Riemannian Neural SDE: Learning Stochastic Representations on Manifolds

Sung Woo Park, Hyomin Kim, Hyeseong Kim, Junseok Kwon

Keywords: Stochastic differential equation, Riemannian manifold, Density estimation

TL;DR: We proposed a general framework for modeling stochastic representations on Riemannian manifolds.

Abstract: In recent years, the neural stochastic differential equation (NSDE) has gained attention in modeling stochastic representations, while NSDE brings a great success in various types of applications. However, it typically loses the expressivity when the data representation is manifold-valued. To overcome such an issue, we suggest a principled way to express the stochastic representation with the Riemannian neural SDE (RNSDE), which extends the conventional Euclidean NSDE. Empirical results on the density estimation on manifolds show that the proposed method significantly outperforms baseline methods.