Abstract: This talk will be divided into two independent parts. The first part will present some recent results on the Gromov-Wasserstein, in the important case of cost of negative type. On the theoretical side, we prove that the entropic Gromov-Wasserstein cost can be debiased, similarly to the Sinkhorn divergence for entropic optimal transport. On the numerical side, we show how to scale the computation to a large number of points. The second part of the talk will present a simple approach to learning Monge maps encoded by input convex neural networks. Inspired by Wasserstein gradient flow, we first study a simple gradient flow on the space of L2 maps, proving its global convergence, using minimizing movement schemes. Then, we propose a scheme based on explicit Euler method to actually obtain approximate solutions in the space of input convex neural networks. We will highlight the similarities and differences of our scheme with the recently introduced drifting generative models.

For further information please contact elisur.magrini@unibocconi.it