We apply this scheme to minimize the MMD with kernels based on the Sliced-Wasserstein distance. And as applications, we flow dataset of images to solve tasks such as transfer learning and dataset distillation.

We leverage this gradient to do optimization over this space. We update each particle using this gradient, and observe several layers of interactions, between the particles and between the classes.

To solve this task, we endow the space with the Wasserstein over Wasserstein (WoW) distance, and exploit its Riemannian structure. It gives us a way to define a notion of gradient.

In our work, we propose to model labeled datasets as probability over probability distributions, and to frame the task of flowing datasets as a minimization of a discrepancy over this space.

🎉 Happy to share that our work "Flowing Datasets with Wasserstein over Wasserstein Gradient Flows" was accepted at #ICML2025 as an oral!

This is a joint work with the amazing Christophe Vauthier and @akorba.bsky.social !

Link: openreview.net/forum?id=I1O...