Related papers: Learning Partial Equivariances from Data
Convolutional Neural Networks (CNNs) are extremely efficient, since they exploit the inherent translation-invariance of natural images. However, translation is just one of a myriad of useful spatial transformations. Can the same efficiency…
Machine learning has recently entered into the mainstream of coarse-grained (CG) molecular modeling and simulation. While a variety of methods for incorporating deep learning into these models exist, many of them involve training neural…
While convolutional neural networks (CNNs) have come to match and exceed human performance in many settings, the tasks these models optimize for are largely constrained to the level of individual objects, such as classification and…
Conformal symmetries, i.e.\ coordinate transformations that preserve angles, play a key role in many fields, including physics, mathematics, computer vision and (geometric) machine learning. Here we build a neural network that is…
This paper introduces a new model to learn graph neural networks equivariant to rotations, translations, reflections and permutations called E(n)-Equivariant Graph Neural Networks (EGNNs). In contrast with existing methods, our work does…
Graph neural networks (GNNs) have gained traction over the past few years for their superior performance in numerous machine learning tasks. Graph Convolutional Neural Networks (GCN) are a common variant of GNNs that are known to have high…
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 space, and layers…
Convolutional neural networks (CNNs) give state of the art performance in many pattern recognition problems but can be fooled by carefully crafted patterns of noise. We report that CNN face recognition systems also make surprising "errors".…
Convolutional Neural Networks(CNN) are inherently equivariant under translations, however, they do not have an equivalent embedded mechanism to handle other transformations such as rotations and change in scale. Several approaches exist…
Learning and reasoning about 3D molecular structures with varying size is an emerging and important challenge in machine learning and especially in drug discovery. Equivariant Graph Neural Networks (GNNs) can simultaneously leverage the…
Geometric deep learning refers to the scenario in which the symmetries of a dataset are used to constrain the parameter space of a neural network and thus, improve their trainability and generalization. Recently this idea has been…
Learning rich and diverse representations is critical for the performance of deep convolutional neural networks (CNNs). In this paper, we consider how to use privileged information to promote inherent diversity of a single CNN model such…
Group-convolutional neural networks (GCNNs) are among the most important methods for introducing symmetry as an inductive bias in deep learning: In each linear layer, GCNNs sample a transformation group $G$ densely and correlate data and…
Graph neural networks have been widely used for learning representations of nodes for many downstream tasks on graph data. Existing models were designed for the nodes on a single graph, which would not be able to utilize information across…
This paper is concerned with a fundamental problem in geometric deep learning that arises in the construction of convolutional neural networks on surfaces. Due to curvature, the transport of filter kernels on surfaces results in a…
Convolutional Neural Network (CNN) is a popular model in computer vision and has the advantage of making good use of the correlation information of data. However, CNN is challenging to learn efficiently if the given dimension of data or…
Twisted Convolutional Networks (TCNs) are proposed as a novel deep learning architecture for classifying one-dimensional data with arbitrary feature order and minimal spatial relationships. Unlike conventional Convolutional Neural Networks…
The principle of translation equivariance (if an input image is translated an output image should be translated by the same amount), led to the development of convolutional neural networks that revolutionized machine vision. Other…
Due to a huge volume of information in many domains, the need for classification methods is imperious. In spite of many advances, most of the approaches require a large amount of labeled data, which is often not available, due to costs and…
Recent research has shown that incorporating equivariance into neural network architectures is very helpful, and there have been some works investigating the equivariance of networks under group actions. However, as digital images and…