相关论文: General $E(2)$-Equivariant Steerable CNNs

Group equivariant neural networks have been explored in the past few years and are interesting from theoretical and practical standpoints. They leverage concepts from group representation theory, non-commutative harmonic analysis and…

Steerable convolutional neural networks (CNNs) provide a general framework for building neural networks equivariant to translations and transformations of an origin-preserving group $G$, such as reflections and rotations. They rely on…

We present a convolutional network that is equivariant to rigid body motions. The model uses scalar-, vector-, and tensor fields over 3D Euclidean space to represent data, and equivariant convolutions to map between such representations.…

Steerable CNN imposes the prior knowledge of transformation invariance or equivariance in the network architecture to enhance the the network robustness on geometry transformation of data and reduce overfitting. It has been an intuitive and…

It has long been recognized that the invariance and equivariance properties of a representation are critically important for success in many vision tasks. In this paper we present Steerable Convolutional Neural Networks, an efficient and…

We present an alternative way of solving the steerable kernel constraint that appears in the design of steerable equivariant convolutional neural networks. We find explicit real and complex bases which are ready to use, for different…

In many machine learning tasks it is desirable that a model's prediction transforms in an equivariant way under transformations of its input. Convolutional neural networks (CNNs) implement translational equivariance by construction; for…

Group equivariant convolutional networks (GCNNs) endow classical convolutional networks with additional symmetry priors, which can lead to a considerably improved performance. Recent advances in the theoretical description of GCNNs revealed…

A wide range of techniques have been proposed in recent years for designing neural networks for 3D data that are equivariant under rotation and translation of the input. Most approaches for equivariance under the Euclidean group…

The effectiveness of Convolutional Neural Networks (CNNs) has been substantially attributed to their built-in property of translation equivariance. However, CNNs do not have embedded mechanisms to handle other types of transformations. In…

This paper presents a novel framework for non-linear equivariant neural network layers on homogeneous spaces. The seminal work of Cohen et al. on equivariant $G$-CNNs on homogeneous spaces characterized the representation theory of such…

State-of-the-art deep learning systems often require large amounts of data and computation. For this reason, leveraging known or unknown structure of the data is paramount. Convolutional neural networks (CNNs) are successful examples of…

Invariance under symmetry is an important problem in machine learning. Our paper looks specifically at equivariant neural networks where transformations of inputs yield homomorphic transformations of outputs. Here, steerable CNNs have…

Convolutional neural networks (CNNs) allow for parameter sharing and translational equivariance by using convolutional kernels in their linear layers. By restricting these kernels to be SO(3)-steerable, CNNs can further improve parameter…

Clifford-Steerable CNNs (CSCNNs) provide a unified framework that allows incorporating equivariance to arbitrary pseudo-Euclidean groups, including isometries of Euclidean space and Minkowski spacetime. In this work, we demonstrate that the…

Rotation-invariance is a desired property of machine-learning models for medical image analysis and in particular for computational pathology applications. We propose a framework to encode the geometric structure of the special Euclidean…

Convolutional neural networks revolutionized computer vision and natrual language processing. Their efficiency, as compared to fully connected neural networks, has its origin in the architecture, where convolutions reflect the translation…

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…

For many years, it has been shown how much exploiting equivariances can be beneficial when solving image analysis tasks. For example, the superiority of convolutional neural networks (CNNs) compared to dense networks mainly comes from an…

An important goal in visual recognition is to devise image representations that are invariant to particular transformations. In this paper, we address this goal with a new type of convolutional neural network (CNN) whose invariance is…