mlsanityData to 14 Oct 2026

THOR: Tool-Integrated Hierarchical Optimization via RL for Mathematical Reasoning

arXiv 2509.13761 ↗First posted 17 Sep 2025cs.AI cs.CLcited by 9

On the map: LLM reasoning → Mathematical reasoning

Abstract (arXiv)

Large Language Models (LLMs) have made remarkable progress in mathematical reasoning, but still continue to struggle with high-precision tasks like numerical computation and formal symbolic manipulation. Integrating external tools has emerged as a promising approach to bridge this gap. Despite recent advances, existing methods struggle with three key challenges: constructing tool-integrated reasoning data, performing fine-grained optimization, and enhancing inference. To overcome these limitations, we propose THOR (Tool-Integrated Hierarchical Optimization via RL). First, we introduce TIRGen, a multi-agent based pipeline for constructing high-quality datasets of tool-integrated reasoning paths, aligning with the policy and generalizing well across diverse models. Second, to perform fine-grained hierarchical optimization, we introduce an RL strategy that jointly optimizes for both episode-level problem solving and step-level code generation. This is motivated by our key insight that the success of an intermediate tool call is a strong predictor of the final answer's correctness. Finally, THOR incorporates a self-correction mechanism that leverages immediate tool feedback to dynamically revise erroneous reasoning paths during inference. Our approach demonstrates strong generalization across diverse models, performing effectively in both reasoning and non-reasoning models. It further achieves state-of-the-art performance for models of a similar scale on multiple mathematical benchmarks, while also delivering consistent improvements on code benchmarks. Our code will be publicly available at https://github.com/JingMog/THOR.

Key facts. Cited by 9 papers in the map (data through 14 Oct 2026). Placed in Mathematical reasoning, one of 17 directions in LLM reasoning. Builds on 52 of its 60 references that are in the map. First posted on arXiv 17 Sep 2025.

Builds on

52 of 60 references.

Closest ancestors · 7

Same direction, newest first

  1. 2025AIMO-2 Winning Solution: Building State-of-the-Art Mathematical Reasoning Models with OpenMathReasoning dataset23 Apr
  2. 2025Teaching LLMs According to Their Aptitude: Adaptive Reasoning for Mathematical Problem Solving17 Feb
  3. 2025rStar-Math: Small LLMs Can Master Math Reasoning with Self-Evolved Deep Thinking8 Jan
  4. 2024DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models5 Feb
  5. 2023OVM, Outcome-supervised Value Models for Planning in Mathematical Reasoning16 Nov
  6. 2023ToRA: A Tool-Integrated Reasoning Agent for Mathematical Problem Solving29 Sep
  7. 2022Solving Quantitative Reasoning Problems with Language Models29 Jun

