Learning Normal Coordinates on Riemannian Manifolds with Flow Charts
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.
ProofPaper ↗
Key points
- 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.
- With this approach, the exponential and logarithmic maps can be approximated by fast Euclidean operations in the model's learned coordinate space.
- Across sixteen synthetic and data-derived geometries, flow charts are competitive with a specialized neural geodesic interpolator for logarithmic map estimation, while also being able to estimate the exponential map.
Sources (1)
- [1]Learning Normal Coordinates on Riemannian Manifolds with Flow ChartsarXiv (AI, ML, NLP, CV, robotics, multi-agent) · Oct 20, 02:45 PM
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.
Riemannian manifolds are powerful models for problems with non-Euclidean structure.
Extractive summary: sentences quoted from the sources.