Related papers: Lorentz Group Equivariant Neural Network for Parti…

Equivariant neural networks have shown improved performance, expressiveness and sample complexity on symmetrical domains. But for some specific symmetries, representations, and choice of coordinates, the most common point-wise activations,…

Lattice gauge equivariant convolutional neural networks (L-CNNs) are a framework for convolutional neural networks that can be applied to non-Abelian lattice gauge theories without violating gauge symmetry. We demonstrate how L-CNNs can be…

The development of efficient machine learning models for molecular systems representation is becoming crucial in scientific research. We introduce TensorNet, an innovative O(3)-equivariant message-passing neural network architecture that…

Group equivariance is a strong inductive bias useful in a wide range of deep learning tasks. However, constructing efficient equivariant networks for general groups and domains is difficult. Recent work by Finzi et al. (2021) directly…

Existing equivariant neural networks require prior knowledge of the symmetry group and discretization for continuous groups. We propose to work with Lie algebras (infinitesimal generators) instead of Lie groups. Our model, the Lie algebra…

This paper introduces a new Convolutional Neural Network (ConvNet) architecture inspired by a class of partial differential equations (PDEs) called quasi-linear hyperbolic systems. With comparable performance on the image classification…

The Lorentz group is the fundamental language for space-time symmetries of relativistic particles. This group can these days be derived from the symmetries observed in other branches of physics. It is shown that this group can be derived…

In the past decade the phenomenology of quantum gravity has been dominated by the search of violations of Lorentz invariance. However, there are very serious arguments that led us to assume that this invariance is a symmetry in Nature. This…

We present in the article the formulation of a version of Lorentz covariant quantum mechanics based on a group theoretical construction from a Heisenberg-Weyl symmetry with position and momentum operators transforming as Minkowski…

Many learning tasks, including learning potential energy surfaces from ab initio calculations, involve global spatial symmetries and permutational symmetry between atoms or general particles. Equivariant graph neural networks are a standard…

Euclidean deep learning is often inadequate for addressing real-world signals where the representation space is irregular and curved with complex topologies. Interpreting the geometric properties of such feature spaces has become paramount…

Equivariance of linear neural network layers is well studied. In this work, we relax the equivariance condition to only be true in a projective sense. We propose a way to construct a projectively equivariant neural network through building…

We prove an impossibility result, which in the context of function learning says the following: under certain conditions, it is impossible to simultaneously learn symmetries and functions equivariant under them using an ansatz consisting of…

Despite the successes of deep learning in computer vision, difficulties persist in recognizing objects that have undergone group-symmetric transformations rarely seen during training$\unicode{x2013}$for example objects seen in unusual…

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,…

Equivariant neural networks offer strong inductive biases for learning from molecular and geometric data but often rely on specialized, computationally expensive tensor operations. We present a framework to transfers existing tensor field…

Based on the theory of homogeneous spaces we derive geometrically optimal edge attributes to be used within the flexible message-passing framework. We formalize the notion of weight sharing in convolutional networks as the sharing of…

In recent years, deep learning techniques have shown great success in various tasks related to inverse problems, where a target quantity of interest can only be observed through indirect measurements by a forward operator. Common approaches…

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…

The difficult problem of relating the static structure of glassy liquids and their dynamics is a good target for Machine Learning, an approach which excels at finding complex patterns hidden in data. Indeed, this approach is currently a hot…