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:2608.31045v1 Announce Type: new
Abstract: Rotational symmetry is one of the most important structural principles in machine learning on 3D data. In applications ranging from physics and materia...
By Peter Lippmann, Fred A. Hamprecht
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:2609.37817v1 Announce Type: new
Abstract: Geometric representation learning predominantly scaffolds representations onto flat Euclidean subspaces or compact product tori ($\mathbb{T}^K$). Howev...
By Zhongping Ji
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: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
arXiv:2608. 12010v1 Announce Type: new Abstract: Equivariant Neural Networks (ENNs) have empowered numerous applications in scientific fields.
By Ning Lin, Jiacheng Cen, Anyi Li, Wenbing Huang, Hao Sun
arXiv:2606. 03260v1 Announce Type: cross Abstract: Deep learning surrogates for 3D Partial Differential Equations (PDEs) often fail to generalize across geometric transformations because they depend heavily on specific coordinate systems.
By Sungwon Kim, Juho Song, Seungmin Shin, Guimok Cho, Sangkook Kim, Chanyoung Park
Equivariant Neural Networks (ENNs) have empowered numerous applications in scientific fields. Despite their remarkable capacity for representing geometric structures, ENNs suffer from degraded expressivity when processing symmetric inputs: the output representations are invariant to transformations that extend beyond the input's symmetries.
arXiv:2410. 06665v4 Announce Type: replace-cross Abstract: This paper explores the characterization of equivariant linear layers for representations of permutations and related groups.
By Yonatan Sverdlov, Ido Springer, Nadav Dym
arXiv:2609.25987v1 Announce Type: new
Abstract: Equivariant convolutional neural networks are usually built from a group acting globally on the space of signals. This hypothesis is inappropriate for...
By Alberto Ibort, Maria Jimenez-Vazquez, Juan M. Perez-Pardo
arXiv:2207. 03116v4 Announce Type: replace Abstract: We introduce a general method for learning representations that are equivariant to symmetries of data.
By Giovanni Luca Marchetti, Gustaf Tegn\'er, Anastasiia Varava, Danica Kragic