OctoThinker: Mid-training Incentivizes Reinforcement Learning Scaling
On the map: LLM reasoning → Reinforcement learning for reasoning
Abstract (arXiv)
Different base language model families, such as Llama and Qwen, exhibit divergent behaviors during post-training with reinforcement learning (RL), especially on reasoning-intensive tasks. What makes a base language model suitable for reinforcement learning? Gaining deeper insight into this question is essential for developing RL-scalable foundation models of the next generation. In this work, we investigate how mid-training strategies shape RL dynamics, focusing on two representative model families: Qwen and Llama. Our study reveals that (1) high-quality mathematical corpora, such as MegaMath-Web-Pro, significantly improve both base model and RL performance, while existing alternatives (e.g., FineMath-4plus) fail to do so; (2) further adding QA-style data, particularly long chain-of-thought (CoT) reasoning examples, enhances RL outcomes, and instruction data further unlocks this effect; (3) while long-CoT improves reasoning depth, it can also induce verbosity of model responses and unstability of RL training, underscoring the importance of data formatting; (4) scaling mid-training consistently leads to stronger downstream RL performance. Building on these insights, we introduce a two-stage mid-training strategy, Stable-then-Decay, in which base models are first trained on 200B tokens with a constant learning rate, followed by 20B tokens across three CoT-focused branches with learning rate decay. This yields OctoThinker, a family of models demonstrating strong RL compatibility and closing the performance gap with more RL-friendly model families, i.e., Qwen. We hope our work will help shape pre-training strategies for foundation models in the RL era. To support further research, we release our open-source models along with a curated math reasoning-intensive corpus of over 70 billion tokens (i.e., MegaMath-Web-Pro-Max).
Key facts. Cited by 110 papers in the map (data through 7 Oct 2026). Placed in Reinforcement learning for reasoning, one of 17 directions in LLM reasoning. Builds on 42 of its 48 references that are in the map. First posted on arXiv 25 Jun 2025.
Builds on
42 of 48 references.
Closest ancestors · 10
Same direction, newest first
- 2025Spurious Rewards: Rethinking Training Signals in RLVR12 Jun
- 2025Reinforcement Learning for Reasoning in Large Language Models with One Training Example29 Apr
- 2025Open-Reasoner-Zero: An Open Source Approach to Scaling Up Reinforcement Learning on the Base Model31 Mar
- 2025Understanding R1-Zero-Like Training: A Critical Perspective26 Mar
- 2025SimpleRL-Zoo: Investigating and Taming Zero Reinforcement Learning for Open Base Models in the Wild24 Mar
- 2025DAPO: An Open-Source LLM Reinforcement Learning System at Scale18 Mar
- 2025Cognitive Behaviors that Enable Self-Improving Reasoners, or, Four Habits of Highly Effective STaRs3 Mar
- 2025DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning22 Jan
- 2024Tulu 3: Pushing Frontiers in Open Language Model Post-Training22 Nov
- 2023Let's Verify Step by Step31 May
Other references · 32
- 2024The Llama 3 Herd of Modelscited by 14,192
- 2022Chain-of-Thought Prompting Elicits Reasoning in Large Language Modelscited by 12,302
- 2021Training Verifiers to Solve Math Word Problemscited by 9,743
- 2024DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Modelscited by 8,851
- 2025Qwen3 Technical Reportcited by 8,195
- 2021Measuring Mathematical Problem Solving With the MATH Datasetcited by 5,203
