Saved in:
Bibliographic Details
Main Author: Calegari, Danny
Format: Preprint
Published: 2025
Subjects:
Online Access:https://arxiv.org/abs/2505.07137
Tags: Add Tag
No Tags, Be the first to tag this record!
Table of Contents:
  • We show that every piecewise linear function $f:R^d \to R$ with compact support a polyhedron $P$ has a representation as a sum of so-called `simplex functions'. Such representations arise from degree 1 triangulations of the relative homology class (in $R^{d+1}$) bounded by $P$ and the graph of $f$, and give a short elementary proof of the existence of efficient universal ReLU neural networks that simultaneously compute all such functions $f$ of bounded complexity.