Characterizing the Discrete Geometry of ReLU Networks
It is well established that ReLU networks define continuous piecewise-linear functions, and that their linear regions are polyhedra in the input space. These regions form a complex that fully partitions the input space. The way these regions fit together is fundamental to the behavior of the network, as nonlinearities occur only at the boundaries where these regions connect. However, relatively little is known about the geometry of these complexes beyond bounds on the total number of regions, and calculating the complex exactly is intractable for most networks. In this work, we prove new theoretical results about these complexes that hold for all fully-connected ReLU networks, specificall...
| Authors | Blake B. Gaines, Jinbo Bi |
|---|---|
| Primary category | cs.LG |
| Published | 5 June 2026 |
| Last updated at source | 5 June 2026 |
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