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

arXiv: https://arxiv.org/abs/2602.03950 · HTML: https://mlsanity.com/paper/2602.03950/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Mathematical reasoning, one of 17 directions in LLM reasoning.
- Builds on 21 of its 32 references that are in the map.
- First posted on arXiv 3 Feb 2026.

## Placed in

- LLM reasoning / [Mathematical reasoning](https://mlsanity.com/lr/mathematical-reasoning/)

## Builds on (most cited first, 21 of 21)

- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Reflexion: Language Agents with Verbal Reinforcement Learning](https://mlsanity.com/paper/2303.11366/) (2023)
- [Program of Thoughts Prompting: Disentangling Computation from Reasoning for Numerical Reasoning Tasks](https://mlsanity.com/paper/2211.12588/) (2022)
- [Large Language Models Cannot Self-Correct Reasoning Yet](https://mlsanity.com/paper/2310.01798/) (2023)
- [Large Language Models Can Be Easily Distracted by Irrelevant Context](https://mlsanity.com/paper/2302.00093/) (2023)
- [PAL: Program-aided Language Models](https://mlsanity.com/paper/2211.10435/) (2022)
- [Why Do Multi-Agent LLM Systems Fail?](https://mlsanity.com/paper/2503.13657/) (2025)
- [OpenCodeInterpreter: Integrating Code Generation with Execution and Refinement](https://mlsanity.com/paper/2402.14658/) (2024)
- [Solving Challenging Math Word Problems Using GPT-4 Code Interpreter with Code-based Self-Verification](https://mlsanity.com/paper/2308.07921/) (2023)
- [LLM-SR: Scientific Equation Discovery via Programming with Large Language Models](https://mlsanity.com/paper/2404.18400/) (2024)
- [Cumulative Reasoning with Large Language Models](https://mlsanity.com/paper/2308.04371/) (2023)
- [Agents Thinking Fast and Slow: A Talker-Reasoner Architecture](https://mlsanity.com/paper/2410.08328/) (2024)
- [LLMPhy: Parameter-Identifiable Physical Reasoning Combining Large Language Models and Physics Engines](https://mlsanity.com/paper/2411.08027/) (2024)
- [How Is LLM Reasoning Distracted by Irrelevant Context? An Analysis Using a Controlled Benchmark](https://mlsanity.com/paper/2505.18761/) (2025)
- [Beyond Final Answers: Evaluating Large Language Models for Math Tutoring](https://mlsanity.com/paper/2503.16460/) (2025)
- [When Large Language Model Meets Optimization](https://mlsanity.com/paper/2405.10098/) (2024)
- [Reasoning Through Execution: Unifying Process and Outcome Rewards for Code Generation](https://mlsanity.com/paper/2412.15118/) (2024)
- [One Size doesn't Fit All: A Personalized Conversational Tutoring Agent for Mathematics Instruction](https://mlsanity.com/paper/2502.12633/) (2025)
- [A Survey on Mathematical Reasoning and Optimization with Large Language Models](https://mlsanity.com/paper/2503.17726/) (2025)
- [Execution Guided Line-by-Line Code Generation](https://mlsanity.com/paper/2506.10948/) (2025)
- [Evaluating Large Language Models for Financial Reasoning: A CFA-Based Benchmark Study](https://mlsanity.com/paper/2509.04468/) (2025)

## Abstract (arXiv)

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.