用代数结构理论统一处理带权图与神经网络压缩，为模型剪枝提供新思路。
M-Fibration Theory with Applications to Neural Network Compression
- 构建基于交换幺半群的图纤维化理论，支持加权图与复杂标签
- 提出近似纤维化概念，适用于非精确对称的神经网络结构
- 首次为卷积神经网络压缩提供系统性数学依据，适合几何深度学习研究者
本文旨在建立一个通用且全面的理论框架，用于处理标定于交换幺半群上的图纤维化问题。该理论是对经典图纤维化理论（见《离散数学》2002年卷）的真正拓展，使其能够处理带权图及其它代数结构标注的图。所推导的理论自然支持近似纤维化的分析。作为应用实例，本文展示了如何将该框架用于任意神经网络（包括卷积神经网络）的压缩，为《几何深度学习中的纤维化对称性作用》（2026年美国国家科学院院刊）中近期结果提供了坚实的理论基础。
原文摘要 · Abstract (English)
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 this framework can be applied to the compression of arbitrary neural networks (including CNNs), providing a strong theoretical underpinning to the recent results in "The role of fibration symmetries in geometric deep learning" [Proc. Natl. Acad. Sci. USA, vol. 123, no. 4, p. e2416552123, 2026]
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