Computer Science > Machine Learning
arXiv:2502.09954 (cs)
[Submitted on 14 Feb 2025]
Title:On Space Folds of ReLU Neural Networks
View a PDF of the paper titled On Space Folds of ReLU Neural Networks, by Michal Lewandowski and 4 other authors
View PDFHTML (experimental)Abstract:Recent findings suggest that the consecutive layers of ReLU neural networks can be understood geometrically as space folding transformations of the input space, revealing patterns of self-similarity. In this paper, we present the first quantitative analysis of this space folding phenomenon in ReLU neural networks. Our approach focuses on examining how straight paths in the Euclidean input space are mapped to their counterparts in the Hamming activation space. In this process, the convexity of straight lines is generally lost, giving rise to non-convex folding behavior. To quantify this effect, we introduce a novel measure based on range metrics, similar to those used in the study of random walks, and provide the proof for the equivalence of convexity notions between the input and activation spaces. Furthermore, we provide empirical analysis on a geometrical analysis benchmark (CantorNet) as well as an image classification benchmark (MNIST). Our work advances the understanding of the activation space in ReLU neural networks by leveraging the phenomena of geometric folding, providing valuable insights on how these models process input information.
| Comments: | Accepted at Transactions on Machine Learning Research (TMLR), 2025 |
| Subjects: | Machine Learning (cs.LG); Neural and Evolutionary Computing (cs.NE) |
| Cite as: | arXiv:2502.09954 [cs.LG] |
| (orarXiv:2502.09954v1 [cs.LG] for this version) | |
| https://doi.org/10.48550/arXiv.2502.09954 arXiv-issued DOI via DataCite |
Submission history
From: Michal Lewandowski [view email][v1] Fri, 14 Feb 2025 07:22:24 UTC (6,403 KB)
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View a PDF of the paper titled On Space Folds of ReLU Neural Networks, by Michal Lewandowski and 4 other authors
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