mlsanityData to 14 Oct 2026

On Space Folds of ReLU Neural Networks

arXiv 2502.09954 ↗First posted 14 Feb 2025cs.LG cs.NEcited by 3

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Abstract (arXiv)

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.

Key facts. Cited by 3 papers in the map (data through 14 Oct 2026). Builds on 30 of its 59 references that are in the map. First posted on arXiv 14 Feb 2025.

Builds on

30 of 59 references.

References · 30

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18 more
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Cited by year (2026 to 14 Oct)

Citing papers per year: 2025: 2; 2026: 1.

3 papers.

  1. 2025The Resurrection of the ReLUcited by 6
  2. 2025The Space Between: On Folding, Symmetries and Samplingcited by 0
  3. 2026Bounding Box Anomaly Scoring for simple and efficient Out-of-Distribution detectioncited by 0