Erlangen Hub Seminar: Riemannian Neural Optimal Transport, Alessandro Micheli

Computational optimal transport (OT) provides a principled framework for generative modelling. Neural OT methods learn transport maps from data using neural networks and can be evaluated out of sample after training; however, existing approaches are largely restricted to Euclidean settings. Extending neural OT to high-dimensional Riemannian manifolds presents significant theoretical and computational challenges.

In this talk, Alessandro Micheli will show that discretisation-based OT methods on manifolds inherently face severe dimensionality scaling limitations. To address this, he introduces Riemannian Neural Optimal Transport (RNOT), a continuous neural parameterisation of OT maps that avoids discretisation and incorporates geometric structure directly. Under mild regularity assumptions, RNOT achieves sub-exponential complexity in the manifold dimension. Empirical results on synthetic and real datasets demonstrate improved scalability and competitive performance relative to existing approaches.

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