Reproduce “GradNetOT: Learning Optimal Transport Maps with GradNets” on OpenResearch
Turn your favorite coding agents into research agents that review literature, develop hypotheses, and run experiments.
Universal app for Apple silicon and Intel. Requires macOS 11 or later.
About this paper
Shreyas Chaudhari, Srinivasa Pranav, José M. F. Moura
GradNetOT introduces a method for learning optimal transport maps by directly parameterizing monotone gradients using mGradNets, trained with a loss function derived from the Monge-Ampère pushforward equation. The approach accurately approximates analytical solutions for Gaussian distributions and generates visually consistent image morphing sequences comparable to computationally intensive methods.
Key insights
- The inherent 'structural bias' of mGradNets ensures that the learned map is intrinsically a monotone gradient of a convex function, aligning with a key theoretical property of optimal transport maps.
- Directly incorporating the Monge-Ampère equation into the loss function provides a principled, theoretically-grounded training objective, leading to more robust and accurate solutions.
- Directly parameterizing the transport map and optimizing with its Jacobian offers computational efficiency advantages, particularly in higher-dimensional settings, over methods that rely on parameterizing a potential function and its Hessian.
Summary by alphaXiv.
Tip: change arxiv.org to autoarxiv.org in any arXiv abstract link to open the paper here.