mlsanityData to 7 Oct 2026

VERIFY-RL: Verifiable Recursive Decomposition for Reinforcement Learning in Mathematical Reasoning

arXiv 2602.07559 ↗First posted 7 Feb 2026cs.AI cs.CC cs.NAcited by 0

On the map: LLM reasoning → Mathematical reasoning

Abstract (arXiv)

Training language models to solve complex mathematical problems benefits from curriculum learning progressively training on simpler subproblems. However, existing decomposition methods are often heuristic, offering no guarantees that subproblems are simpler, that solving them aids the parent task, or that their relationships are mathematically grounded. We observe that symbolic differentiation provides a natural structure for verified decomposition: calculus rules explicitly define how expressions reduce to simpler components with provable properties. We introduce Verify-RL, a framework where every parent-child decomposition satisfies three verifiable conditions: strictly decreasing structural complexity, solution containment, and formal rule derivation. Unlike heuristic methods where a significant fraction of decompositions are invalid our properties admit automatic verification through symbolic computation, achieving "verification by construction" Experiments demonstrate that eliminating invalid decompositions yields sizable gains, accuracy on the hardest problems more than doubles from 32% to 68%, with a 40% relative improvement overall.

Key facts. No citing papers in the map yet (data through 7 Oct 2026). Placed in Mathematical reasoning, one of 17 directions in LLM reasoning. Builds on 25 of its 36 references that are in the map. First posted on arXiv 7 Feb 2026.

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25 of 36 references.

Closest ancestors · 4

Same direction, newest first

  1. 2024DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models5 Feb
  2. 2023Llemma: An Open Language Model For Mathematics16 Oct
  3. 2023MathCoder: Seamless Code Integration in LLMs for Enhanced Mathematical Reasoning5 Oct
  4. 2022Solving Quantitative Reasoning Problems with Language Models29 Jun

Other references · 21

  1. 2017Proximal Policy Optimization Algorithmscited by 14,441
  2. 2021Training Verifiers to Solve Math Word Problemscited by 9,743
  3. 2025DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learningcited by 6,146
  4. 2022Self-Consistency Improves Chain of Thought Reasoning in Language Modelscited by 5,601
  5. 2023Let's Verify Step by Stepcited by 3,598
  6. 2023Tree of Thoughts: Deliberate Problem Solving with Large Language Modelscited by 3,155
  7. 2022Least-to-Most Prompting Enables Complex Reasoning in Large Language Modelscited by 1,397
  8. 2022STaR: Bootstrapping Reasoning With Reasoningcited by 895
  9. 2022Solving math word problems with process- and outcome-based feedbackcited by 871
  10. 2024ReST-MCTS*: LLM Self-Training via Process Reward Guided Tree Searchcited by 338
  11. 2023Beyond Human Data: Scaling Self-Training for Problem-Solving with Language Modelscited by 325
  12. 2025Reinforcement Learning with Verifiable Rewards Implicitly Incentivizes Correct Reasoning in Base LLMscited by 276
9 more
  1. 2024DeepSeek-Prover: Advancing Theorem Proving in LLMs through Large-Scale Synthetic Datacited by 225
  2. 2024V-STaR: Training Verifiers for Self-Taught Reasonerscited by 214
  3. 2024VinePPO: Refining Credit Assignment in RL Training of LLMscited by 168
  4. 2025Curriculum Reinforcement Learning from Easy to Hard Tasks Improves LLM Reasoningcited by 89
  5. 2025GRPO-LEAD: A Difficulty-Aware Reinforcement Learning Approach for Concise Mathematical Reasoning in Language Modelscited by 81
  6. 2024Lean Copilot: Large Language Models as Copilots for Theorem Proving in Leancited by 52
  7. 2025LADDER: Self-Improving LLMs Through Recursive Problem Decompositioncited by 24
  8. 2025Recursive Decomposition of Logical Thoughts: Framework for Superior Reasoning and Knowledge Propagation in Large Language Modelscited by 3
  9. 2025Complexity Agnostic Recursive Decomposition of Thoughtscited by 1

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  1. 2025CriticLean: Critic-Guided Reinforcement Learning for Mathematical Formalization
  2. 2025From Accuracy to Robustness: A Study of Rule- and Model-based Verifiers in Mathematical Reasoning
  3. 2026Reinforcement Learning with Verifiable Physics: Post-training LLMs with Continuous Rewards
  4. 2025VerIF: Verification Engineering for Reinforcement Learning in Instruction Following
  5. 2026When RL Suppresses Its Own Vocabulary: Recovering Reasoning Diversity in Puzzle-to-Math Transfer
  6. 2025DeepSeek-Prover-V2: Advancing Formal Mathematical Reasoning via Reinforcement Learning for Subgoal Decomposition
  7. 2025NFT: Bridging Supervised Learning and Reinforcement Learning in Math Reasoning
  8. 2025Trust, But Verify: A Self-Verification Approach to Reinforcement Learning with Verifiable Rewards