- 2024Qwen2.5 Technical Reportcited by 4,713
- 2024HybridFlow: A Flexible and Efficient RLHF Frameworkcited by 1,980
- 2024Phi-3 Technical Report: A Highly Capable Language Model Locally on Your Phonecited by 1,883
- 2022Solving Quantitative Reasoning Problems with Language Modelscited by 1,359
- 2024OlympiadBench: A Challenging Benchmark for Promoting AGI with Olympiad-Level Bilingual Multimodal Scientific Problemscited by 1,099
- 2024Qwen2.5-Math Technical Report: Toward Mathematical Expert Model via Self-Improvementcited by 1,057
20 more
- 2021Are NLP Models really able to Solve Simple Math Word Problems?cited by 861
- 2023Enhancing Chat Language Models by Scaling High-quality Instructional Conversationscited by 825
- 2024MiniCPM: Unveiling the Potential of Small Language Models with Scalable Training Strategiescited by 694
- 2024Phi-4 Technical Reportcited by 675
- 2019MathQA: Towards Interpretable Math Word Problem Solving with Operation-Based Formalismscited by 653
- 2024DeepSeek LLM: Scaling Open-Source Language Models with Longtermismcited by 621
- 2024WildChat: 1M ChatGPT Interaction Logs in the Wildcited by 598
- 2023Llemma: An Open Language Model For Mathematicscited by 385
- 2024DataComp-LM: In search of the next generation of training sets for language modelscited by 381
- 2022Dynamic Prompt Learning via Policy Gradient for Semi-structured Mathematical Reasoningcited by 347
- 2021A Diverse Corpus for Evaluating and Developing English Math Word Problem Solverscited by 314
- 2025SmolLM2: When Smol Goes Big -- Data-Centric Training of a Small Language Modelcited by 307
- 20242 OLMo 2 Furiouscited by 302
- 2023OpenWebMath: An Open Dataset of High-Quality Mathematical Web Textcited by 151
- 2025Llama-Nemotron: Efficient Reasoning Modelscited by 151
- 2023MathPile: A Billion-Token-Scale Pretraining Corpus for Mathcited by 67
- 2025MegaMath: Pushing the Limits of Open Math Corporacited by 47
- 2024InfiMM-WebMath-40B: Advancing Multimodal Pre-Training for Enhanced Mathematical Reasoningcited by 36
- 2024Puzzle: Distillation-Based NAS for Inference-Optimized LLMscited by 17
- 2024Yi-Lightning Technical Reportcited by 11
Built on by
Citing papers per year: 2025: 55; 2026: 55.
110 papers.
Sort:
By area:
- 2025SAM 3D: 3Dfy Anything in Imagescited by 230
- 2025R-Zero: Self-Evolving Reasoning LLM from Zero Datacited by 210
- 2025A Survey of Reinforcement Learning for Large Reasoning Modelscited by 175
- 2025SPIRAL: Self-Play on Zero-Sum Games Incentivizes Reasoning via Multi-Agent Multi-Turn Reinforcement Learningcited by 89
- 2025Reasoning or Memorization? Unreliable Results of Reinforcement Learning Due to Data Contaminationcited by 81
- 2025SPICE: Self-Play In Corpus Environments Improves Reasoningcited by 78
- 2025Defeating the Training-Inference Mismatch via FP16cited by 62
- 2025Blending Supervised and Reinforcement Fine-Tuning with Prefix Samplingcited by 57
- 2025MegaScience: Pushing the Frontiers of Post-Training Datasets for Science Reasoningcited by 56
- 2025BAPO: Stabilizing Off-Policy Reinforcement Learning for LLMs via Balanced Policy Optimization with Adaptive Clippingcited by 47
- 2025Evolving Language Models without Labels: Majority Drives Selection, Novelty Promotes Variationcited by 44
- 2025Depth-Breadth Synergy in RLVR: Unlocking LLM Reasoning Gains with Adaptive Explorationcited by 40
38 more
- 2025RaC: Robot Learning for Long-Horizon Tasks by Scaling Recovery and Correctioncited by 35
- 2025Reinforcement Learning Meets Large Language Models: A Survey of Advancements and Applications Across the LLM Lifecyclecited by 34
