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

We introduce a unified framework for group equivariant networks on homogeneous spaces
derived from a Fourier perspective. We consider tensor-valued feature fields, before and …

We analyze the role of rotational equivariance in convolutional neural networks (CNNs)
applied to spherical images. We compare the performance of the group equivariant …

In this paper, we present a new model for Direction of Arrival (DOA) estimation of sound
sources based on an Icosahedral Convolutional Neural Network (CNN) applied over SRP …

High-resolution wide-angle fisheye images are becoming more and more important for
robotics applications such as autonomous driving. However using ordinary convolutional …

It is often said that a deep learning model is``invariant''to some specific type of
transformation. However, what is meant by this statement strongly depends on the context in …

Convolutional neural networks (CNNs) constructed natively on the sphere have been
developed recently and shown to be highly effective for the analysis of spherical data. While …

Many areas of science and engineering encounter data defined on spherical manifolds.
Modelling and analysis of spherical data often necessitates spherical harmonic transforms …

Spherical CNNs generalize CNNs to functions on the sphere, by using spherical
convolutions as the main linear operation. The most accurate and efficient way to compute …

Steerable models can provide very general and flexible equivariance by formulating
equivariance requirements in the language of representation theory and feature fields …