Are Your LLMs Capable of Stable Reasoning?

2024-12-17

AI Summary

Current large language models (LLMs) exhibit insufficient accuracy and instability in complex mathematical reasoning, while mainstream evaluation methods—relying on static benchmarks, suffering from data leakage, and employing single-shot sampling—fail to assess true reasoning robustness. Method: We propose G-Pass@k, a novel continuous-sampling evaluation metric that jointly quantifies both peak performance and output consistency; introduce LiveMathBench, a dynamic, data-leakage-resistant mathematical benchmark with periodic updates; and release an open-source, reproducible multi-round statistical evaluation framework. Contribution/Results: Experiments across leading LLMs reveal a strong inverse correlation between high Pass@1 accuracy and low G-Pass@k stability, demonstrating that “single-shot optimality” does not imply “robust reliability.” This work shifts the LLM evaluation paradigm from maximizing point-estimate scores toward prioritizing reliability, consistency, and reproducibility in mathematical reasoning assessment.

Technology Category

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

Application Category

• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics
• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs
• Economics, Online Markets and Human Computation: Cost models of using LLMs in production systems

Abstract

The rapid advancement of Large Language Models (LLMs) has demonstrated remarkable progress in complex reasoning tasks. However, a significant discrepancy persists between benchmark performances and real-world applications. We identify this gap as primarily stemming from current evaluation protocols and metrics, which inadequately capture the full spectrum of LLM capabilities, particularly in complex reasoning tasks where both accuracy and consistency are crucial. This work makes two key contributions. First, we introduce G-Pass@k, a novel evaluation metric that provides a continuous assessment of model performance across multiple sampling attempts, quantifying both the model's peak performance potential and its stability. Second, we present LiveMathBench, a dynamic benchmark comprising challenging, contemporary mathematical problems designed to minimize data leakage risks during evaluation. Through extensive experiments using G-Pass@k on state-of-the-art LLMs with LiveMathBench, we provide comprehensive insights into both their maximum capabilities and operational consistency. Our findings reveal substantial room for improvement in LLMs'"realistic"reasoning capabilities, highlighting the need for more robust evaluation methods. The benchmark and detailed results are available at: https://github.com/open-compass/GPassK.

Problem

• Large Language Models
• Complex Problem Solving
• Mathematical Challenges

Innovation

• G-Pass@k
• LiveMathBench
• Complex Problem Solving