mlsanityData to 7 Oct 2026

DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models

arXiv 2402.03300 ↗First posted 5 Feb 2024cs.CL cs.AI cs.LGcited by 8,851

On the map: LLM reasoning → Mathematical reasoning

Abstract (arXiv)

Mathematical reasoning poses a significant challenge for language models due to its complex and structured nature. In this paper, we introduce DeepSeekMath 7B, which continues pre-training DeepSeek-Coder-Base-v1.5 7B with 120B math-related tokens sourced from Common Crawl, together with natural language and code data. DeepSeekMath 7B has achieved an impressive score of 51.7% on the competition-level MATH benchmark without relying on external toolkits and voting techniques, approaching the performance level of Gemini-Ultra and GPT-4. Self-consistency over 64 samples from DeepSeekMath 7B achieves 60.9% on MATH. The mathematical reasoning capability of DeepSeekMath is attributed to two key factors: First, we harness the significant potential of publicly available web data through a meticulously engineered data selection pipeline. Second, we introduce Group Relative Policy Optimization (GRPO), a variant of Proximal Policy Optimization (PPO), that enhances mathematical reasoning abilities while concurrently optimizing the memory usage of PPO.

Key facts. Cited by 8,851 papers in the map (data through 7 Oct 2026). Placed in Mathematical reasoning, one of 17 directions in LLM reasoning. Builds on 46 of its 57 references that are in the map. First posted on arXiv 5 Feb 2024.

Builds on

46 of 57 references.

Closest ancestors · 8

Same direction, newest first

  1. 2023Llemma: An Open Language Model For Mathematics16 Oct
  2. 2023OpenWebMath: An Open Dataset of High-Quality Mathematical Web Text10 Oct
  3. 2023ToRA: A Tool-Integrated Reasoning Agent for Mathematical Problem Solving29 Sep
  4. 2023WizardMath: Empowering Mathematical Reasoning for Large Language Models via Reinforced Evol-Instruct18 Aug
  5. 2023Scaling Relationship on Learning Mathematical Reasoning with Large Language Models3 Aug
  6. 2022Language Models are Multilingual Chain-of-Thought Reasoners6 Oct
  7. 2022Solving Quantitative Reasoning Problems with Language Models29 Jun
  8. 2020Generative Language Modeling for Automated Theorem Proving7 Sep

