ChenCaiOSU/awesomeequivariantnetwork
Paper list for equivariant neural network
repo name  ChenCaiOSU/awesomeequivariantnetwork 
repo link  https://github.com/ChenCaiOSU/awesomeequivariantnetwork 
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awesomeequivariantnetwork
Paper list for equivariant neural network. Workinprogress.
Feel free to suggest relevant papers in the following format.
**Group Equivariant Convolutional Networks**
Taco S. Cohen, Max Welling ICML 2016 [paper](https://arxiv.org/pdf/1602.07576.pdf)
Acknowledgement: I would like to thank Maurice Weiler, Fabian Fuchs, Tess Smidt, Rui Wang, David Pfau, Jonas Köhler, Taco Cohen, Gregor Simm, Erik J Bekkers, JeanBaptiste Cordonnier, David W. Romero, Ivan Sosnovik for paper suggestions! Thank Weihao Xia for helping out typesetting!
Table of Contents
 Equivariance and Group convolution
 Theory
 Equivariant Density Estimation and Sampling
 Application
 Permutation Equivariance
 Talk and Tutorial
 TO READ
Equivariance and Group convolution
 Group Equivariant Convolutional Networks
Taco S. Cohen, Max Welling ICML 2016 paper
Note: first paper; discrete group;  Steerable CNNs
Taco S. Cohen, Max Welling ICLR 2017 paper  Harmonic Networks: Deep Translation and Rotation Equivariance
Daniel E. Worrall, Stephan J. Garbin, Daniyar Turmukhambetov, Gabriel J. Brostow CVPR 2017 paper  Spherical CNNs
Taco S. Cohen, Mario Geiger, Jonas Koehler, Max Welling ICLR 2018 best paper paper
Note: use generalized FFT to speed up convolution on $S^2$ and $SO(3)$  Clebsch–Gordan Nets: a Fully Fourier Space Spherical Convolutional Neural Network
Risi Kondor, Zhen Lin, Shubhendu Trivedi NeurIPS 2018 paper
Note: perform equivariant nonlinearity in Fourier space;  General E(2)Equivariant Steerable CNNs
Maurice Weiler, Gabriele Cesa NeurIPS 2019 paper
Note: nice benchmark on different reprsentations  Learning Steerable Filters for Rotation Equivariant CNNs
Maurice Weiler, Fred A. Hamprecht, Martin Storath CVPR 2018 paper
Note: group convolutions, kernels parameterized in circular harmonic basis (steerable filters);  Learning SO(3) Equivariant Representations with Spherical CNNs
Carlos Esteves, Christine AllenBlanchette, Ameesh Makadia, Kostas Daniilidis ECCV 2018 paper
Note: SO(3) equivariance; zonal filter  3D Steerable CNNs: Learning Rotationally Equivariant Features in Volumetric Data
Maurice Weiler, Mario Geiger, Max Welling, Wouter Boomsma, Taco Cohen NeurIPS 2018 paper
Note: SE(3) equivariance; characterize the basis of steerable kernel  Tensor field networks: Rotation and translationequivariant neural networks for 3D point clouds
Nathaniel Thomas, Tess Smidt, Steven Kearnes, Lusann Yang, Li Li, Kai Kohlhoff, Patrick Riley paper
Note: SE(3) equivariance for point clouds  Gauge Equivariant Convolutional Networks and the Icosahedral CNN
Taco S. Cohen, Maurice Weiler, Berkay Kicanaoglu, Max Welling ICML 2019 paper, talk
Note: gauge equivariance on general manifold  Cormorant: Covariant Molecular Neural Networks
Brandon Anderson, TruongSon Hy, Risi Kondor NeurIPS 2019 paper  Deep Scalespaces: Equivariance Over Scale
Daniel Worrall, Max Welling NeurIPS 2019 paper  ScaleEquivariant Steerable Networks
Ivan Sosnovik, Michał Szmaja, Arnold Smeulders ICLR 2020 paper  BSpline CNNs on Lie Groups
Erik J Bekkers ICLR 2020 paper  SE(3)Transformers: 3D RotoTranslation Equivariant Attention Networks
Fabian B. Fuchs, Daniel E. Worrall, Volker Fischer, Max Welling NeurIPS 2020 paper, blog
