M-Fibration Theory with Applications to Neural Network Compression

2026-08-26

AI Summary

本文扩展了图纤维化理论，以处理带权重及其它代数结构标记的图，并应用于神经网络压缩，为几何深度学习中的纤维对称性提供理论基础。

Abstract

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]

Problem

• M-Fibration
• Neural Network Compression
• Weighted Graphs
• Commutative Monoid

Innovation

• M-Fibration Theory
• Commutative Monoid
• Approximate Fibrations
• Neural Network Compression
• Graph Labeling