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 three mathematical reasoning datasets demonstrate 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.

In the past decade, despite significant advancements in Artificial Intelligence (AI) and deep learning technologies, they still fall short of fully replicating the complex functions of the human brain. This highlights the importance of researching human-machine collaborative systems. This study introduces a statistical framework capable of finely modeling integrated performance, breaking it down into the individual performance term and the diversity term, thereby enhancing interpretability and estimation accuracy. Extensive multi-granularity experiments were conducted using this framework on various image classification datasets, revealing the differences between humans and machines in classification tasks from macro to micro levels. This difference is key to improving human-machine collaborative performance, as it allows for complementary strengths. The study found that Human-Machine collaboration (HM) often outperforms individual human (H) or machine (M) performances, but not always. The superiority of performance depends on the interplay between the individual performance term and the diversity term. To further enhance the performance of human-machine collaboration, a novel Human-Adapter-Machine (HAM) model is introduced. Specifically, HAM can adaptively adjust decision weights to enhance the complementarity among individuals. Theoretical analysis and experimental results both demonstrate that HAM outperforms the traditional HM strategy and the individual agent (H or M).

In the evolving artificial intelligence domain, hybrid human-machine systems have emerged as a transformative research area. While many studies have concentrated on individual human-machine interactions, there is a lack of focus on multi-human and multi-machine dynamics. This paper delves into these nuances by introducing a novel statistical framework that discerns integration accuracy in terms of precision and diversity. Empirical studies reveal that performance surges consistently with scale, either in human or machine settings. However, hybrid systems present complexities. Their performance is intricately tied to the human-to-machine ratio. Interestingly, as the scale expands, integration performance growth isn't limitless. It reaches a threshold influenced by model diversity. This introduces a pivotal `knee point', signifying the optimal balance between performance and scale. This knowledge is vital for resource allocation in practical applications. Grounded in rigorous evaluations using public datasets, our findings emphasize the framework's robustness in refining integrated systems.