Advancing Multi-Step Mathematical Reasoning in Large Language Models through Multi-Layered Self-Reflection with Auto-Prompting

TL;DR

MAPS tackles the challenge of multi-step mathematical reasoning in LLMs by integrating Chain-of-Thought with multi-layer self-reflection and auto-prompting to iteratively refine reasoning. The framework generates tailored reflection prompts per layer, enabling deeper error diagnosis and correction across diverse models and benchmarks (GSM8K, GSM-Symbolic, AIME 2025, MATH 500). Results show MAPS achieves state-of-the-art-like performance for general-purpose models, sometimes matching specialized reasoning systems, with a clear trade-off in token usage and cost that is mitigated by limiting reflection depth. The work provides a detailed methodology, empirical analysis, and public release of MAPS resources, advancing cognitively inspired prompting for robust mathematical reasoning.

Abstract

Recent advancements in Large Language Models (LLMs) have significantly improved their problem-solving capabilities. However, these models still struggle when faced with complex multi-step reasoning tasks. In this paper, we propose the Multi-Layered Self-Reflection with Auto-Prompting (MAPS) framework, a novel approach designed to enhance multi-step mathematical reasoning in LLMs by integrating techniques such as Chain of Thought (CoT), Self-Reflection, and Auto-Prompting. Unlike traditional static prompting methods, MAPS employs an iterative refinement process. Initially, the model generates a solution using CoT prompting. When errors are detected, an adaptive self-reflection mechanism identifies and analyzes them, generating tailored prompts to guide corrections. These dynamically adjusted prompts enable the model to iteratively refine its reasoning. Experiments on four well-established benchmarks across multiple LLMs show that MAPS significantly outperforms standard CoT and achieves competitive results with reasoning-optimized models. In addition, MAPS enables general-purpose LLMs to reach performance levels comparable to specialized reasoning models. While deeper reflection layers improve accuracy, they also increase token usage and costs. To balance this trade-off, MAPS strategically limits reflection depth, ensuring an optimal balance between cost and reasoning performance.

Figures (6)

• Figure 1: Comparison of (a) Self-Reflection with single-pass and (b) Multi-layer Auto-Prompted Self-Reflection (MAPS).
• Figure 2: Meta-prompt (template) to apply MAPS.
• Figure 3: Instance of question and expected answer from GSM-symbolic-p2.
• Figure 4: Excerpt of the auto-generated reflection prompt from the second MAPS cycle ($2L$).
• Figure 5: Nemenyi post-hoc test applied to the accuracy results from Table \ref{['tab:accuracy_table']} to statistically assess (a) the performance of prompting techniques and (b) their impact on LLM performance.