Piecewise linear functions and neural network expressivity via discriminantal arrangements
Combinatorics
2026-04-06 v1 Algebraic Geometry
Abstract
We extend the hyperplane arrangement framework for neural network expressivity from the braid to discriminantal arrangements. Compatible piecewise linear functions are characterized by circuit relations and admit a matroidal description via Mobius inversion, with dimension equal to the number of independent sets. For circuits of size three, functions are determined by values on subsets of size at most two.
Cite
@article{arxiv.2604.02480,
title = {Piecewise linear functions and neural network expressivity via discriminantal arrangements},
author = {Pragnya Das},
journal= {arXiv preprint arXiv:2604.02480},
year = {2026}
}