Riemannian Deep Learning:Modules, Networks, and Geometries

Chen Ziheng|July 21, 2026arXiv

Key Takeaway

You can now build neural networks on curved spaces using reusable, theoretically-grounded components instead of ad-hoc manifold-specific solutions, with practical efficiency improvements for important geometric representations.

Summary

This thesis develops a unified framework for building deep neural networks that work with data on curved mathematical spaces (manifolds) rather than flat Euclidean space.

architecture training efficiency

Key Terms

riemannian-geometry manifold spd-manifold hyperbolic-space lie-groups