Note: TFN + equivariant selfattention; improved spherical harmonics computation  Gauge Equivariant Mesh CNNs: Anisotropic convolutions on geometric graphs
Pim de Haan, Maurice Weiler, Taco Cohen, Max Welling ICLR 2021 paper
Note: anisotropic gauge equivariant kernels + message passing by parallel transporting features over mesh edges  Lorentz Group Equivariant Neural Network for Particle Physics
Alexander Bogatskiy, Brandon Anderson, Jan T. Offermann, Marwah Roussi, David W. Miller, Risi Kondor ICML 2020 paper
Note: SO(1, 3) equivariance  Generalizing Convolutional Neural Networks for Equivariance to Lie Groups on Arbitrary Continuous Data
Marc Finzi, Samuel Stanton, Pavel Izmailov, Andrew Gordon Wilson ICML 2020 paper
Note: fairly generic architecture; use Monte Carlo sampling to achieve equivariance in expectation;  SpinWeighted Spherical CNNs
Carlos Esteves, Ameesh Makadia, Kostas Daniilidis NeurIPS 2020 paper
Note: anisotropic filter for vector field on sphere  Learning Invariances in Neural Networks
Gregory Benton, Marc Finzi, Pavel Izmailov, Andrew Gordon Wilson NeurIPS 2020 paper
Note: very interesting approch; enfore “soft” invariance via learning over both model parameters and distributions over augmentations  Lie Algebra Convolutional Neural Networks with Automatic Symmetry Extraction
Nima Dehmamy, Yanchen Liu, Robin Walters, Rose Yu paper
Note: very interesting paper; It’s unfortunate that it is rejected by ICLR 2021  LieTransformer: Equivariant selfattention for Lie Groups
Michael Hutchinson, Charline Le Lan, Sheheryar Zaidi, Emilien Dupont, Yee Whye Teh, Hyunjik Kim paper
Note: equivariant self attention to arbitrary Lie groups and their discrete subgroups  CoAttentive Equivariant Neural Networks: Focusing Equivariance On Transformations CoOccurring In Data
David W. Romero, Mark Hoogendoorn ICLR 2020 paper  Attentive Group Equivariant Convolutional Networks
David W. Romero, Erik J. Bekkers, Jakub M. Tomczak, Mark Hoogendoorn ICML 2020 paper  Wavelet Networks: Scale Equivariant Learning From Raw Waveforms
David W. Romero, Erik J. Bekkers, Jakub M. Tomczak, Mark Hoogendoorn paper  Group Equivariant StandAlone SelfAttention For Vision David W. Romero, JeanBaptiste Cordonnier ICLR 2021 paper
 MDP Homomorphic Networks: Group Symmetries in Reinforcement Learning
Elise van der Pol, Daniel E. Worrall, Herke van Hoof, Frans A. Oliehoek, Max Welling NeurIPS 2020 paper  Isometric Transformation Invariant and Equivariant Graph Convolutional Networks Masanobu Horie, Naoki Morita, Toshiaki Hishinuma, Yu Ihara, Naoto Mitsume ICLR 2021 paper
Theory

On the Generalization of Equivariance and Convolution in Neural Networks to the Action of Compact Groups
Risi Kondor, Shubhendu Trivedi ICML 2018 paper
Note: convolution is all you need (for scalar fields) 
A General Theory of Equivariant CNNs on Homogeneous Spaces
Taco Cohen, Mario Geiger, Maurice Weiler NeurIPS 2019 paper
Note: convolution is all you need (for general fields) 
Equivariance Through ParameterSharing
Siamak Ravanbakhsh, Jeff Schneider, Barnabas Poczos ICML 2017 paper 
Universal approximations of invariant maps by neural networks
Dmitry Yarotsky paper 
A WignerEckart Theorem for Group Equivariant Convolution Kernels
Leon Lang, Maurice Weiler ICLR 2021 paper
Note: steerable kernel spaces are fully understood and parameterized in terms of 1) generalized reduced matrix elements, 2) ClebschGordan coefficients, and 3) harmonic basis functions on homogeneous spaces. 
