Learning to Generate Wasserstein Barycenters
This work addresses the computational bottleneck in optimal transport for machine learning applications, enabling faster barycenter computations in tasks like image processing, though it is incremental as it builds on existing methods with a neural network approach.
The paper tackled the computationally demanding problem of computing Wasserstein barycenters by training a deep convolutional neural network, achieving a 60x speed improvement over the fastest state-of-the-art GPU method, resulting in millisecond computational times on 512x512 grids.
Optimal transport is a notoriously difficult problem to solve numerically, with current approaches often remaining intractable for very large scale applications such as those encountered in machine learning. Wasserstein barycenters -- the problem of finding measures in-between given input measures in the optimal transport sense -- is even more computationally demanding as it requires to solve an optimization problem involving optimal transport distances. By training a deep convolutional neural network, we improve by a factor of 60 the computational speed of Wasserstein barycenters over the fastest state-of-the-art approach on the GPU, resulting in milliseconds computational times on $512\times512$ regular grids. We show that our network, trained on Wasserstein barycenters of pairs of measures, generalizes well to the problem of finding Wasserstein barycenters of more than two measures. We demonstrate the efficiency of our approach for computing barycenters of sketches and transferring colors between multiple images.