MATH-Perturb: Benchmarking LLMs' Math Reasoning Abilities against Hard Perturbations

2025-02-10

AI Summary

This work investigates the reasoning robustness of large language models (LLMs) on mathematical problems under “hard perturbations”—semantic alterations that fundamentally invalidate original solution strategies—thereby distinguishing genuine reasoning from memory-dependent behavior. Method: To address the lack of standardized hard-perturbation evaluation, the authors construct two new benchmarks—MATH-P-Simple and MATH-P-Hard—derived from the most challenging problems in the MATH dataset and generated via a hybrid human-and-rule-driven perturbation process. Contribution/Results: This is the first systematic definition and empirical assessment of hard perturbations in mathematical reasoning. It reveals a novel memorization phenomenon: LLMs blindly reuse solution templates during in-context learning, even when contextually inappropriate. Cross-model experiments show that MATH-P-Hard induces up to a −16.49% accuracy drop on state-of-the-art models (e.g., o1-mini), exposing severe contextual misdirection and pattern mismatch in current mathematical reasoning capabilities.

Technology Category

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

Application Category

• Search and Retrieval-Augmented AI: Large language models for search
• User Modeling, Personalization and Recommendation: Large Language Models (LLM) for user modeling and recommendation
• Economics, Online Markets and Human Computation: Cost models of using LLMs in production systems

Abstract

Large language models have demonstrated impressive performance on challenging mathematical reasoning tasks, which has triggered the discussion of whether the performance is achieved by true reasoning capability or memorization. To investigate this question, prior work has constructed mathematical benchmarks when questions undergo simple perturbations -- modifications that still preserve the underlying reasoning patterns of the solutions. However, no work has explored hard perturbations, which fundamentally change the nature of the problem so that the original solution steps do not apply. To bridge the gap, we construct MATH-P-Simple and MATH-P-Hard via simple perturbation and hard perturbation, respectively. Each consists of 279 perturbed math problems derived from level-5 (hardest) problems in the MATH dataset (Hendrycksmath et. al., 2021). We observe significant performance drops on MATH-P-Hard across various models, including o1-mini (-16.49%) and gemini-2.0-flash-thinking (-12.9%). We also raise concerns about a novel form of memorization where models blindly apply learned problem-solving skills without assessing their applicability to modified contexts. This issue is amplified when using original problems for in-context learning. We call for research efforts to address this challenge, which is critical for developing more robust and reliable reasoning models.

Problem

• Assessing LLMs' true math reasoning vs. memorization.
• Exploring hard perturbations' impact on math problem-solving.
• Identifying memorization risks in modified problem contexts.

Innovation

• Hard perturbation analysis
• MATH-P benchmark construction
• Memorization issue identification