Riemannian Neural SDE: Learning Stochastic Representations on ManifoldsDownload PDF

02 Mar 2022, 12:21 (edited 26 Apr 2022)GTRL 2022 PosterReaders: Everyone
  • 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.
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