Large language models (LLMs) have shown excellent performance in natural language processing but struggle with mathematical reasoning. As the training mode gradually solidifies, researchers propose a data-centric concept of artificial intelligence, emphasizing the development of higher-quality data to empower LLMs. Existing studies construct synthetic data for mathematical reasoning by expanding public datasets, thereby performing supervised fine-tuning of LLMs. However, these methods mostly focus on quantity while neglecting quality. The challenging samples fail to receive adequate consideration during data synthesis process, resulting in high construction costs, low-quality density, and serious data homogenization. This paper proposes a multi-agent environment called Virtual ClassRoom (VCR), which leverages various agents driven by LLM to construct high-quality diversified synthetic data. Inspired by the "Cone of Experience" educational theory, VCR introduces three experience levels (direct, iconic, and symbolic) into data synthesis process by analogy with human learning. A user-friendly instruction set and role-playing system are carefully designed, enabling VCR to autonomously plan the scale of synthetic data. This system covers various educational scenarios, including lecture, discussion, problem design and problem-solving. The Adaboost idea embodied in the global iterative process further promotes steady performance improvement. Extensive experiments show that the synthetic data generated by VCR possess higher quality density and generalization capability, which can give LLMs superior mathematical reasoning performance with the same scale.

The large language models (LLMs) learning framework for math problem generation (MPG) mostly performs homogeneous training in different epochs on small-scale manually annotated data.This pattern struggles to provide large-scale new quality data to support continual improvement, and fails to stimulate the mutual promotion reaction between generation and reasoning ability of math problem, resulting in the lack of reliable solving process.This paper proposes a synthetic data based continual learning framework to improve LLMs ability for MPG and math reasoning.The framework cycles through three stages, "supervised fine-tuning, data synthesis, direct preference optimization", continuously and steadily improve performance.We propose a synthetic data method with dual mechanism of model self-play and multi-agent cooperation is proposed, which ensures the consistency and validity of synthetic data through sample filtering and rewriting strategies, and overcomes the dependence of continual learning on manually annotated data.A data replay strategy that assesses sample importance via loss differentials is designed to mitigate catastrophic forgetting.Experimental analysis on abundant authoritative math datasets demonstrates the superiority and effectiveness of our framework.

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.