The GroupMax neural network approximation of convex functions

TL;DR

This paper introduces GroupMax, a neural network designed to efficiently approximate convex functions, capable of handling partial convexity, with proven universal approximation properties and supporting numerical validation.

Contribution

The paper proposes the GroupMax neural network architecture for convex function approximation, including a universal approximation theorem and adaptability to partial convexity.

Findings

Proves universal approximation theorem for convex functions

Demonstrates efficiency through numerical experiments

Supports adaptation to partial convexity

Abstract

We present a new neural network to approximate convex functions. This network has the particularity to approximate the function with cuts and can be easily adapted to partial convexity. We give an universal approximation theorem in the full convex case and give many numerical results proving it efficiency.