Automatically Generating Hard Math Problems from Hypothesis-Driven Error Analysis
Summary: arXiv:2604.04386v1 Announce Type: new
Abstract
Numerous math benchmarks exist to evaluate LLMs’ mathematical capabilities. However, most involve extensive manual effort and are difficult to scale. Consequently, they cannot keep pace with LLM development or easily provide new instances to mitigate overfitting. Some researchers have proposed automatic benchmark generation methods, but few focus on identifying the specific math concepts and skills on which LLMs are error-prone, and most can only generate category-specific benchmarks.
Introduction
This article presents a novel approach to generating math benchmarks that addresses the limitations of existing methods. Our proposed pipeline leverages AI-generated hypotheses to pinpoint the specific mathematical concepts and skills that LLMs struggle with. By targeting these weaknesses, we can generate new benchmark problems that are not only relevant but also challenging.
Methodology
Our benchmark generation pipeline operates through a series of steps:
- Hypothesis Generation: We utilize AI models to generate hypotheses regarding the weaknesses of LLMs in specific mathematical areas.
- Problem Generation: Based on these hypotheses, we create new math problems that focus on the identified areas of difficulty.
- Evaluation: The problems are then evaluated for difficulty and relevance, ensuring they adequately challenge the LLMs.
Results
Our experiments demonstrate a strong correlation between the accuracy of the generated hypotheses and the difficulty level of the problems produced. Specifically, problems generated from the most accurate hypotheses resulted in a significant drop in performance for Llama-3.3-70B-Instruct, reducing its accuracy to as low as 45% compared to a baseline of 77% on the original MATH benchmark.
Implications
This new methodology not only enhances the testing of LLMs’ mathematical capabilities but also offers a scalable solution that can adapt to the rapid advancements in AI. The implications of this research extend beyond mathematics, as our pipeline can be applied to various domains to evaluate LLM performance across different skills.
Conclusion
In summary, our proposed benchmark generation pipeline provides a robust framework for creating targeted mathematical problems that reflect LLM weaknesses. This approach fosters a deeper understanding of LLM capabilities and promotes the development of more effective educational tools and resources. As AI continues to evolve, methodologies like this will be crucial in maintaining an accurate assessment of machine learning models in diverse areas.