Learning to Generate Wasserstein Barycenters

Understand

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.