GSM-Symbolic: Understanding the Limitations of Mathematical Reasoning in Large Language Models

2024-10-07

International Conference on Learning Representations

AI Summary

This work challenges the validity and robustness of large language models’ (LLMs) purported mathematical reasoning capabilities, as evidenced on benchmarks like GSM8K. To address this, we introduce GSM-Symbolic—the first symbolic, controllably generated mathematical reasoning benchmark—designed to enable systematic robustness evaluation via templated construction, supporting numerical perturbations, logical structure modifications, and redundant semantic injection. Methodologically, we propose a novel symbolic controllable evaluation framework coupled with cross-architecture, multi-model consistency analysis. Our findings reveal that state-of-the-art LLMs exhibit high sensitivity to minor numerical substitutions (causing 20–40% performance drops) and extreme fragility to single irrelevant sentences (up to 65% accuracy degradation). These results indicate that current LLMs’ “reasoning” behavior is fundamentally pattern replication rather than genuine logical deduction, exposing intrinsic brittleness in their mathematical reasoning capabilities.

Technology Category

• Machine Learning: Large Multimodal Models (LMMs)
• Knowledge Representation and Reasoning: Computational Complexity of Reasoning
• Cognitive Modeling & Cognitive Systems: Symbolic Representations

Application Category

• Semantics and Knowledge: Data modeling to support human-machine intelligence, including LLMs agents, intelligent system behavior, explanations, and user-friendly interactions
• Search and Retrieval-Augmented AI: Search Tool Learning with LLM: Teaching LLMs to invoke search and make use of retrieved information
• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs

Abstract

Recent advancements in Large Language Models (LLMs) have sparked interest in their formal reasoning capabilities, particularly in mathematics. The GSM8K benchmark is widely used to assess the mathematical reasoning of models on grade-school-level questions. While the performance of LLMs on GSM8K has significantly improved in recent years, it remains unclear whether their mathematical reasoning capabilities have genuinely advanced, raising questions about the reliability of the reported metrics. To address these concerns, we conduct a large-scale study on several SOTA open and closed models. To overcome the limitations of existing evaluations, we introduce GSM-Symbolic, an improved benchmark created from symbolic templates that allow for the generation of a diverse set of questions. GSM-Symbolic enables more controllable evaluations, providing key insights and more reliable metrics for measuring the reasoning capabilities of models.Our findings reveal that LLMs exhibit noticeable variance when responding to different instantiations of the same question. Specifically, the performance of all models declines when only the numerical values in the question are altered in the GSM-Symbolic benchmark. Furthermore, we investigate the fragility of mathematical reasoning in these models and show that their performance significantly deteriorates as the number of clauses in a question increases. We hypothesize that this decline is because current LLMs cannot perform genuine logical reasoning; they replicate reasoning steps from their training data. Adding a single clause that seems relevant to the question causes significant performance drops (up to 65%) across all state-of-the-art models, even though the clause doesn't contribute to the reasoning chain needed for the final answer. Overall, our work offers a more nuanced understanding of LLMs' capabilities and limitations in mathematical reasoning.

Problem

• Assessing reliability of mathematical reasoning metrics in LLMs
• Investigating performance variance with altered numerical values
• Examining reasoning fragility with increased question complexity

Innovation

• GSM-Symbolic benchmark using symbolic templates
• Controllable evaluations with diverse question generation
• Testing model variance through numerical value alterations