Equivariant Neural Network Architecture

Equivariant neural networks are designed to leverage the inherent symmetries within data, improving efficiency and performance by incorporating group-theoretic principles into their architecture. Current research focuses on developing architectures that are equivariant to various transformation groups, including rotations (SO(3)), reflections (O(n)), and unitary transformations (U(n)), often employing techniques like group convolutions and steerable kernels. These models find applications in diverse fields such as 3D medical imaging, molecular dynamics, and neuroimaging, where exploiting inherent symmetries leads to more accurate and efficient analysis of complex data. The development of general frameworks and software libraries for constructing such networks is also a significant area of ongoing work.

Papers

April 24, 2024

On the Fourier analysis in the SO(3) space : EquiLoPO Network
Dmitrii Zhemchuzhnikov, Sergei Grudinin
Deep Space Inter Part Equivariance Rotation Equivariance Q Network Fourier Analysis Equivariant Deep Equivariant Neural Network Architecture

December 4, 2023

Expressive Sign Equivariant Networks for Spectral Geometric Learning
Derek Lim, Joshua Robinson, Stefanie Jegelka, Haggai Maron
Equivariant Network Equivariant Model Spectral Learning Group Equivariance Equivariant Neural Network Architecture

May 31, 2023

A General Framework for Equivariant Neural Networks on Reductive Lie Groups
Ilyes Batatia, Mario Geiger, Jose Munoz, Tess Smidt, Lior Silberman, Christoph Ortner
General Framework Approximate Symmetry Equivariant Neural Network Lie Group Equivariant Neural Network Architecture

May 26, 2023

Higher Order Gauge Equivariant CNNs on Riemannian Manifolds and Applications
Gianfranco Cortes, Yue Yu, Robin Chen, Melissa Armstrong, David Vaillancourt, Baba C. Vemuri
Financial Application Inter Part Equivariance Riemannian Manifold Spherical Convolutional Neural Network Equivariant Convolution Equivariant Neural Network Architecture Gauge Equivariant Neural Network

May 24, 2023

O$n$ Learning Deep O($n$)-Equivariant Hyperspheres
Pavlo Melnyk, Michael Felsberg, Mårten Wadenbäck, Andreas Robinson, Cuong Le
Deep Feature Deeper Network Equivariant Deep Equivariant Neural Network Architecture

May 5, 2023

Equivariant Neural Networks for Spin Dynamics Simulations of Itinerant Magnets
Yu Miyazaki
Equivariant Neural Network Equivariant Neural Network Architecture Spin Dynamic

December 12, 2022

Implicit Convolutional Kernels for Steerable CNNs
Maksim Zhdanov, Nico Hoffmann, Gabriele Cesa
Equivariant Model Steerable Convolution Equivariance Constraint Equivariant Neural Network Architecture

August 25, 2022

A Feedforward Unitary Equivariant Neural Network
Pui-Wai Ma, T. -H. Hubert Chan
Neural Network Convolution Layer Higher Order Unitary Operator Equivariant Neural Network Architecture

May 5, 2022

Low Dimensional Invariant Embeddings for Universal Geometric Learning
Nadav Dym, Steven J. Gortler
Invariant Representation Dynamical Invariant Geometric Learning Separable Representation Equivariant Neural Network Architecture Invariant Learning Method