Topological Signatures of ReLU Neural Network Activation Patterns
Fuente:
arXiv
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| Autores principales: | , , , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866911599677145088 |
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| author | Bosca, Vicente Rask, Tatum Tanweer, Sunia Tawfeek, Andrew R. Stone, Branden |
| author_facet | Bosca, Vicente Rask, Tatum Tanweer, Sunia Tawfeek, Andrew R. Stone, Branden |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_12700 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Topological Signatures of ReLU Neural Network Activation Patterns Bosca, Vicente Rask, Tatum Tanweer, Sunia Tawfeek, Andrew R. Stone, Branden Machine Learning Artificial Intelligence Computational Geometry Algebraic Topology 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. |
| title | Topological Signatures of ReLU Neural Network Activation Patterns |
| topic | Machine Learning Artificial Intelligence Computational Geometry Algebraic Topology |
| url | https://arxiv.org/abs/2510.12700 |