Abstract

A common assumption in machine learning is that the data lie near a low dimensional manifold, which the shortest paths between points should respect. In this talk, we focus on differential geometry and present computational methods that enables us to learn and use this underlying structure. We rely on the latent space of generative models, where we capture the geometry of the data manifold. We can then compute the associated shortest paths, which is a distance measure invariant under reparametrizations of the latent space. We demonstrate though that this approach requires to quantify meaningfully the uncertainty of the generative process. Finally, we show that we can use the latent geometry in several ways, as well as for applications in robotics and life sciences.