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: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: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
arXiv:2505. 21736v2 Announce Type: replace-cross Abstract: Translation equivariance is a central reason convolutional neural networks have been successful in computer vision.
By Siqi Fang, Zachary Schlamowitz, Andrew Bennecke, Daniel J. Tward
arXiv:2606. 27864v1 Announce Type: cross Abstract: Vision transformers have become a dominant architecture for visual recognition.
By T\={\i}kun \^Ong, Georg B\"okman
arXiv:2510. 03511v3 Announce Type: replace-cross Abstract: While widespread, Transformers lack inductive biases for geometric symmetries common in science and computer vision.
By Mohammad Mohaiminul Islam, Rishabh Anand, David R. Wessels, Friso de Kruiff, Thijs P. Kuipers, Rex Ying, Clara I. S\'anchez, Sharvaree Vadgama, Georg B\"okman, Erik J. Bekkers
arXiv:2607. 08987v1 Announce Type: new Abstract: Spectral embedding methods are widely used for dimensionality reduction and clustering of high-dimensional datasets with intrinsic low-dimensional structures.
By Yeari Vigder, Paulina Hoyos, David Thong, Joakim and\'en, Joe Kileel, Amit Moscovich