Enhancing Mathematical Problem Solving in LLMs through Execution-Driven Reasoning Augmentation

TL;DR

This paper introduces IIPC, a novel iterative reasoning method that refines programmatic solutions using execution feedback, significantly improving mathematical problem-solving accuracy in large language models.

Contribution

The paper presents IIPC, a new approach that enhances LLM reasoning by iteratively refining solutions with execution feedback, addressing limitations of previous methods.

Findings

IIPC outperforms existing methods on multiple reasoning benchmarks.

It maintains high-level contextual focus during iterative refinement.

Code and implementations are openly available.

Abstract

Mathematical problem solving is a fundamental benchmark for assessing the reasoning capabilities of artificial intelligence and a gateway to applications in education, science, and engineering where reliable symbolic reasoning is essential. Although recent advances in multi-agent LLM-based systems have enhanced their mathematical reasoning capabilities, they still lack a reliably revisable representation of the reasoning process. Existing agents either operate in rigid sequential pipelines that cannot correct earlier steps or rely on heuristic self-evaluation that can fail to identify and fix errors. In addition, programmatic context can distract language models and degrade accuracy. To address these gaps, we introduce Iteratively Improved Program Construction (IIPC), a reasoning method that iteratively refines programmatic reasoning chains and combines execution feedback with the native Chain-of-thought abilities of the base LLM to maintain high-level contextual focus. IIPC surpasses competing approaches in the majority of reasoning benchmarks on multiple base LLMs. All code and implementations are released as open source.