- 2025RL Squeezes, SFT Expands: A Comparative Study of Reasoning LLMscited by 32
- 2026Rethinking the Trust Region in LLM Reinforcement Learningcited by 32
- 2026Tool-R0: Self-Evolving LLM Agents for Tool-Learning from Zero Datacited by 31
- 2026STEP3-VL-10B Technical Reportcited by 28
- 2025Single-stream Policy Optimizationcited by 27
- 2025Front-Loading Reasoning: The Synergy between Pretraining and Post-Training Datacited by 26
- 2025Nudging the Boundaries of LLM Reasoningcited by 25
- 2025Reasoning as an Adaptive Defense for Safetycited by 22
- 2025Hybrid Reinforcement: When Reward Is Sparse, It's Better to Be Densecited by 19
- 2025A Survey on LLM Mid-Trainingcited by 18
- 2025Don't Just Fine-tune the Agent, Tune the Environmentcited by 17
- 2026Reuse your FLOPs: Scaling RL on Hard Problems by Conditioning on Very Off-Policy Prefixescited by 16
- 2026daVinci-Dev: Agent-native Mid-training for Software Engineeringcited by 15
- 2025SSRL: Self-Search Reinforcement Learningcited by 13
- 2025RESTRAIN: From Spurious Votes to Signals -- Self-Driven RL with Self-Penalizationcited by 13
- 2025Scaling Generalist Data-Analytic Agentscited by 11
- 2025Pushing on Multilingual Reasoning Models with Language-Mixed Chain-of-Thoughtcited by 10
- 2025DatasetResearch: Benchmarking Agent Systems for Demand-Driven Dataset Discoverycited by 9
- 2025Let it Calm: Exploratory Annealed Decoding for Verifiable Reinforcement Learningcited by 9
- 2025LaSeR: Reinforcement Learning with Last-Token Self-Rewardingcited by 9
- 2025DuPO: Enabling Reliable LLM Self-Verification via Dual Preference Optimizationcited by 7
- 2025Beneficial Reasoning Behaviors in Agentic Search and Effective Post-training to Obtain Themcited by 7
- 2025Better LLM Reasoning via Dual-Playcited by 7
- 2026Unveiling Implicit Advantage Symmetry: Why GRPO Struggles with Exploration and Difficulty Adaptationcited by 7
- 2025Reinforcement Mid-Trainingcited by 6
- 2025MobileLLM-R1: Exploring the Limits of Sub-Billion Language Model Reasoners with Open Training Recipescited by 6
- 2025RePro: Training Language Models to Faithfully Recycle the Web for Pretrainingcited by 6
- 2025SAGE: Training Smart Any-Horizon Agents for Long Video Reasoning with Reinforcement Learningcited by 6
- 2026Paying Less Generalization Tax: A Cross-Domain Generalization Study of RL Training for LLM Agentscited by 6
- 2025URPO: A Unified Reward & Policy Optimization Framework for Large Language Modelscited by 5
- 2025Thinking-Free Policy Initialization Makes Distilled Reasoning Models More Effective and Efficient Reasonerscited by 5
- 2026DARC: Decoupled Asymmetric Reasoning Curriculum for LLM Evolutioncited by 5
- 2026Towards a Mechanistic Understanding of Large Reasoning Models: A Survey of Training, Inference, and Failurescited by 5
- 2025Thinking Augmented Pre-trainingcited by 4
- 2025Zero Reinforcement Learning Towards General Domainscited by 4
- 2026Aletheia: What Makes RLVR For Code Verifiers Tick?cited by 4
50 most cited of 110 All 110 (JSON)
- 2026Sharpen Before You Adapt: Data-Free Entry-State Sharpening for Test-Time Reinforcement Learning1 Oct 2026
- 2026Learning Beyond What You Sample: Off-Policy-Aware Cross-Model Trajectory Exchange for RLVR29 Sep 2026
- 2026Inducing Process Supervision from Outcome-Only Reinforcement Learning29 Sep 2026
- 2026ROSS: Relearning from Self-Generated Rollouts through Selective Supervision28 Sep 2026
- 2026MiST: Mid-Training LLMs for Cybersecurity16 Sep 2026
- 2026Knowledge Distillation During Mid-Training Favors Reasoning over Factual Recall1 Sep 2026
- 2026R3: Training Robots to Reason in Natural Language via Reinforcement Learning26 Aug 2026
