' + '\n' + tool['function']['arguments'] + '\n' + '```' + '<｜tool▁call▁end｜>'}}{%- endif %}{%- set ns.is_first = true -%}{%- else %}{{'\n' + '<｜tool▁call▁begin｜>' + tool['type'] + '<｜tool▁sep｜>' + tool['function']['name'] + '\n' + '```json' + '\n' + tool['function']['arguments'] + '\n' + '```' + '<｜tool▁call▁end｜>'}}{%- endif %}{%- endfor %}{{'<｜tool▁calls▁end｜><｜end▁of▁sentence｜>'}}{%- endif %}{%- if message['role'] == 'assistant' and (message['tool_calls'] is not defined or message['tool_calls'] is none)%}{%- set ns.is_last_user = false -%}{%- if ns.is_tool %}{{'<｜tool▁outputs▁end｜>' + message['content'] + '<｜end▁of▁sentence｜>'}}{%- set ns.is_tool = false -%}{%- else %}{% set content = message['content'] %}{{content + '<｜end▁of▁sentence｜>'}}{%- endif %}{%- endif %}{%- if message['role'] == 'tool' %}{%- set ns.is_last_user = false -%}{%- set ns.is_tool = true -%}{%- if ns.is_output_first %}{{'<｜tool▁outputs▁begin｜><｜tool▁output▁begin｜>' + message['content'] + '<｜tool▁output▁end｜>'}}{%- set ns.is_output_first = false %}{%- else %}{{'\n<｜tool▁output▁begin｜>' + message['content'] + '<｜tool▁output▁end｜>'}}{%- endif %}{%- endif %}{%- endfor -%}{% if ns.is_tool %}{{'<｜tool▁outputs▁end｜>'}}{% endif %}{% if add_generation_prompt and not ns.is_last_user and not ns.is_tool %}{{'<｜Assistant｜>'}}{% endif %}",
+  "clean_up_tokenization_spaces": false,
+  "eos_token": "<｜end▁of▁sentence｜>",
+  "extra_special_tokens": {},
+  "legacy": true,
+  "model_max_length": 131072,
+  "pad_token": "<｜end▁of▁sentence｜>",
+  "sp_model_kwargs": {},
+  "tokenizer_class": "LlamaTokenizerFast",
+  "unk_token": null,
+  "use_default_system_prompt": false
+}