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

arXiv: https://arxiv.org/abs/2508.03396 · HTML: https://mlsanity.com/paper/2508.03396/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Mathematical reasoning, one of 17 directions in LLM reasoning.
- Builds on 20 of its 26 references that are in the map.
- First posted on arXiv 5 Aug 2025.

## Placed in

- LLM reasoning / [Mathematical reasoning](https://mlsanity.com/lr/mathematical-reasoning/)
- Synthetic data and self-improvement for LLMs / [Self-play RL for reasoning](https://mlsanity.com/synth/self-play-rl-for-reasoning/)

## Builds on (most cited first, 20 of 20)

- [Training language models to follow instructions with human feedback](https://mlsanity.com/paper/2203.02155/) (2022)
- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [Direct Preference Optimization: Your Language Model is Secretly a Reward Model](https://mlsanity.com/paper/2305.18290/) (2023)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [Qwen3 Embedding: Advancing Text Embedding and Reranking Through Foundation Models](https://mlsanity.com/paper/2506.05176/) (2025)
- [Large Language Models Cannot Self-Correct Reasoning Yet](https://mlsanity.com/paper/2310.01798/) (2023)
- [CRITIC: Large Language Models Can Self-Correct with Tool-Interactive Critiquing](https://mlsanity.com/paper/2305.11738/) (2023)
- [rStar-Math: Small LLMs Can Master Math Reasoning with Self-Evolved Deep Thinking](https://mlsanity.com/paper/2501.04519/) (2025)
- [Skywork-Reward-V2: Scaling Preference Data Curation via Human-AI Synergy](https://mlsanity.com/paper/2507.01352/) (2025)
- [Large Language Models for Education: A Survey and Outlook](https://mlsanity.com/paper/2403.18105/) (2024)
- [On a Formal Model of Safe and Scalable Self-driving Cars](https://mlsanity.com/paper/1708.06374/) (2017)
- [CriticBench: Benchmarking LLMs for Critique-Correct Reasoning](https://mlsanity.com/paper/2402.14809/) (2024)
- [Prover-Verifier Games improve legibility of LLM outputs](https://mlsanity.com/paper/2407.13692/) (2024)
- [HaluEval-Wild: Evaluating Hallucinations of Language Models in the Wild](https://mlsanity.com/paper/2403.04307/) (2024)
- [GrammarGPT: Exploring Open-Source LLMs for Native Chinese Grammatical Error Correction with Supervised Fine-Tuning](https://mlsanity.com/paper/2307.13923/) (2023)
- [Assessing Student Errors in Experimentation Using Artificial Intelligence and Large Language Models: A Comparative Study with Human Raters](https://mlsanity.com/paper/2308.06088/) (2023)
- [UloRL:An Ultra-Long Output Reinforcement Learning Approach for Advancing Large Language Models' Reasoning Abilities](https://mlsanity.com/paper/2507.19766/) (2025)
- [MathDebugger: Detecting and Diagnosing Errors in Synthetic Mathematical Data](https://mlsanity.com/paper/2502.19058/) (2025)

## Abstract (arXiv)

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.