- 2026One Symptom, Three Levers: A Critical Review of On-Policy Self-Distillation26 Aug 2026
- 2026TailSFT: Filtered Fine-Tuning Improves Post-Training Performance26 Aug 2026
- 2026LittleLearner: Language Models Under Pedagogically Controlled Knowledge Exposure13 Aug 2026
- 2026OctoLong: Mid-Training On Cross-Repository Code Contexts Enhances Long-Context Modeling5 Aug 2026
- 2026ReCo: Reweighting GRPO Against Distributional Concentration29 Jul 2026
38 more
- 2026When LLMs Read Tables Carelessly: Measuring and Reducing Data Referencing Errors30 Jun 2026
- 2026Reinforcement Learning without Ground-Truth Solutions can Improve LLMs25 Jun 2026
- 2026Sumi: Open Uniform Diffusion Language Model from Scratch17 Jun 2026
- 2026ExpRL: Exploratory RL for LLM Mid-Training15 Jun 2026
- 2026OrderGrad: Optimizing Beyond the Mean with Order-Statistic Policy Gradient Estimation4 Jun 2026
- 2026On Advantage Estimates for Max@K Policy Gradients4 Jun 2026
- 2026GRAIL: Gradient-Reweighted Advantages for Reinforcement Learning with Verifiable Rewards3 Jun 2026
- 2026Exploiting Verification-Generation Gap: Test-Time Reinforcement Learning with Confidence-Conditioned Verification2 Jun 2026
- 2026MIRA: Mid-training Rubric Anchoring for Source-Aware Data Selection28 May 2026
- 2026Zipping the Thought: When and How Compressed Reasoning Data Works in LLM Post-Training27 May 2026
- 2026The Future of Facts: Tracing the Factual Generation-Verification Gap26 May 2026
- 2026Text-to-SPARQL Generation with Reinforcement Learning: A GRPO-based Approach on DBLP19 May 2026
- 2026Knowledge-to-Verification: Exploring RLVR for LLMs in Knowledge-Intensive Domains18 May 2026
- 2026Query-Conditioned Test-Time Self-Training for Large Language Models13 May 2026
- 2026Preference Tuning as Spectral Update Reorganization12 May 2026
- 2026EmbodiedMidtrain: Bridging the Gap between Vision-Language Models and Vision-Language-Action Models via Mid-training21 Apr 2026
- 2026When Can LLMs Learn to Reason with Weak Supervision?20 Apr 2026
- 2026From P(y|x) to P(y): Investigating Reinforcement Learning in Pre-train Space15 Apr 2026
- 2026Probing How Scalable Table Data Enhances General Long-Context Reasoning23 Mar 2026
- 2026WIST: Web-Grounded Iterative Self-Play Tree for Domain-Targeted Reasoning Improvement22 Mar 2026
- 2026Reasoning over mathematical objects: on-policy reward modeling and test time aggregation19 Mar 2026
- 2026Level Up: Defining and Exploiting Transitional Problems for Curriculum Learning14 Mar 2026
- 2026CHIMERA: Compact Synthetic Data for Generalizable LLM Reasoning1 Mar 2026
- 2026Tool-R0: Self-Evolving LLM Agents for Tool-Learning from Zero Data24 Feb 2026
- 2026ComplLLM: Fine-tuning LLMs to Discover Complementary Signals for Decision-making23 Feb 2026
- 2026Think Longer to Explore Deeper: Learn to Explore In-Context via Length-Incentivized Reinforcement Learning12 Feb 2026
- 2026Data Science and Technology Towards AGI Part I: Tiered Data Management9 Feb 2026
- 2026TTSR: Test-Time Self-Evolving via Reflection6 Feb 2026
- 2026Unveiling Implicit Advantage Symmetry: Why GRPO Struggles with Exploration and Difficulty Adaptation5 Feb 2026
- 2026Rethinking the Trust Region in LLM Reinforcement Learning4 Feb 2026
- 2026CPMobius: Iterative Coach-Player Reasoning for Data-Free Reinforcement Learning3 Feb 2026
- 2026Dispersion Loss Counteracts Embedding Condensation and Improves Generalization in Small Language Models30 Jan 2026
- 2026Reuse your FLOPs: Scaling RL on Hard Problems by Conditioning on Very Off-Policy Prefixes26 Jan 2026
