THOR: Tool-Integrated Hierarchical Optimization via RL for Mathematical Reasoning
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
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- 2025Teaching LLMs According to Their Aptitude: Adaptive Reasoning for Mathematical Problem Solving17 Feb
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- 2024DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models5 Feb
- 2023OVM, Outcome-supervised Value Models for Planning in Mathematical Reasoning16 Nov
- 2023ToRA: A Tool-Integrated Reasoning Agent for Mathematical Problem Solving29 Sep
- 2022Solving Quantitative Reasoning Problems with Language Models29 Jun
Other references · 45
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- 2025The Lessons of Developing Process Reward Models in Mathematical Reasoningcited by 415
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Built on by
Citing papers per year: 2025: 3; 2026: 6.
9 papers.
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- 2026PEARL: Training Socratic Tutors with Pedagogically Aligned Reinforcement Learning28 May 2026
- 2026Neuro-Symbolic Financial Reasoning via Deterministic Fact Ledgers and Adversarial Low-Latency Hallucination Detector4 Mar 2026
- 2026Reward Modeling for Reinforcement Learning-Based LLM Reasoning: Design, Challenges, and Evaluation10 Feb 2026
- 2026Unveiling the Cognitive Compass: Theory-of-Mind-Guided Multimodal Emotion Reasoning1 Feb 2026
- 2026MatchTIR: Fine-Grained Supervision for Tool-Integrated Reasoning via Bipartite Matching15 Jan 2026
- 2025AgentMath: Empowering Mathematical Reasoning for Large Language Models via Tool-Augmented Agent23 Dec 2025
- 2025DiG: Differential Grounding for Enhancing Fine-Grained Perception in Multimodal Large Language Model14 Dec 2025
- 2025AgentEvolver: Towards Efficient Self-Evolving Agent System13 Nov 2025
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