On the Universality of Rotation Equivariant Point Cloud Networks
Nadav Dym, Haggai Maron ICLR 2021 paper,
Note: universality for TFN and se3transformer 
Universal Equivariant Multilayer Perceptrons
Siamak Ravanbakhsh paper
Equivariant Density Estimation and Sampling
 Equivariant Flows: Exact Likelihood Generative Learning for Symmetric Densities
Jonas Köhler, Leon Klein, Frank Noé ICML 2020 paper
Note: general framework for constructing equivariant normalizing flows on euclidean spaces. Instantiation for particle systems/point clouds = simultanoues SE(3) and permutation equivariance.  Equivariant Hamiltonian Flows
Danilo Jimenez Rezende, Sébastien Racanière, Irina Higgins, Peter Toth NeurIPS 2019 ML4Phys workshop paper
Note: general framework for constructing equivariant normalizing flows in phase space utilizing Hamiltonian dynamics. Instantiation for SE(2) equivariance.  Sampling using SU(N) gauge equivariant flows
Denis Boyda, Gurtej Kanwar, Sébastien Racanière, Danilo Jimenez Rezende, Michael S. Albergo, Kyle Cranmer, Daniel C. Hackett, Phiala E. Shanahan paper
Note: normalizing flows for lattice gauge theory. Instantiation for SU(2)/SU(3) equivariance.  Exchangeable neural ode for set modeling
Yang Li, Haidong Yi, Christopher M. Bender, Siyuan Shan, Junier B. Oliva NeurIPS 2020 paper
Note: framework for permutation equivariant flows for set data. Instantiation for permutation equivariance.  Equivariant Normalizing Flows for Point Processes and Sets
Marin Biloš, Stephan Günnemann NeurIPS 2020 paper
Note: framework for permutation equivariant flows for set data. Instantiation for permutation equivariance.  The Convolution Exponential and Generalized Sylvester Flows
Emiel Hoogeboom, Victor Garcia Satorras, Jakub M. Tomczak, Max Welling NeurIPS 2020 paper
Note: invertible convolution operators. Instantiation for permutation equivariance.  Targeted free energy estimation via learned mappings
Peter Wirnsberger, Andrew J. Ballard, George Papamakarios, Stuart Abercrombie, Sébastien Racanière, Alexander Pritzel, Danilo Jimenez Rezende, Charles Blundell J Chem Phys. 2020 Oct 14;153(14):144112. paper
Note: normalizing flows for particle systems on a torus. Instantiation for permutation equivariance.  Temperaturesteerable flows
Manuel Dibak, Leon Klein, Frank Noé NeurIPS 2020 ML4Phys workshops paper
Note: normalizing flows in phase space with equivariance with respect to changes in temperature.
Application
 Trajectory Prediction using Equivariant Continuous Convolution
Robin Walters, Jinxi Li, Rose Yu ICLR 2021 paper  Incorporating Symmetry into Deep Dynamics Models for Improved Generalization
Rui Wang, Robin Walters, Rose Yu ICLR 2021 paper  SE(3)Equivariant Graph Neural Networks for DataEfficient and Accurate Interatomic Potentials
Simon Batzner, Tess E. Smidt, Lixin Sun, Jonathan P. Mailoa, Mordechai Kornbluth, Nicola Molinari, Boris Kozinsky paper  Finding Symmetry Breaking Order Parameters with Euclidean Neural Networks
Tess E. Smidt, Mario Geiger, Benjamin Kurt Miller paper  Group Equivariant Generative Adversarial Networks
Neel Dey, Antong Chen, Soheil Ghafurian ICLR 2021 paper  AbInitio Solution of the ManyElectron Schrödinger Equation with Deep Neural Networks
David Pfau, James S. Spencer, Alexander G. de G. Matthews, W. M. C. Foulkes paper  SymmetryAware ActorCritic for 3D Molecular Design
Gregor N. C. Simm, Robert Pinsler, Gábor Csányi, José Miguel HernándezLobato ICLR 2021 paper  Rototranslation equivariant convolutional networks: Application to histopathology image analysis
Maxime W. Lafarge, Erik J. Bekkers, Josien P.W. Pluim, Remco Duits, Mitko Veta MedIA paper  Scale Equivariance Improves Siamese Tracking
Ivan Sosnovik*, Artem Moskalev*, Arnold Smeulders WACV 2021 paper  3D GCNNs for Pulmonary Nodule Detection Marysia Winkels, Taco S. Cohen paper International Conference on Medical Imaging with Deep Learning (MIDL), 2018.
 Rototranslation covariant convolutional networks for medical image analysis
Erik J. Bekkers, Maxime W. Lafarge, Mitko Veta, Koen A.J. Eppenhof, Josien P.W. Pluim, Remco Duits MICCAI 2018 Young Scientist Award paper
Permutation Equivariance
There are many paper on this topics. I only added very few of them.
 PointNet: Deep Learning on Point Sets for 3D Classification and Segmentation
Charles R. Qi, Hao Su, Kaichun Mo, