arXiv AI By Ziheng Chen

Building Transformation Layers for Riemannian Neural Networks

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arXiv AI
Jul 24

Riemannian Deep Learning: Modules, Networks, and Geometries

arXiv:2607. 19305v2 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.

By Chen Ziheng
arXiv AI
Jul 22

Riemannian Deep Learning:Modules, Networks, and Geometries

arXiv:2607. 19305v1 Announce Type: 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.

By Chen Ziheng
Hugging Face Trending Papers
Jul 1

Group-Equivariant Poincaré Convolutional Networks

While recent advancements like the Poincaré ResNet have demonstrated the potential of learning visual representations directly in hyperbolic space, their optimisation remains hampered by the computationally intensive nature of Riemannian gradients and the strict boundaries of the manifold. Furthermore, standard hyperbolic networks treat spatial transformations of the same object as distinct hierarchical concepts, leading to redundant parameter usage and vanishing signals.

arXiv AI
Jul 2

Group-Equivariant Poincar\'e Convolutional Networks

arXiv:2607. 00556v1 Announce Type: cross Abstract: While recent advancements like the Poincar\'e ResNet have demonstrated the potential of learning visual representations directly in hyperbolic space, their optimisation remains hampered by the computationally intensive nature of Riemannian gradients and the strict boundaries of the manifold.

By Aiden Durrant, Rahul Baburajan, Georgios Leontidis