GSM-Symbolic: Understanding the Limitations of Mathematical Reasoning in Large Language Models (AI summary)

Key Points

1. The paper introduces GSM-Symbolic, an enhanced benchmark that generates diverse variants of the GSM8K math question dataset using symbolic templates. This enables more nuanced and reliable evaluation of LLMs' performance across various setups, moving beyond single-point accuracy metrics.

2. The paper questions the reliability of currently reported results on GSM8K, demonstrating that the performance of LLMs can be viewed as a distribution with unwarranted variance across different instantiations of the same question. It shows that the performance of all models drops on GSM-Symbolic, hinting at potential data contamination.

3. LLMs exhibit more robustness to changes in superficial elements like proper names but are very sensitive to changes in numerical values.

4. As the number of clauses in the questions increases, LLM performance degradation and variance increase, indicating that their reasoning capabilities struggle with increased complexity.

5. The paper introduces the GSM-NoOp dataset, which adds seemingly relevant but ultimately irrelevant information to problems. This reveals a critical flaw in the models' ability to discern relevant information for problem-solving, likely due to their reasoning being based on pattern matching rather than formal logic.

6. Even when provided with multiple examples of the same question or examples containing similar irrelevant information, LLMs struggle to overcome the challenges posed by GSM-NoOp, suggesting deeper issues in their reasoning processes.

7. The paper provides a comprehensive understanding of the limitations of LLMs in mathematical reasoning, emphasizing the need for more reliable evaluation methodologies and further research into the reasoning capabilities of large language models.

8. The results suggest that the reasoning process in LLMs is not formal and is instead a form of probabilistic pattern-matching, where the models attempt to replicate the reasoning steps observed in their training data.

9. The paper concludes that further research is essential to develop AI models capable of formal reasoning, moving beyond pattern recognition to achieve more robust and generalizable problem-solving skills.

Summary

This research paper explores the mathematical reasoning capabilities of large language models (LLMs). It introduces a new benchmark called GSM-Symbolic, which generates diverse variants of questions from the widely used GSM8K dataset, to provide more controlled and reliable evaluations of LLM performance.

The key findings from this study are: 1. Reliability of GSM8K results: The paper questions the reliability of currently reported results on GSM8K, as it demonstrates significant variance in model responses across different instantiations of the same question. The performance of all models tested was found to be lower on GSM-Symbolic compared to GSM8K, hinting at potential data contamination. 2. Fragility of mathematical reasoning: The study shows that LLMs exhibit more robustness to changes in superficial elements like proper names, but are very sensitive to changes in numerical values. As the number of clauses in the questions increases, model performance declines significantly, and the variance in performance increases. This suggests that current LLMs are not capable of genuine logical reasoning, and their reasoning is likely based on probabilistic pattern-matching. 3. Limitations in understanding mathematical concepts: The introduction of the GSM-NoOp dataset, which adds seemingly relevant but ultimately irrelevant information to the questions, reveals a critical flaw in LLMs' ability to discern relevant information for problem-solving. All state-of-the-art models tested experienced substantial performance drops (up to 65%) on this dataset, even when provided with multiple examples containing similar irrelevant information. This indicates deeper issues in their reasoning processes that cannot be easily mitigated through few-shot learning or fine-tuning.

Overall, this work provides a comprehensive understanding of the limitations of LLMs in mathematical reasoning, emphasizing the need for more reliable evaluation methodologies and further research into the reasoning capabilities of large language models. The findings suggest that current LLMs may be relying more on pattern-matching than genuine logical reasoning, and highlights the importance of developing AI models capable of formal reasoning to achieve more robust and generalizable problem-solving skills.

Reference: https://arxiv.org/abs/2410.05229