Constraining the outputs of ReLU neural networks
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866908479717900288 |
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| author | Alexandr, Yulia Montúfar, Guido |
| author_facet | Alexandr, Yulia Montúfar, Guido |
| contents | We introduce a class of algebraic varieties naturally associated with ReLU neural networks, arising from the piecewise linear structure of their outputs across activation regions in input space, and the piecewise multilinear structure in parameter space. By analyzing the rank constraints on the network outputs within each activation region, we derive polynomial equations that characterize the functions representable by the network. We further investigate conditions under which these varieties attain their expected dimension, providing insight into the expressive and structural properties of ReLU networks. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_03867 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Constraining the outputs of ReLU neural networks Alexandr, Yulia Montúfar, Guido Algebraic Geometry Machine Learning We introduce a class of algebraic varieties naturally associated with ReLU neural networks, arising from the piecewise linear structure of their outputs across activation regions in input space, and the piecewise multilinear structure in parameter space. By analyzing the rank constraints on the network outputs within each activation region, we derive polynomial equations that characterize the functions representable by the network. We further investigate conditions under which these varieties attain their expected dimension, providing insight into the expressive and structural properties of ReLU networks. |
| title | Constraining the outputs of ReLU neural networks |
| topic | Algebraic Geometry Machine Learning |
| url | https://arxiv.org/abs/2508.03867 |