Related papers: Compact Matrix Quantum Group Equivariant Neural Ne…

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…

We present the group equivariant conditional neural process (EquivCNP), a meta-learning method with permutation invariance in a data set as in conventional conditional neural processes (CNPs), and it also has transformation equivariance in…

Equivariance is a nice property to have as it produces much more parameter efficient neural architectures and preserves the structure of the input through the feature mapping. Even though some combinations of transformations might never…

Local gauge symmetry underlies fundamental interactions and strongly correlated quantum matter, yet existing machine-learning approaches lack a general, principled framework for learning under site-dependent symmetries, particularly for…

Supervised learning with deep models has tremendous potential for applications in materials science. Recently, graph neural networks have been used in this context, drawing direct inspiration from models for molecules. However, materials…

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…

Recent work has identified non-compact symmetric spaces U/H as a promising class of homogeneous manifolds to develop a geometrically consistent theory of neural networks. An initial implementation of these concepts has been presented in a…

In recent years, the use of machine learning has become increasingly popular in the context of lattice field theories. An essential element of such theories is represented by symmetries, whose inclusion in the neural network properties can…

Symmetries and equivariance are fundamental to the generalization of neural networks on domains such as images, graphs, and point clouds. Existing work has primarily focused on a small number of groups, such as the translation, rotation,…

Reductive Lie Groups, such as the orthogonal groups, the Lorentz group, or the unitary groups, play essential roles across scientific fields as diverse as high energy physics, quantum mechanics, quantum chromodynamics, molecular dynamics,…

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…

Neural networks that process the parameters of other neural networks find applications in domains as diverse as classifying implicit neural representations, generating neural network weights, and predicting generalization errors. However,…

There has been much recent interest in designing neural networks (NNs) with relaxed equivariance, which interpolate between exact equivariance and full flexibility for consistent performance gains. In a separate line of work, structured…

We introduce Clifford Group Equivariant Neural Networks: a novel approach for constructing $\mathrm{O}(n)$- and $\mathrm{E}(n)$-equivariant models. We identify and study the $\textit{Clifford group}$, a subgroup inside the Clifford algebra…

Group convolutions and cross-correlations, which are equivariant to the actions of group elements, are commonly used in mathematics to analyze or take advantage of symmetries inherent in a given problem setting. Here, we provide efficient…

Invariance and equivariance to geometrical transformations have proven to be very useful inductive biases when training (convolutional) neural network models, especially in the low-data regime. Much work has focused on the case where the…

Neural networks are a promising tool for simulating quantum many body systems. Recently, it has been shown that neural network-based models describe quantum many body systems more accurately when they are constrained to have the correct…

The set of functions parameterized by a linear fully-connected neural network is a determinantal variety. We investigate the subvariety of functions that are equivariant or invariant under the action of a permutation group. Examples of such…

The crucial role played by the underlying symmetries of high energy physics and lattice field theories calls for the implementation of such symmetries in the neural network architectures that are applied to the physical system under…

Neural functional networks (NFNs) have recently gained significant attention due to their diverse applications, ranging from predicting network generalization and network editing to classifying implicit neural representation. Previous NFN…