Non-Abelian braiding has attracted substantial attention because of its pivotal role in describing the exchange behaviour of anyons, in which the input and outcome of non-Abelian braiding are connected by a unitary matrix. Implementing braiding in a classical system can assist the experimental investigation of non-Abelian physics. However, the design of non-Abelian gauge fields faces numerous challenges stemmed from the intricate interplay of group structures, Lie algebra properties, representation theory, topology, and symmetry breaking. The extreme diversity makes it a powerful tool for the study of condensed matter physics. Whereas the widely used artificial intelligence with data-driven approaches has greatly promoted the development of physics, most works are limited on the data-to-data design. Here we propose a self-reasoning assistant learning framework capable of directly generating non-Abelian gauge fields. This framework utilizes the forward diffusion process to capture and reproduce the complex patterns and details inherent in the target distribution through continuous transformation. Then the reverse diffusion process is used to make the generated data closer to the distribution of the original situation. Thus, it owns strong self-reasoning capabilities, allowing to automatically discover the feature representation and capture more subtle relationships from the dataset. Moreover, the self-reasoning eliminates the need for manual feature engineering and simplifies the process of model building. Our framework offers a disruptive paradigm shift to parse complex physical processes, automatically uncovering patterns from massive datasets.

翻译：非阿贝尔编织因其在描述任意子交换行为中的关键作用而受到广泛关注，其中编织的输入与输出通过酉矩阵相联系。在经典系统中实现编织操作有助于非阿贝尔物理的实验研究。然而，非阿贝尔规范场的设计面临诸多挑战，这些挑战源于群结构、李代数性质、表示理论、拓扑特性与对称性破缺之间错综复杂的相互作用。其极高的多样性使其成为凝聚态物理研究的强有力工具。尽管基于数据驱动的人工智能方法已极大推动了物理学发展，现有工作大多局限于数据到数据的设计范式。本文提出一种能够直接生成非阿贝尔规范场的自推理辅助学习框架。该框架利用前向扩散过程，通过连续变换捕捉并复现目标分布中固有的复杂模式与细节；继而采用反向扩散过程使生成数据更接近原始情境的分布。因此，该框架具备强大的自推理能力，能够自动发现特征表示并从数据集中捕捉更细微的关联关系。此外，自推理机制无需人工特征工程，简化了模型构建流程。本框架为解析复杂物理过程提供了颠覆性的范式转变，能够从海量数据集中自动发掘潜在规律。