M-Fibration Theory with Applications to Neural Network Compression
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Computer Science > Machine Learning
Title:M-Fibration Theory with Applications to Neural Network Compression
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]
| Subjects: | Machine Learning (cs.LG) |
| MSC classes: | 05C22 (Primary), 05C50, 05C85, 18A30, 68T07 (Secondary) |
| ACM classes: | G.2.2; F.2.2; I.2.6 |
| Cite as: | arXiv:2608.25598 [cs.LG] |
| (or arXiv:2608.25598v1 [cs.LG] for this version) | |
| https://doi.org/10.48550/arXiv.2608.25598
arXiv-issued DOI via DataCite (pending registration)
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