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

• URL: http://arxiv.org/abs/2410.05229v1
• Date: Mon, 7 Oct 2024 17:36:37 GMT
• Title: GSM-Symbolic: Understanding the Limitations of Mathematical Reasoning in Large Language Models
• Authors: Iman Mirzadeh, Keivan Alizadeh, Hooman Shahrokhi, Oncel Tuzel, Samy Bengio, Mehrdad Farajtabar,
• Abstract summary: The GSM8K benchmark is widely used to assess the mathematical reasoning of models on grade-school-level questions. We introduce GSM-Symbolic, an improved benchmark created from symbolic templates. Our findings reveal that LLMs exhibit noticeable variance when responding to different instantiations of the same question.
• Score: 24.266973481633755
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

Related papers

• CounterBench: A Benchmark for Counterfactuals Reasoning in Large Language Models [5.409370027524351]
  We evaluate the performance of large language models (LLMs) in counterfactual reasoning. We introduce a new benchmark dataset, CounterBench, comprising 1K counterfactual reasoning questions.
  arXiv  Detail & Related papers  (2025-02-16T06:19:37Z)
• GSM-Infinite: How Do Your LLMs Behave over Infinitely Increasing Context Length and Reasoning Complexity? [37.399561533852506]
  We develop a grade school math problem generator capable of producing arithmetic problems with infinite difficulty and context length under fine-grained control. We find a consistent sigmoid decline in reasoning performance as complexity increases, along with a systematic inference scaling trend.
  arXiv  Detail & Related papers  (2025-02-07T17:05:25Z)
• MathHay: An Automated Benchmark for Long-Context Mathematical Reasoning in LLMs [61.74749961334557]
  MathHay is an automated benchmark designed to assess the long-context mathematical reasoning capabilities of LLMs. We conduct extensive experiments on MathHay to assess the long-context mathematical reasoning abilities of eight top-performing models.
  arXiv  Detail & Related papers  (2024-10-07T02:30:07Z)
• Not All LLM Reasoners Are Created Equal [58.236453890457476]
  We study the depth of grade-school math problem-solving capabilities of LLMs. We evaluate their performance on pairs of existing math word problems together.
  arXiv  Detail & Related papers  (2024-10-02T17:01:10Z)
• SIaM: Self-Improving Code-Assisted Mathematical Reasoning of Large Language Models [54.78329741186446]
  We propose a novel paradigm that uses a code-based critic model to guide steps including question-code data construction, quality control, and complementary evaluation. Experiments across both in-domain and out-of-domain benchmarks in English and Chinese demonstrate the effectiveness of the proposed paradigm.
  arXiv  Detail & Related papers  (2024-08-28T06:33:03Z)
• A Careful Examination of Large Language Model Performance on Grade School Arithmetic [4.573055530800853]
  Large language models (LLMs) have achieved impressive success on many benchmarks for mathematical reasoning. There is growing concern that some of this performance actually reflects dataset contamination.
  arXiv  Detail & Related papers  (2024-05-01T05:52:05Z)
• Evaluating Consistency and Reasoning Capabilities of Large Language Models [0.0]
  Large Language Models (LLMs) are extensively used today across various sectors, including academia, research, business, and finance. Despite their widespread adoption, these models often produce incorrect and misleading information, exhibiting a tendency to hallucinate. This paper aims to evaluate and compare the consistency and reasoning capabilities of both public and proprietary LLMs.
  arXiv  Detail & Related papers  (2024-04-25T10:03:14Z)
• GSM-Plus: A Comprehensive Benchmark for Evaluating the Robustness of LLMs as Mathematical Problem Solvers [68.77382332826167]
  Large language models (LLMs) have achieved impressive performance across various mathematical reasoning benchmarks. One essential and frequently occurring evidence is that when the math questions are slightly changed, LLMs can behave incorrectly. This motivates us to evaluate the robustness of LLMs' math reasoning capability by testing a wide range of question variations.
  arXiv  Detail & Related papers  (2024-02-29T15:26:14Z)
• Premise Order Matters in Reasoning with Large Language Models [57.18850969634412]
  We show that large language models (LLMs) are surprisingly brittle to the ordering of the premises. We observe that LLMs achieve the best performance when the premise order aligns with the context required in intermediate reasoning steps.
  arXiv  Detail & Related papers  (2024-02-14T04:50:18Z)
• The ART of LLM Refinement: Ask, Refine, and Trust [85.75059530612882]
  We propose a reasoning with refinement objective called ART: Ask, Refine, and Trust. It asks necessary questions to decide when an LLM should refine its output. It achieves a performance gain of +5 points over self-refinement baselines.
  arXiv  Detail & Related papers  (2023-11-14T07:26:32Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.