Riemannian Neural SDE: Learning Stochastic Representations on Manifolds

Sung Woo Park, Hyomin Kim, Kyungjae Lee, Junseok Kwon

Keywords: Stochastic representation on Manifolds, Riemannian neural stochastic differential equation

TL;DR: We express the stochastic representation with the Riemannian neural SDE (RNSDE), which extends the conventional Euclidean NSDE.

Abstract: In recent years, the neural stochastic differential equation (NSDE) has gained attention for modeling stochastic representations with great success in various types of applications. However, it typically loses expressivity when the data representation is manifold-valued. To address this issue, we suggest a principled method for expressing the stochastic representation with the Riemannian neural SDE (RNSDE), which extends the conventional Euclidean NSDE. Empirical results for various tasks demonstrate that the proposed method significantly outperforms baseline methods.