mlsanityData to 7 Oct 2026

Topological Signatures of ReLU Neural Network Activation Patterns

arXiv 2510.12700 ↗First posted 14 Oct 2025cs.LG cs.AI cs.CGcited by 2

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Abstract (arXiv)

This paper explores the topological signatures of ReLU neural network activation patterns. We consider feedforward neural networks with ReLU activation functions and analyze the polytope decomposition of the feature space induced by the network. Mainly, we investigate how the Fiedler partition of the dual graph and show that it appears to correlate with the decision boundary -- in the case of binary classification. Additionally, we compute the homology of the cellular decomposition -- in a regression task -- to draw similar patterns in behavior between the training loss and polyhedral cell-count, as the model is trained.

Key facts. Cited by 2 papers in the map (data through 7 Oct 2026). Builds on 15 of its 28 references that are in the map. First posted on arXiv 14 Oct 2025.

Builds on

15 of 28 references.

References · 15

  1. 2023Progress measures for grokking via mechanistic interpretabilitycited by 822
  2. 2020A Survey of Convolutional Neural Networks: Analysis, Applications, and Prospectscited by 396
  3. 2016On the Expressive Power of Deep Neural Networkscited by 302
  4. 2019Complexity of Linear Regions in Deep Networkscited by 166
  5. 2015A roadmap for the computation of persistent homologycited by 126
  6. 2020Topology of deep neural networkscited by 111
  7. 2019A Topology Layer for Machine Learningcited by 79
  8. 2024Deep Networks Always Grok and Here is Whycited by 49
  9. 2022Algorithmic Determination of the Combinatorial Structure of the Linear Regions of ReLU Neural Networkscited by 21
  10. 2021Activation Landscapes as a Topological Summary of Neural Network Performancecited by 17
  11. 2023Loss Spike in Training Neural Networkscited by 15
  12. 2023Polyhedral Complex Extraction from ReLU Networks using Edge Subdivisioncited by 14
3 more
  1. 2023ReLU Neural Networks, Polyhedral Decompositions, and Persistent Homologcited by 10
  2. 2023Hamming Similarity and Graph Laplacians for Class Partitioning and Adversarial Image Detectioncited by 4
  3. 2024Exploring Physics-Informed Neural Networks: From Fundamentals to Applications in Complex Systemscited by 2

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2026: 2.

2 papers.

  1. 2026Neural Networks as Local-to-Global Computationscited by 2
  2. 2026Learning Transfers: Kan Extensions for Neural Invariantscited by 0