aiqbench analysis
This research introduces Function-Structured Graph Reinforcement Learning (FSG-RL), a novel framework that enhances mathematical reasoning by integrating executable code verification with multi-verifier feedback loops. By leveraging Group Relative Policy Optimization, the method significantly boosts solution accuracy on standard benchmarks like GSM8K and MATH, addressing the critical gap where successful code execution does not guarantee mathematical correctness. The work advances the field of AI-driven symbolic reasoning by establishing a robust protocol for training models that can decompose complex problems while maintaining rigorous verification standards.
Function-Structured Reinforcement Learning with Executable Verifiers for Mathematical Reasoning
arXiv:2610.01729v1 Announce Type: new Abstract: Algorithmic mathematical reasoning requires reliable decomposition, computation, and aggregation. Final-answer rewards provide limited guidance on intermediate errors, while successful execution does not guarantee mathematical correctness. This work proposes Function-Structured Graph Reinforcement Learning (FSG-RL), connecting subproblem graphs and Python implementations with multi-verifier feedback. The policy first learns to generate code from function graphs through supervised fine-tuning (SFT). Group Relative Policy Optimization (GRPO) then optimizes the policy using answer-gated rewards and span-level credit assignment. The framework also supports teacher supervision and structured memory. A benchmark curated from Grade School Math 8K (GSM8K), MathQA, MATH, and Omni-MATH pairs public function graphs with private verification specifications. Under a unified evaluation protocol, GRPO improves final-answer accuracy from 43.25% to 67.50% and full solution success from 32.25% to 52.25% over SFT. Continued reinforcement learning (RL) with teacher supervision yields additional gains. The gains extend beyond producing correctly formatted code, supporting verifier-guided reinforcement learning for mathematical reasoning. Code is available at https://github.com/ZihanLiummyycc/FSG-RL.
Abstract:Algorithmic mathematical reasoning requires reliable decomposition, computation, and aggregation. Final-answer rewards provide limited guidance on intermediate errors, while successful execution does not guarantee mathematical correctness. This work proposes Function-Structured Graph Reinforcement Learning (FSG-RL), connecting subproblem graphs and Python implementations with multi-verifier feedback. The policy first learns to generate code from function graphs through supervised fine-tuning (SFT). Group Relative Policy Optimization (GRPO) then optimizes the policy using answer-gated rewards and span-level credit assignment. The framework also supports teacher supervision and structured memory. A benchmark curated from Grade School Math 8K (GSM8K), MathQA, MATH, and Omni-MATH pairs public function graphs with private verification specifications. Under a unified evaluation protocol, GRPO improves final-answer accuracy from 43.25% to 67.50% and full solution success from 32.25% to 52.25% over SFT. Continued reinforcement learning (RL) with teacher supervision yields additional gains. The gains extend beyond producing correctly formatted code, supporting verifier-guided reinforcement learning for mathematical reasoning. Code is available at this https URL.
Machine Learning (cs.LG)
arXiv:2610.01729 [cs.LG]
(or arXiv:2610.01729v1 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2610.01729 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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