- 2026daVinci-Dev: Agent-native Mid-training for Software Engineering26 Jan 2026
- 2026Paying Less Generalization Tax: A Cross-Domain Generalization Study of RL Training for LLM Agents26 Jan 2026
- 2026Rethinking Reinforcement fine-tuning of LLMs: A Multi-armed Bandit Learning Perspective21 Jan 2026
- 2026DARC: Decoupled Asymmetric Reasoning Curriculum for LLM Evolution20 Jan 2026
- 2026Aletheia: What Makes RLVR For Code Verifiers Tick?17 Jan 2026
50 newest of 110 All 110 (JSON)
- 2025R-Zero: Self-Evolving Reasoning LLM from Zero Datacited by 210
- 2025A Survey of Reinforcement Learning for Large Reasoning Modelscited by 175
- 2025SPIRAL: Self-Play on Zero-Sum Games Incentivizes Reasoning via Multi-Agent Multi-Turn Reinforcement Learningcited by 89
- 2025Reasoning or Memorization? Unreliable Results of Reinforcement Learning Due to Data Contaminationcited by 81
- 2025Blending Supervised and Reinforcement Fine-Tuning with Prefix Samplingcited by 57
- 2025MegaScience: Pushing the Frontiers of Post-Training Datasets for Science Reasoningcited by 56
- 2025Depth-Breadth Synergy in RLVR: Unlocking LLM Reasoning Gains with Adaptive Explorationcited by 40
- 2025RL Squeezes, SFT Expands: A Comparative Study of Reasoning LLMscited by 32
- 2026Rethinking the Trust Region in LLM Reinforcement Learningcited by 32
- 2025Single-stream Policy Optimizationcited by 27
- 2025Front-Loading Reasoning: The Synergy between Pretraining and Post-Training Datacited by 26
- 2025Nudging the Boundaries of LLM Reasoningcited by 25
12 most cited of 57 All 57 (JSON)
- 2026Learning Beyond What You Sample: Off-Policy-Aware Cross-Model Trajectory Exchange for RLVR29 Sep 2026
- 2026Inducing Process Supervision from Outcome-Only Reinforcement Learning29 Sep 2026
- 2026Knowledge Distillation During Mid-Training Favors Reasoning over Factual Recall1 Sep 2026
- 2026R3: Training Robots to Reason in Natural Language via Reinforcement Learning26 Aug 2026
- 2026ReCo: Reweighting GRPO Against Distributional Concentration29 Jul 2026
- 2026ExpRL: Exploratory RL for LLM Mid-Training15 Jun 2026
- 2026On Advantage Estimates for Max@K Policy Gradients4 Jun 2026
- 2026GRAIL: Gradient-Reweighted Advantages for Reinforcement Learning with Verifiable Rewards3 Jun 2026
- 2026Exploiting Verification-Generation Gap: Test-Time Reinforcement Learning with Confidence-Conditioned Verification2 Jun 2026
- 2026Zipping the Thought: When and How Compressed Reasoning Data Works in LLM Post-Training27 May 2026
- 2026Text-to-SPARQL Generation with Reinforcement Learning: A GRPO-based Approach on DBLP19 May 2026
- 2026Knowledge-to-Verification: Exploring RLVR for LLMs in Knowledge-Intensive Domains18 May 2026
12 newest of 57 All 57 (JSON)
- 2026Tool-R0: Self-Evolving LLM Agents for Tool-Learning from Zero Datacited by 31
- 2025Don't Just Fine-tune the Agent, Tune the Environmentcited by 17
- 2026daVinci-Dev: Agent-native Mid-training for Software Engineeringcited by 15
- 2025SSRL: Self-Search Reinforcement Learningcited by 13
- 2025Scaling Generalist Data-Analytic Agentscited by 11
- 2025DatasetResearch: Benchmarking Agent Systems for Demand-Driven Dataset Discoverycited by 9
- 2026Paying Less Generalization Tax: A Cross-Domain Generalization Study of RL Training for LLM Agentscited by 6
- 2026TailSFT: Filtered Fine-Tuning Improves Post-Training Performancecited by 2
- 2026OctoLong: Mid-Training On Cross-Repository Code Contexts Enhances Long-Context Modelingcited by 1
- 2026TailSFT: Filtered Fine-Tuning Improves Post-Training Performance26 Aug 2026
- 2026OctoLong: Mid-Training On Cross-Repository Code Contexts Enhances Long-Context Modeling5 Aug 2026
