M-纤维化理论及其在神经网络压缩中的应用
M-Fibration Theory with Applications to Weighted Graphs
- Università degli Studi di Milano（米兰大学）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文提出M-纤维化理论框架，将图纤维化理论扩展至交换幺半群带标签图等场景，并将其应用于任意神经网络压缩，为相关几何深度学习成果提供理论支撑。
AI中文摘要：
本文旨在提供一个通用、全面的理论框架，用于处理交换幺半群上带标签图的纤维化。该框架是图纤维化理论（源自《图的纤维化》[Discrete Math., vol. 243, pp. 21-66, 2002]）的真正扩展，可处理加权图及带其他代数结构标签的图。衍生理论还自然适用于近似纤维化。作为示例，本文展示该框架如何应用于任意神经网络（含CNN）的压缩，为《纤维化对称性在几何深度学习中的作用》[Proc. Natl. Acad. Sci. USA, vol. 123, no. 4, p. e2416552123, 2026]的最新成果提供了坚实的理论支撑。
英文摘要：
The purpose of this paper is to provide a general, comprehensive, theoretical framework that allows one to deal with fibrations on graphs labelled on a commutative monoid. This is a genuine extension of the theory of graph fibrations (as introduced in "Fibrations of Graphs" [Discrete Math., vol. 243, pp. 21-66, 2002]), that makes it possible to deal with weighted graphs, and also graphs labelled with other algebraic structures. The derived theory also lends itself naturally to consider approximate fibrations. As an example, we show how the derived theory can be applied to the reduction of weighted networks, providing a strong theoretical underpinning to recent empirical results.
