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:2609.35436v2 Announce Type: replace
Abstract: Recently, deep neural networks on manifold-valued representations have garnered significant attention across various machine learning applications....
By Ziheng Chen
arXiv:2607. 08783v1 Announce Type: cross Abstract: Manifold-valued measurements are prevalent in various machine learning tasks.
By Ziheng Chen, Yue Song, Rui Wang, Xiao-Jun Wu, Nicu Sebe
Controlling the Lipschitz constant of a neural network is a standard way to promote robustness and stability. Most existing constraining strategies are designed for Euclidean spaces.
arXiv:2607. 19335v1 Announce Type: cross Abstract: Controlling the Lipschitz constant of a neural network is a standard way to promote robustness and stability.
By Davide Murari, Marta Ghirardelli, Ben Adcock, Elena Celledoni, Brynjulf Owren, Carola-Bibiane Sch\"onlieb
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.