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The gradients of convex functions are expressive models of non-trivial vector fields. For example, the optimal transport map between any two measures on Euclidean spaces under the squared distance is realized as a convex gradients via Brenier's theorem, which is a key insight used in recent machine learning 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 modeling the gradient by taking the derivative of an input-convex neural network, demonstrating that ICGNs can efficiently parameterize convex gradients.
Author Information
Jack Richter-Powell (McGill University)
Jonathan Lorraine (University Of Toronto)
Brandon Amos (Carnegie Mellon University)
Related Events (a corresponding poster, oral, or spotlight)
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2021 : Input Convex Gradient Networks »
Dates n/a. Room
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