Related papers: Lorentz Group Equivariant Neural Network for Parti…
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…
The translational equivariant nature of Convolutional Neural Networks (CNNs) is a reason for its great success in computer vision. However, networks do not enjoy more general equivariance properties such as rotation or scaling, ultimately…
The Matrix-Element Method (MEM) has long been a cornerstone of data analysis in high-energy physics. It leverages theoretical knowledge of parton-level processes and symmetries to evaluate the likelihood of observed events. In parallel, the…
Lorentz's group represented by the hypercomplex system of numbers, which is based on dirac matrices, is investigated. This representation is similar to the space rotation representation by quaternions. This representation has several…
Group equivariant neural networks are growing in importance owing to their ability to generalise well in applications where the data has known underlying symmetries. Recent characterisations of a class of these networks that use high-order…
We describe the class of convexified convolutional neural networks (CCNNs), which capture the parameter sharing of convolutional neural networks in a convex manner. By representing the nonlinear convolutional filters as vectors in a…
In this paper we prove theorems characterizing the decomposition of equivariant feature spaces, filters and a structural preservation theorem for invariant subspace chains in group equivariant convolutional neural networks(G-CNN).…
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…
Most equivariant neural networks rely on a single global symmetry, limiting their use in domains where symmetries are instead local. We introduce Torsor CNNs, a framework for learning on graphs with local symmetries encoded as edge…
This work investigates use of equivariant neural networks as efficient and high-performance frameworks for image reconstruction and denoising in nuclear medicine. Our work aims to tackle limitations of conventional Convolutional Neural…
Neural network-based algorithms have garnered considerable attention in condensed matter physics for their ability to learn complex patterns from very high dimensional data sets towards classifying complex long-range patterns of…
Equivariant machine learning is an approach for designing deep learning models that respect the symmetries of the problem, with the aim of reducing model complexity and improving generalization. In this paper, we focus on an extension of…
We provide a full characterisation of all of the possible alternating group ($A_n$) equivariant neural networks whose layers are some tensor power of $\mathbb{R}^{n}$. In particular, we find a basis of matrices for the learnable, linear,…
Neural network is a dynamical system described by two different types of degrees of freedom: fast-changing non-trainable variables (e.g. state of neurons) and slow-changing trainable variables (e.g. weights and biases). We show that the…
We introduce a practical construction of group-equivariant and permutation-invariant functions of $N$ variables given a finite-dimensional space stable with respect to the group action. The construction applies to any connected linear Lie…
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…
Previous work on symmetric group equivariant neural networks generally only considered the case where the group acts by permuting the elements of a single vector. In this paper we derive formulae for general permutation equivariant layers,…
We consider a model of Quantum Gravity phenomenology, based on the idea that space-time may have some unknown granular structure that respects the Lorentz symmetry. The proposal involves non-trivial couplings of curvature to matter fields…
Soft, porous mechanical metamaterials exhibit pattern transformations that may have important applications in soft robotics, sound reduction and biomedicine. To design these innovative materials, it is important to be able to simulate them…
Group theory has been used in machine learning to provide a theoretically grounded approach for incorporating known symmetry transformations in tasks from robotics to protein modeling. In these applications, equivariant neural networks use…