Other references · 45

  1. 2017Proximal Policy Optimization Algorithmscited by 15,215
  2. 2022Chain-of-Thought Prompting Elicits Reasoning in Large Language Modelscited by 12,459
  3. 2025Qwen3 Technical Reportcited by 8,820
  4. 2022ReAct: Synergizing Reasoning and Acting in Language Modelscited by 8,695
  5. 2021Evaluating Large Language Models Trained on Codecited by 8,320
  6. 2025DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learningcited by 6,330
  7. 2021Measuring Mathematical Problem Solving With the MATH Datasetcited by 5,371
  8. 2024GPT-4o System Cardcited by 4,588
  9. 2023Toolformer: Language Models Can Teach Themselves to Use Toolscited by 4,182
  10. 2023Tree of Thoughts: Deliberate Problem Solving with Large Language Modelscited by 3,211
  11. 2025DAPO: An Open-Source LLM Reinforcement Learning System at Scalecited by 2,810
  12. 2023Voyager: An Open-Ended Embodied Agent with Large Language Modelscited by 2,191
33 more
  1. 2024LiveCodeBench: Holistic and Contamination Free Evaluation of Large Language Models for Codecited by 2,004
  2. 2023Is Your Code Generated by ChatGPT Really Correct? Rigorous Evaluation of Large Language Models for Code Generationcited by 1,391
  3. 2019ZeRO: Memory Optimizations Toward Training Trillion Parameter Modelscited by 1,301
  4. 2025Kimi k1.5: Scaling Reinforcement Learning with LLMscited by 1,210
  5. 2024OlympiadBench: A Challenging Benchmark for Promoting AGI with Olympiad-Level Bilingual Multimodal Scientific Problemscited by 1,136
  6. 2024Qwen2.5-Math Technical Report: Toward Mathematical Expert Model via Self-Improvementcited by 1,090
  7. 2022Program of Thoughts Prompting: Disentangling Computation from Reasoning for Numerical Reasoning Taskscited by 1,076
  8. 2025Does Reinforcement Learning Really Incentivize Reasoning Capacity in LLMs Beyond the Base Model?cited by 982
  9. 2023Math-Shepherd: Verify and Reinforce LLMs Step-by-step without Human Annotationscited by 928
  10. 2023Graph of Thoughts: Solving Elaborate Problems with Large Language Modelscited by 886
  11. 2025Group Sequence Policy Optimizationcited by 835
  12. 2024Self-Play Fine-Tuning Converts Weak Language Models to Strong Language Modelscited by 557
  13. 2025Process Reinforcement through Implicit Rewardscited by 504
  14. 2024Generative Verifiers: Reward Modeling as Next-Token Predictioncited by 480
  15. 2025Search-o1: Agentic Search-Enhanced Large Reasoning Modelscited by 433
  16. 2025The Lessons of Developing Process Reward Models in Mathematical Reasoningcited by 415
  17. 2025ReTool: Reinforcement Learning for Strategic Tool Use in LLMscited by 392
  18. 2024Interpretable Preferences via Multi-Objective Reward Modeling and Mixture-of-Expertscited by 376
  19. 2025ToolRL: Reward is All Tool Learning Needscited by 362
  20. 2025VAPO: Efficient and Reliable Reinforcement Learning for Advanced Reasoning Taskscited by 285
  21. 2025DeepMath-103K: A Large-Scale, Challenging, Decontaminated, and Verifiable Mathematical Dataset for Advancing Reasoningcited by 280
  22. 2023The False Promise of Imitating Proprietary LLMscited by 263
  23. 2023Universal Self-Consistency for Large Language Model Generationcited by 203
  24. 2024Mulberry: Empowering MLLM with o1-like Reasoning and Reflection via Collective Monte Carlo Tree Searchcited by 175
  25. 2025ToRL: Scaling Tool-Integrated RLcited by 169
  26. 2024Marco-o1: Towards Open Reasoning Models for Open-Ended Solutionscited by 144
  27. 2025Agentic Reasoning and Tool Integration for LLMs via Reinforcement Learningcited by 110
  28. 2025What's Behind PPO's Collapse in Long-CoT? Value Optimization Holds the Secretcited by 98
  29. 2025Agent RL Scaling Law: Agent RL with Spontaneous Code Execution for Mathematical Problem Solvingcited by 62
  30. 2025START: Self-taught Reasoner with Toolscited by 47
  31. 2025AutoTIR: Autonomous Tools Integrated Reasoning via Reinforcement Learningcited by 33
  32. 2025Enhancing the Geometric Problem-Solving Ability of Multimodal LLMs via Symbolic-Neural Integrationcited by 18
  33. 2025PRM-BAS: Enhancing Multimodal Reasoning through PRM-guided Beam Annealing Searchcited by 12

Built on by

Cited by year (2026 to 14 Oct)

Citing papers per year: 2025: 3; 2026: 6.

9 papers.

Similar, not cited

Close in wording, no citation either way

  1. 2025MiroMind-M1: An Open-Source Advancement in Mathematical Reasoning via Context-Aware Multi-Stage Policy Optimization
  2. 2026Implicit Hierarchical GRPO: Decoupling Tool Invocation from Execution for Tool-Integrated Mathematical Reasoning
  3. 2025A Survey on Mathematical Reasoning and Optimization with Large Language Models
  4. 2025Agentic-R1: Distilled Dual-Strategy Reasoning
  5. 2025Distilling Tool Knowledge into Language Models via Back-Translated Traces
  6. 2026ThinkTwice: Jointly Optimizing Large Language Models for Reasoning and Self-Refinement
  7. 2025A Toolbox, Not a Hammer -- Multi-TAG: Scaling Math Reasoning with Multi-Tool Aggregation
  8. 2025Towards Effective Code-Integrated Reasoning