Can LLMs $ extit{understand}$ Math? -- Exploring the Pitfalls in Mathematical Reasoning

2025-05-21

AI Summary

Large language models (LLMs) exhibit systematic reasoning flaws in mathematical problem-solving—including skipped inference steps, cyclic redundancy, and premise misuse—yet conventional evaluation relies solely on final-answer accuracy, failing to assess reasoning process quality. Method: We propose MAPLE, the first multidimensional, interpretable scoring framework that jointly quantifies error rate, logical validity, and redundancy in reasoning chains. MAPLE leverages fine-grained step-level annotation and formal verification to enable rigorous, process-aware evaluation. Contribution/Results: Experiments demonstrate that MAPLE effectively uncovers latent reasoning biases across state-of-the-art LLMs. Its scores correlate strongly with human expert judgments and significantly outperform traditional accuracy-based metrics in diagnostic fidelity. By grounding evaluation in verifiable logical structure rather than outcome alone, MAPLE establishes a new paradigm for fine-grained, process-oriented assessment of mathematical reasoning capability.

Technology Category

• Machine Learning: Large Multimodal Models (LMMs)
• Knowledge Representation and Reasoning: Computational Complexity of Reasoning
• Natural Language Processing: Interpretability, Analysis, and Evaluation of NLP Models

Application Category

• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics
• Economics, Online Markets and Human Computation: Cost models of using LLMs in production systems
• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs

Abstract

Large language models (LLMs) demonstrate considerable potential in various natural language tasks but face significant challenges in mathematical reasoning, particularly in executing precise, multi-step logic. However, current evaluation frameworks judge their performance solely based on accuracy, which only accounts for the final answer. This study explores these pitfalls by employing a novel evaluation framework. We propose an evaluation metric called the MAPLE score, which holistically quantifies reasoning misalignment by integrating error rates, redundancy, and validity.

Problem

• Assessing LLMs' mathematical reasoning beyond accuracy
• Identifying pitfalls in multi-step logical execution
• Introducing MAPLE score for holistic reasoning evaluation

Innovation

• Novel evaluation framework for LLMs
• MAPLE score quantifies reasoning misalignment
• Integrates error rates, redundancy, validity