Related papers: Equivariant Wavelets: Fast Rotation and Translatio…

A rigid-motion scattering computes adaptive invariants along translations and rotations, with a deep convolutional network. Convolutions are calculated on the rigid-motion group, with wavelets defined on the translation and rotation…

This paper proposes a set of rules to revise various neural networks for 3D point cloud processing to rotation-equivariant quaternion neural networks (REQNNs). We find that when a neural network uses quaternion features under certain…

The purpose of this short and simple note is to clarify a common misconception about convolutional neural networks (CNNs). CNNs are made up of convolutional layers which are shift equivariant due to weight sharing. However, convolutional…

Equivariant neural networks (ENNs) are graph neural networks embedded in $\mathbb{R}^3$ and are well suited for predicting molecular properties. The ENN library e3nn has customizable convolutions, which can be designed to depend only on…

This paper introduces a novel deep neural network architecture for solving the inverse scattering problem in frequency domain with wide-band data, by directly approximating the inverse map, thus avoiding the expensive optimization loop of…

Many problems across computer vision and the natural sciences require the analysis of spherical data, for which representations may be learned efficiently by encoding equivariance to rotational symmetries. We present a generalized spherical…

Image registration is a fundamental task that aligns anatomical structures between images. While CNNs perform well, they lack rotation equivariance - a rotated input does not produce a correspondingly rotated output. This hinders…

Spherical equivariant graph neural networks (EGNNs) provide a principled framework for learning on three-dimensional molecular and biomolecular systems, where predictions must respect the rotational symmetries inherent in physics. These…

This paper presents a novel framework combining group equivariant convolutional neural networks (G-CNNs) with equivariant-aware structured pruning to produce compact, transformation-invariant models for resource-constrained environments.…

Rotation invariance has been studied in the computer vision community primarily in the context of small in-plane rotations. This is usually achieved by building invariant image features. However, the problem of achieving invariance for…

Incorporating either rotation equivariance or scale equivariance into CNNs has proved to be effective in improving models' generalization performance. However, jointly integrating rotation and scale equivariance into CNNs has not been…

Self-supervised image denoising methods have garnered significant research attention in recent years, for this kind of method reduces the requirement of large training datasets. Compared to supervised methods, self-supervised methods rely…

We propose a novel visual context-aware filter generation module which incorporates contextual information present in images into Convolutional Neural Networks (CNNs). In contrast to traditional CNNs, we do not employ the same set of…

We propose a framework for rotation and translation covariant deep learning using $SE(2)$ group convolutions. The group product of the special Euclidean motion group $SE(2)$ describes how a concatenation of two roto-translations results in…

Recent years have seen a surge in data-driven surrogates for dynamical systems that can be orders of magnitude faster than numerical solvers. However, many machine learning-based models such as neural operators exhibit spectral bias,…

In this paper we construct and theoretically analyse group equivariant convolutional kernel networks (CKNs) which are useful in understanding the geometry of (equivariant) CNNs through the lens of reproducing kernel Hilbert spaces (RKHSs).…

In this paper we propose integrating a priori knowledge into both design and training of convolutional neural networks (CNNs) to learn object representations that are invariant to affine transformations (i.e., translation, scale, rotation).…

Vision transformers have gained significant attention and achieved state-of-the-art performance in various computer vision tasks, including image classification, instance segmentation, and object detection. However, challenges remain in…

Convolutions encode equivariance symmetries into neural networks leading to better generalisation performance. However, symmetries provide fixed hard constraints on the functions a network can represent, need to be specified in advance, and…

Convolutional neural networks owe much of their success to hard-coding translation equivariance. Quantum convolutional neural networks (QCNNs) have been proposed as near-term quantum analogues, but the relevant notion of translation depends…