Hide and Seek with LLMs: An Adversarial Game for Sneaky Error Generation and Self-Improving Diagnosis

TL;DR

This paper introduces a dynamic adversarial framework called Hide and Seek Game (HSG) that enhances error generation and diagnosis in large language models, significantly improving their ability to detect subtle reasoning errors in math problems.

Contribution

The paper presents a novel adversarial co-evolution framework for error generation and diagnosis, advancing beyond static error methods to improve deep diagnostic capabilities in LLMs.

Findings

HSG improves error diagnosis accuracy by 16.8%–31.4%.

HSG generates more subtle and deceptive errors.

A new benchmark dataset of deceptive errors is released.

Abstract

Large Language Models (LLMs) excel in reasoning and generation across domains, but still struggle with identifying and diagnosing complex errors. This stems mainly from training objectives that prioritize correct answers, limiting exposure to and learning from errors. While recent studies have begun to address this by introducing error signals, most rely on shallow, static errors, restricting improvement in deep diagnostic ability. To overcome this, we propose Hide and Seek Game (HSG), a dynamic adversarial framework for error generation and diagnosis, and evaluate it on mathematical problem-solving. HSG involves two adversarial roles: Sneaky, which "hides" by generating subtle, deceptive reasoning errors, and Diagnosis, which "seeks" to accurately detect them. Through adversarial co-evolution, both error stealth and diagnostic precision are enhanced. Experiments on several math reasoning tasks show that HSG significantly boosts error diagnosis, achieving 16.8\%--31.4\% higher accuracy than baselines like GPT-4o. We also release a challenging dataset of deceptive errors and diagnostic annotations as a benchmark for future research.