Other references · 38

  1. 2022Training language models to follow instructions with human feedbackcited by 15,712
  2. 2017Proximal Policy Optimization Algorithmscited by 14,441
  3. 2023Llama 2: Open Foundation and Fine-Tuned Chat Modelscited by 12,865
  4. 2022Chain-of-Thought Prompting Elicits Reasoning in Large Language Modelscited by 12,302
  5. 2021Training Verifiers to Solve Math Word Problemscited by 9,743
  6. 2021Evaluating Large Language Models Trained on Codecited by 8,053
  7. 2023Direct Preference Optimization: Your Language Model is Secretly a Reward Modelcited by 7,916
  8. 2020Measuring Massive Multitask Language Understandingcited by 7,768
  9. 2023Efficient Memory Management for Large Language Model Serving with PagedAttentioncited by 5,767
  10. 2021Measuring Mathematical Problem Solving With the MATH Datasetcited by 5,203
  11. 2023Let's Verify Step by Stepcited by 3,598
  12. 2021Program Synthesis with Large Language Modelscited by 3,509
26 more
  1. 2023Qwen Technical Reportcited by 3,273
  2. 2023Tree of Thoughts: Deliberate Problem Solving with Large Language Modelscited by 3,155
  3. 2023Mistral 7Bcited by 3,065
  4. 2015High-Dimensional Continuous Control Using Generalized Advantage Estimationcited by 1,916
  5. 2022Challenging BIG-Bench Tasks and Whether Chain-of-Thought Can Solve Themcited by 1,767
  6. 2022Fast Inference from Transformers via Speculative Decodingcited by 1,615
  7. 2024DeepSeek-Coder: When the Large Language Model Meets Programming -- The Rise of Code Intelligencecited by 1,154
  8. 2022Program of Thoughts Prompting: Disentangling Computation from Reasoning for Numerical Reasoning Taskscited by 1,057
  9. 2021GLM: General Language Model Pretraining with Autoregressive Blank Infillingcited by 1,026
  10. 2023Math-Shepherd: Verify and Reinforce LLMs Step-by-step without Human Annotationscited by 895
  11. 2023MetaMath: Bootstrap Your Own Mathematical Questions for Large Language Modelscited by 724
  12. 2023AGIEval: A Human-Centric Benchmark for Evaluating Foundation Modelscited by 701
  13. 2024DeepSeek LLM: Scaling Open-Source Language Models with Longtermismcited by 621
  14. 2023MAmmoTH: Building Math Generalist Models through Hybrid Instruction Tuningcited by 483
  15. 2023RRHF: Rank Responses to Align Language Models with Human Feedback without tearscited by 454
  16. 2023Weak-to-Strong Generalization: Eliciting Strong Capabilities With Weak Supervisioncited by 445
  17. 2021MiniF2F: a cross-system benchmark for formal Olympiad-level mathematicscited by 380
  18. 2016FastText.zip: Compressing text classification modelscited by 331
  19. 2023Preference Ranking Optimization for Human Alignmentcited by 283
  20. 2022Draft, Sketch, and Prove: Guiding Formal Theorem Provers with Informal Proofscited by 278
  21. 2024Unlocking Efficiency in Large Language Model Inference: A Comprehensive Survey of Speculative Decodingcited by 266
  22. 2022Speculative Decoding: Exploiting Speculative Execution for Accelerating Seq2seq Generationcited by 169
  23. 2023SeaLLMs -- Large Language Models for Southeast Asiacited by 104
  24. 2023CMATH: Can Your Language Model Pass Chinese Elementary School Math Test?cited by 89
  25. 2023MathPile: A Billion-Token-Scale Pretraining Corpus for Mathcited by 67
  26. 2023Making Large Language Models Better Reasoners with Alignmentcited by 63

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2024: 249; 2025: 3400; 2026: 5202.

8,851 papers.

