Related papers: A Wigner-Eckart Theorem for Group Equivariant Conv…
Bessiere et al. (AAAI'08) showed that several intractable global constraints can be efficiently propagated when certain natural problem parameters are small. In particular, the complete propagation of a global constraint is fixed-parameter…
We present a neural network architecture that is fully equivariant with respect to transformations under the Lorentz group, a fundamental symmetry of space and time in physics. The architecture is based on the theory of the…
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.…
Group convolutional layers with respect to some group $G$ are modeled by convolutions or cross-correlations with a filter, and they provide the fundamental building block for group convolutional neural networks. For entirely unconstrained…
We present an efficient convolution kernel for Convolutional Neural Networks (CNNs) on unstructured grids using parameterized differential operators while focusing on spherical signals such as panorama images or planetary signals. To this…
Incorporating Euclidean symmetries (e.g. rotation equivariance) as inductive biases into graph neural networks has improved their generalization ability and data efficiency in unbounded physical dynamics modeling. However, in various…
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 after a convolutional layer. We present a unified derivation of…
Group equivariance has emerged as a valuable inductive bias in deep learning, enhancing generalization, data efficiency, and robustness. Classically, group equivariant methods require the groups of interest to be known beforehand, which may…
Machine-learning models based on a point-cloud representation of a physical object are ubiquitous in scientific applications and particularly well-suited to the atomic-scale description of molecules and materials. Among the many different…
Group Equivariant CNNs (G-CNNs) have shown promising efficacy in various tasks, owing to their ability to capture hierarchical features in an equivariant manner. However, their equivariance is fixed to the symmetry of the whole group,…
The Heisenberg evolution of a given unitary operator corresponds classically to a fixed canonical transformation that is viewed through a moving coordinate system. The operators that form the bases of the Weyl representation and its Fourier…
Convolutional neural networks have been highly successful in image-based learning tasks due to their translation equivariance property. Recent work has generalized the traditional convolutional layer of a convolutional neural network to…
We introduce a general method for achieving robust group-invariance in group-equivariant convolutional neural networks ($G$-CNNs), which we call the $G$-triple-correlation ($G$-TC) layer. The approach leverages the theory of the…
We consider positive semidefinite kernels valued in the $*$-algebra of adjointable operators on a VE-space (Vector Euclidean space) and that are invariant under actions of $*$-semigroups. A rather general dilation theorem is stated and…
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…
Designing neural network architectures that can handle data symmetry is crucial. This is especially important for geometric graphs whose properties are equivariance under Euclidean transformations. Current equivariant graph neural networks…
Although provably robust to translational perturbations, convolutional neural networks (CNNs) are known to suffer from extreme performance degradation when presented at test time with more general geometric transformations of inputs.…
In this paper, we introduce group convolutional neural networks (GCNNs) equivariant to color variation. GCNNs have been designed for a variety of geometric transformations from 2D and 3D rotation groups, to semi-groups such as scale.…
Binary Neural Network (BNN) represents convolution weights with 1-bit values, which enhances the efficiency of storage and computation. This paper is motivated by a previously revealed phenomenon that the binary kernels in successful BNNs…
Learning graph convolutional networks (GCNs) is an emerging field which aims at generalizing deep learning to arbitrary non-regular domains. Most of the existing GCNs follow a neighborhood aggregation scheme, where the representation of a…