Topological Signatures of ReLU Neural Network Activation Patterns

Vicente Bosca, Tatum Rask, Sunia Tanweer, Andrew R. Tawfeek, Branden Stone
10/14/2025
cs.LGcs.AIcs.CG

No confident code implementation found for this paper.

Abstract

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.

View on arXivView PDF

Code Implementations

No confident code match yet

We couldn't find an author-owned or strongly-evidenced community implementation for this paper. Any repos shown below are weak matches — verify before relying on them.

No code implementations found yet.

Know of an implementation? Let us know in the comments below!

Similar Papers

ReLU Neural Networks, Polyhedral Decompositions, and Persistent Homolog

85% match2023

Topological Expressivity of ReLU Neural Networks

85% match2023

The Geometric Structure of Fully-Connected ReLU Layers

84% match2023

The Geometry of ReLU Networks through the ReLU Transition Graph

83% match2025

Deep ReLU Networks Have Surprisingly Simple Polytopes

83% match2023

Topological Understanding of Neural Networks, a survey

82% match2023

Cite this paper

@article{bosca2025topological,
  title  = {Topological Signatures of ReLU Neural Network Activation Patterns},
  author = {Vicente Bosca and Tatum Rask and Sunia Tanweer and Andrew R. Tawfeek and Branden Stone},
  year   = {2025},
  eprint = {2510.12700},
  archivePrefix = {arXiv},
  url    = {http://arxiv.org/abs/2510.12700v2}
}

Add a badge to your README

Shows whether official code is linked for this paper.

Code of Paper badge
[![Code of Paper](https://codeofpaper.com/badge/2510.12700.svg)](https://codeofpaper.com/paper/2510.12700)

Discussion