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  1. 2025Qwen3 Technical Reportcited by 8,195
  2. 2025DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learningcited by 6,146
  3. 2024Qwen2.5 Technical Reportcited by 4,713
  4. 2025DAPO: An Open-Source LLM Reinforcement Learning System at Scalecited by 2,678
  5. 2024HybridFlow: A Flexible and Efficient RLHF Frameworkcited by 1,980
  6. 2024LlamaFactory: Unified Efficient Fine-Tuning of 100+ Language Modelscited by 1,442
  7. 2025InternVL3.5: Advancing Open-Source Multimodal Models in Versatility, Reasoning, and Efficiencycited by 1,419
  8. 2025Search-R1: Training LLMs to Reason and Leverage Search Engines with Reinforcement Learningcited by 1,371
  9. 2025Understanding R1-Zero-Like Training: A Critical Perspectivecited by 1,276
  10. 2024OlympiadBench: A Challenging Benchmark for Promoting AGI with Olympiad-Level Bilingual Multimodal Scientific Problemscited by 1,099
  11. 2024DeepSeek-V2: A Strong, Economical, and Efficient Mixture-of-Experts Language Modelcited by 1,093
  12. 2024Qwen2.5-Math Technical Report: Toward Mathematical Expert Model via Self-Improvementcited by 1,057
38 more
  1. 2025Qwen-Image Technical Reportcited by 973
  2. 2025Does Reinforcement Learning Really Incentivize Reasoning Capacity in LLMs Beyond the Base Model?cited by 948
  3. 2025Emerging Properties in Unified Multimodal Pretrainingcited by 855
  4. 2025Group Sequence Policy Optimizationcited by 788
  5. 2024Training Large Language Models to Reason in a Continuous Latent Spacecited by 763
  6. 2025DeepSeek-V3.2: Pushing the Frontier of Open Large Language Modelscited by 755
  7. 2024DeepSeek-V3 Technical Reportcited by 724
  8. 2025Vision-R1: Incentivizing Reasoning Capability in Multimodal Large Language Modelscited by 653
  9. 2025Flow-GRPO: Training Flow Matching Models via Online RLcited by 605
  10. 2025Beyond the 80/20 Rule: High-Entropy Minority Tokens Drive Effective Reinforcement Learning for LLM Reasoningcited by 540
  11. 2025VLM-R1: A Stable and Generalizable R1-style Large Vision-Language Modelcited by 515
  12. 2025SimpleRL-Zoo: Investigating and Taming Zero Reinforcement Learning for Open Base Models in the Wildcited by 505
  13. 2026GLM-5: from Vibe Coding to Agentic Engineeringcited by 502
  14. 2025Visual-RFT: Visual Reinforcement Fine-Tuningcited by 501
  15. 2025LIMO: Less is More for Reasoningcited by 488
  16. 2025Process Reinforcement through Implicit Rewardscited by 478
  17. 2025Video-R1: Reinforcing Video Reasoning in MLLMscited by 464
  18. 2025The Entropy Mechanism of Reinforcement Learning for Reasoning Language Modelscited by 463
  19. 2025Stop Overthinking: A Survey on Efficient Reasoning for Large Language Modelscited by 456
  20. 2025GLM-4.5: Agentic, Reasoning, and Coding (ARC) Foundation Modelscited by 446
  21. 2025Group-in-Group Policy Optimization for LLM Agent Trainingcited by 442
  22. 2025GLM-4.5V and GLM-4.1V-Thinking: Towards Versatile Multimodal Reasoning with Scalable Reinforcement Learningcited by 439
  23. 2024Training Language Models to Self-Correct via Reinforcement Learningcited by 405
  24. 2025The Lessons of Developing Process Reward Models in Mathematical Reasoningcited by 402
  25. 2025DeepEyes: Incentivizing "Thinking with Images" via Reinforcement Learningcited by 398
  26. 2025DanceGRPO: Unleashing GRPO on Visual Generationcited by 388
  27. 2026Self-Distilled Reasoner: On-Policy Self-Distillation for Large Language Modelscited by 386
  28. 2025L1: Controlling How Long A Reasoning Model Thinks With Reinforcement Learningcited by 381
  29. 2025Towards Reasoning Era: A Survey of Long Chain-of-Thought for Reasoning Large Language Modelscited by 381
  30. 2025Cognitive Behaviors that Enable Self-Improving Reasoners, or, Four Habits of Highly Effective STaRscited by 373
  31. 2025Scaling up Test-Time Compute with Latent Reasoning: A Recurrent Depth Approachcited by 372
  32. 2024Interpretable Preferences via Multi-Objective Reward Modeling and Mixture-of-Expertscited by 369
  33. 2025RAGEN: Understanding Self-Evolution in LLM Agents via Multi-Turn Reinforcement Learningcited by 357
  34. 2025ToolRL: Reward is All Tool Learning Needscited by 342
  35. 2025Rubrics as Rewards: Reinforcement Learning Beyond Verifiable Domainscited by 328
  36. 2024DeepSeek-Coder-V2: Breaking the Barrier of Closed-Source Models in Code Intelligencecited by 325
  37. 2025Absolute Zero: Reinforced Self-play Reasoning with Zero Datacited by 323
  38. 2025From System 1 to System 2: A Survey of Reasoning Large Language Modelscited by 319

50 most cited of 8,851 All 8,851 (JSON)

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  1. 2025Token-Hungry, Yet Precise: DeepSeek R1 Highlights the Need for Multi-Step Reasoning Over Speed in MATH
  2. 2025MMATH: A Multilingual Benchmark for Mathematical Reasoning
  3. 2025Challenging the Boundaries of Reasoning: An Olympiad-Level Math Benchmark for Large Language Models
  4. 2026PyraMathBench: Evaluating and Improving Mathematical Capability in Large Language Models
  5. 2026PluraMath: Extending Mathematical Reasoning Evaluation Beyond High-Resource Languages
  6. 2024OpenMathInstruct-2: Accelerating AI for Math with Massive Open-Source Instruction Data
  7. 2024MARIO: MAth Reasoning with code Interpreter Output -- A Reproducible Pipeline
  8. 2024MATHSENSEI: A Tool-Augmented Large Language Model for Mathematical Reasoning