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arXiv · 2510.12700

Topological Signatures of ReLU Neural Network Activation Patterns

Vicente Bosca·Tatum Rask·Sunia Tanweer·Andrew R. Tawfeek·Branden Stone
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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.

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Vicente Bosca, Tatum Rask, Sunia Tanweer, Andrew R. Tawfeek, Branden Stone. 2025-10-14. Topological Signatures of ReLU Neural Network Activation Patterns. https://arxiv.org/abs/2510.12700

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