- 2026Tool-R0: Self-Evolving LLM Agents for Tool-Learning from Zero Data24 Feb 2026
- 2026daVinci-Dev: Agent-native Mid-training for Software Engineering26 Jan 2026
- 2026Paying Less Generalization Tax: A Cross-Domain Generalization Study of RL Training for LLM Agents26 Jan 2026
- 2025Don't Just Fine-tune the Agent, Tune the Environment11 Oct 2025
- 2025Scaling Generalist Data-Analytic Agents29 Sep 2025
- 2025SSRL: Self-Search Reinforcement Learning14 Aug 2025
- 2025DatasetResearch: Benchmarking Agent Systems for Demand-Driven Dataset Discovery9 Aug 2025
- 2026Sumi: Open Uniform Diffusion Language Model from Scratchcited by 2
- 2026Sumi: Open Uniform Diffusion Language Model from Scratch17 Jun 2026
- 2025SAM 3D: 3Dfy Anything in Imagescited by 230
- 2025SPICE: Self-Play In Corpus Environments Improves Reasoningcited by 78
- 2025Defeating the Training-Inference Mismatch via FP16cited by 62
- 2025BAPO: Stabilizing Off-Policy Reinforcement Learning for LLMs via Balanced Policy Optimization with Adaptive Clippingcited by 47
- 2025Evolving Language Models without Labels: Majority Drives Selection, Novelty Promotes Variationcited by 44
- 2025RaC: Robot Learning for Long-Horizon Tasks by Scaling Recovery and Correctioncited by 35
- 2025Reinforcement Learning Meets Large Language Models: A Survey of Advancements and Applications Across the LLM Lifecyclecited by 34
- 2026STEP3-VL-10B Technical Reportcited by 28
- 2025A Survey on LLM Mid-Trainingcited by 18
- 2025RePro: Training Language Models to Faithfully Recycle the Web for Pretrainingcited by 6
- 2025SAGE: Training Smart Any-Horizon Agents for Long Video Reasoning with Reinforcement Learningcited by 6
- 2026Aletheia: What Makes RLVR For Code Verifiers Tick?cited by 4
12 most cited of 35 All 35 (JSON)
- 2026Sharpen Before You Adapt: Data-Free Entry-State Sharpening for Test-Time Reinforcement Learning1 Oct 2026
- 2026MiST: Mid-Training LLMs for Cybersecurity16 Sep 2026
- 2026One Symptom, Three Levers: A Critical Review of On-Policy Self-Distillation26 Aug 2026
- 2026LittleLearner: Language Models Under Pedagogically Controlled Knowledge Exposure13 Aug 2026
- 2026When LLMs Read Tables Carelessly: Measuring and Reducing Data Referencing Errors30 Jun 2026
- 2026Reinforcement Learning without Ground-Truth Solutions can Improve LLMs25 Jun 2026
- 2026OrderGrad: Optimizing Beyond the Mean with Order-Statistic Policy Gradient Estimation4 Jun 2026
- 2026MIRA: Mid-training Rubric Anchoring for Source-Aware Data Selection28 May 2026
- 2026The Future of Facts: Tracing the Factual Generation-Verification Gap26 May 2026
- 2026Preference Tuning as Spectral Update Reorganization12 May 2026
- 2026Level Up: Defining and Exploiting Transitional Problems for Curriculum Learning14 Mar 2026
- 2026ComplLLM: Fine-tuning LLMs to Discover Complementary Signals for Decision-making23 Feb 2026
12 newest of 35 All 35 (JSON)
Similar, not cited
Close in wording, no citation either way
- 2025Scaling Behaviors of LLM Reinforcement Learning Post-Training: An Empirical Study in Mathematical Reasoning
- 2025On the Interplay of Pre-Training, Mid-Training, and RL on Reasoning Language Models
- 2025Reshaping Reasoning in LLMs: A Theoretical Analysis of RL Training Dynamics through Pattern Selection
- 2025Scaling Up RL: Unlocking Diverse Reasoning in LLMs via Prolonged Training
- 2024Does RLHF Scale? Exploring the Impacts From Data, Model, and Method
- 2025Demystifying Long Chain-of-Thought Reasoning in LLMs
- 2026Mid-Training with Self-Generated Data Improves Reinforcement Learning in Language Models
- 2025Reinforcement Learning on Pre-Training Data