Learning Normal Coordinates on Riemannian Manifolds with Flow Charts
Riemannian manifolds are powerful models for problems with non-Euclidean structure. Recent work in geometric machine learning has focused on training deep neural networks to learn Riemannian metrics from high-dimensional data. However, many geometric algorithms require repeated evaluations of the exponential and logarithmic maps, whose high computational cost restricts the utility of learned Riemannian manifolds in practice. We propose to address this cost by training a conditional invertible neural network, called a flow chart, to approximate normal coordinates around points on a given Riemannian manifold. With this approach, the exponential and logarithmic maps can be approximated by fa...
| Authors | Edmond Cunningham |
|---|---|
| Primary category | cs.LG |
| Published | 20 October 2026 |
| Last updated at source | 20 October 2026 |
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