Neural Stochastic Differential Equations on Compact State-Spaces

Yue-Jane Liu, Malinda Lu, Matthew K. Nock, Yaniv Yacoby

Keywords: Neural SDEs, Inductive Bias, Viability Theory, Generative Models, Dynamical Systems, Time Series

TL;DR: We introduce neural SDEs with continuous dynamics on compact spaces, offering better inductive bias than existing approaches.

Abstract: Many modern probabilistic models rely on SDEs, but their adoption is hampered by instability, poor inductive bias outside bounded domains, and reliance on restrictive dynamics or training tricks. While recent work constrains SDEs to compact spaces using reflected dynamics, these approaches lack continuous dynamics and efficient high-order solvers, limiting interpretability and applicability. We propose a novel class of neural SDEs on compact spaces with continuous dynamics, amenable to higher-order solvers and with favorable inductive bias.

Submission Number: 45