Neural Ordinary Differential Equations on Manifolds

Understand

Normalizing flows are a powerful technique for obtaining reparameterizable samples from complex multimodal distributions.

• Unfortunately current approaches fall short when the underlying space has a non trivial topology, and are only available for the most basic geometries.
• Recently normalizing flows in Euclidean space based on Neural ODEs show great promise, yet suffer the same limitations.
• Using ideas from differential geometry and geometric control theory, we describe how neural ODEs can be extended to smooth manifolds.