This work introduces E3x, a software package for building neural networks that are equivariant with respect to the Euclidean group $\mathrm{E}(3)$, consisting of translations, rotations, and reflections of three-dimensional space. Compared to ordinary neural networks, $\mathrm{E}(3)$-equivariant models promise benefits whenever input and/or output data are quantities associated with three-dimensional objects. This is because the numeric values of such quantities (e.g. positions) typically depend on the chosen coordinate system. Under transformations of the reference frame, the values change predictably, but the underlying rules can be difficult to learn for ordinary machine learning models. With built-in $\mathrm{E}(3)$-equivariance, neural networks are guaranteed to satisfy the relevant transformation rules exactly, resulting in superior data efficiency and accuracy. The code for E3x is available from https://github.com/google-research/e3x, detailed documentation and usage examples can be found on https://e3x.readthedocs.io.
University of Amsterdam（阿姆斯特丹大学）；AMLab；Informatics Institute（信息学研究所）；AI4Science Lab（AI4Science实验室）；Anton Pannekoek Institute for Astronomy（安东·潘内科克天文研究所）；Microsoft Research（微软研究院）；ELLIS Unit Linz（林茨ELLIS单元）；Institute for Machine Learning（机器学习研究所）；JKU Linz（约翰内斯·开普勒大学林茨分校）；NXAI GmbH（NXAI有限公司）
Istituto Nazionale di Ottica del Consiglio Nazionale delle Ricerche (CNR-INO)（意大利国家光学研究所（国家研究委员会光学研究所））；University of Florence（佛罗伦萨大学）；European Laboratory for Non-Linear Spectroscopy (LENS)（欧洲非线性光谱实验室）
Spin-Weighted Spherical Harmonics Enable Complete and Scalable $\mathrm{E}(3)$-Equivariant Networks
Department of Computer Science and Engineering, Texas A&M University（德克萨斯农工大学计算机科学与工程系）；Lambda, Inc.（Lambda公司）；Department of Materials Science and Engineering, Texas A&M University（德克萨斯农工大学材料科学与工程系）；Department of Electrical and Computer Engineering, Texas A&M University（德克萨斯农工大学电气与计算机工程系）；Department of Physics and Astronomy, Texas A&M University（德克萨斯农工大学物理与天文学系）；Department of Mechanical Engineering, Texas A&M University（德克萨斯农工大学机械工程系）
ESGNN: Towards Equivariant Scene Graph Neural Network for 3D Scene Understanding
College of Engineering and Computer Science, VinUniversity（VinUniversity工程与计算机科学学院）；Department of Mathematics and Computer Science, Indiana State University（印第安纳州立大学数学与计算机科学系）
A General Framework for Equivariant Neural Networks on Reductive Lie Groups
University of Cambridge（剑桥大学）；ENS Paris-Saclay（巴黎萨克雷高等师范学院）；Université Paris-Saclay（巴黎萨克雷大学）；Massachusetts Institute of Technology（麻省理工学院）；EIA University（EIA大学）；University of British Columbia（不列颠哥伦比亚大学）
