Related papers: Equivalence Between SE(3) Equivariant Networks via…
The principle of equivariance to symmetry transformations enables a theoretically grounded approach to neural network architecture design. Equivariant networks have shown excellent performance and data efficiency on vision and medical…
The widespread success of convolutional neural networks may largely be attributed to their intrinsic property of translation equivariance. However, convolutions are not equivariant to variations in scale and fail to generalize to objects of…
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 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…
We propose a general architecture that combines the coefficient learning scheme with a residual operator layer for learning mappings between continuous functions in the 3D Euclidean space. Our proposed model is guaranteed to achieve…
Equivariant machine learning methods have shown wide success at 3D learning applications in recent years. These models explicitly build in the reflection, translation and rotation symmetries of Euclidean space and have facilitated large…
Rotation equivariance is a desirable property in many practical applications such as motion forecasting and 3D perception, where it can offer benefits like sample efficiency, better generalization, and robustness to input perturbations.…
Despite the recent active research on processing point clouds with deep networks, few attention has been on the sensitivity of the networks to rotations. In this paper, we propose a deep learning architecture that achieves discrete…
Convolutional neural networks have shown great success on feature extraction from raw input data such as images. Although convolutional neural networks are invariant to translations on the inputs, they are not invariant to other…
Motivated by objects such as electric fields or fluid streams, we study the problem of learning stochastic fields, i.e. stochastic processes whose samples are fields like those occurring in physics and engineering. Considering general…
Performance of neural networks can be significantly improved by encoding known invariance for particular tasks. Many image classification tasks, such as those related to cellular imaging, exhibit invariance to rotation. We present a novel…
Rotational symmetry is a defining feature of many tomography systems, including computed tomography (CT) and emission computed tomography (ECT), where detectors are arranged in a circular or periodically rotating configuration. This study…
Convolutional neural networks (CNNs) have enabled the state-of-the-art performance in many computer vision tasks. However, little effort has been devoted to establishing convolution in non-linear space. Existing works mainly leverage on the…
The translation equivariance of convolutional layers enables convolutional neural networks to generalize well on image problems. While translation equivariance provides a powerful inductive bias for images, we often additionally desire…
We develop a theory of category-equivariant neural networks (CENNs) that unifies group/groupoid-equivariant networks, poset/lattice-equivariant networks, graph and sheaf neural networks. Equivariance is formulated as naturality in a…
Group convolutional neural networks (G-CNNs) have been shown to increase parameter efficiency and model accuracy by incorporating geometric inductive biases. In this work, we investigate the properties of representations learned by regular…
Encoding the scale information explicitly into the representation learned by a convolutional neural network (CNN) is beneficial for many computer vision tasks especially when dealing with multiscale inputs. We study, in this paper, a…
Numerous studies have recently focused on incorporating different variations of equivariance in Convolutional Neural Networks (CNNs). In particular, rotation-equivariance has gathered significant attention due to its relevance in many…
Automated segmentation plays a pivotal role in medical image analysis and computer-assisted interventions. Despite the promising performance of existing methods based on convolutional neural networks (CNNs), they neglect useful equivariant…
Learning representations through deep generative modeling is a powerful approach for dynamical modeling to discover the most simplified and compressed underlying description of the data, to then use it for other tasks such as prediction.…