Riemannian Deep Learning: Modules, Networks, and Geometries
Quick summary
arXiv:2607.19305v3 Announce Type: replace-cross Abstract: Deep neural networks on manifold-valued representations have attracted growing interest, but many basic components remain tied to specific manifolds, rely on Euclidean approximations, or require costly and numerically fragile geometric operations. This thesis develops a unified framework for Riemannian deep learning from three complementary perspectives: reusable neural modules, manifold-specific network architectures, and the design of underlying geometries. It generalizes batch normalization from Euclidean spaces and individual manifo
Key takeaways
- arXiv:2607.19305v3 Announce Type: replace-cross Abstract: Deep neural networks on manifold-valued representations have attracted growing interest, but many basic components remain tied to specific manifolds, rely on Euclidean approximations, or require costly and numerically fragile geometric operations.
- This thesis develops a unified framework for Riemannian deep learning from three complementary perspectives: reusable neural modules, manifold-specific network architectures, and the design of underlying geometries.
- It generalizes batch normalization from Euclidean spaces and individual manifo
Why it matters
“Riemannian Deep Learning: Modules, Networks, and Geometries” illustrates how changes in the AI ecosystem can affect products, workflows and user expectations together. Its lasting significance depends on measurable adoption, cost and safety outcomes.
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