Input Convex Gradient Networks

• URL: http://arxiv.org/abs/2111.12187v1
• Date: Tue, 23 Nov 2021 22:51:25 GMT
• Title: Input Convex Gradient Networks
• Authors: Jack Richter-Powell, Jonathan Lorraine, Brandon Amos
• Abstract summary: We study how to model convex gradients by integrating a Jacobian-vector product parameterized by a neural network. We empirically demonstrate that a single layer ICGN can fit a toy example better than a single layer ICNN.
• Score: 7.747759814657507
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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