Input Convex Gradient Networks
Abstract
The gradients of convex functions are expressive models of non-trivial vector fields. For example, Brenier's theorem yields that the optimal transport map between any two measures on Euclidean space under the squared distance is realized as a convex gradient, which is a key insight used in recent generative flow models. In this paper, we study how to model convex gradients by integrating a Jacobian-vector product parameterized by a neural network, which we call the Input Convex Gradient Network (ICGN). We theoretically study ICGNs and compare them to taking the gradient of an Input-Convex Neural Network (ICNN), empirically demonstrating that a single layer ICGN can fit a toy example better than a single layer ICNN. Lastly, we explore extensions to deeper networks and connections to constructions from Riemannian geometry.
Keywords
Cite
@article{arxiv.2111.12187,
title = {Input Convex Gradient Networks},
author = {Jack Richter-Powell and Jonathan Lorraine and Brandon Amos},
journal= {arXiv preprint arXiv:2111.12187},
year = {2021}
}
Comments
Accepted to NeurIPS 2021 Optimal Transport and Machine Learning Workshop https://otml2021.github.io