关键词: 纤维丛, 微分几何, 拓扑, 规范场, 神经网络

Abstract: Fiber bundles theory is a mathematical tool to study complex systems and describes profound mathematical and physical phenomena. It has been widely applied in various fields such as differential geometry, topology, physics, and informatics. This article provides a brief overview of the origin, fundamental concepts, and theoretical foundations of fiber bundles theory, and showcases its applications in multiple domains through examples.