Neural Stochastic Differential Equations on Compact State-Spaces
This work addresses a domain-specific problem for researchers and practitioners in probabilistic modeling, offering an incremental improvement over existing methods for constrained SDEs.
The authors tackled the problem of instability and poor inductive bias in neural stochastic differential equations (SDEs) on compact spaces by proposing a novel class with continuous dynamics, resulting in improved interpretability and applicability, including support for higher-order solvers.
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 polyhedral spaces with continuous dynamics, amenable to higher-order solvers, and with favorable inductive bias.