Constraining the outputs of ReLU neural networks

Yulia Alexandr; Guido Montúfar

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arXiv · 2508.03867

Constraining the outputs of ReLU neural networks

Yulia Alexandr·Guido Montúfar

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Abstract

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.

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Yulia Alexandr, Guido Montúfar. 2025-08-05. Constraining the outputs of ReLU neural networks. https://arxiv.org/abs/2508.03867

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