Computing equivariant matrices on homogeneous spaces for Geometric Deep Learning and Automorphic Lie Algebras

2023-03-13 · Vincent Knibbeler

We develop an elementary method to compute spaces of equivariant maps from a homogeneous space $G/H$ of a Lie group $G$ to a module of this group. The Lie group is not required to be compact. More generally, we study spaces of invariant sections in homogeneous vector bundles, and take a special interest in the case where the fibres are algebras. These latter cases have a natural global algebra structure. We classify these automorphic algebras for the case where the homogeneous space has compact stabilisers. This work has applications in the theoretical development of geometric deep learning and also in the theory of automorphic Lie algebras.

📄 PDF Abstract BibTeX arXiv:2303.07157

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Geometric Deep Learning and Equivariant Neural Networks

2021-05-28 · Jan E. Gerken, Jimmy Aronsson, Oscar Carlsson, Hampus Linander 외

We survey the mathematical foundations of geometric deep learning, focusing on group equivariant and gauge equivariant neural networks. We develop gauge equivariant convolutional neural networks on arbitrary manifolds $\…

Deep Learning object-detection Object Detection Semantic Segmentation

Homogeneous vector bundles and $G$-equivariant convolutional neural networks

2021-05-12 · Jimmy Aronsson

$G$-equivariant convolutional neural networks (GCNNs) is a geometric deep learning model for data defined on a homogeneous $G$-space $\mathcal{M}$. GCNNs are designed to respect the global symmetry in $\mathcal{M}$, ther…

Steerable Neural ODEs on Homogeneous Spaces

2026-05-11 · Emma Andersdotter, Daniel Persson, Fredrik Ohlsson arxiv

We introduce steerable neural ordinary differential equations on homogeneous spaces $M=G/H$. These models constitute a novel geometric extension of manifold neural ordinary differential equations (NODEs) that transport a…

A General Theory of Equivariant CNNs on Homogeneous Spaces

2018-11-05 · NeurIPS 2019 12 · Taco Cohen, Mario Geiger, Maurice Weiler

We present a general theory of Group equivariant Convolutional Neural Networks (G-CNNs) on homogeneous spaces such as Euclidean space and the sphere. Feature maps in these networks represent fields on a homogeneous base …

General Classification

Equivariant Eikonal Neural Networks: Grid-Free, Scalable Travel-Time Prediction on Homogeneous Spaces

2025-05-21 · Alejandro García-Castellanos, David R. Wessels, Nicky J. van den Berg, Remco Duits 외

We introduce Equivariant Neural Eikonal Solvers, a novel framework that integrates Equivariant Neural Fields (ENFs) with Neural Eikonal Solvers. Our approach employs a single neural field where a unified shared backbone …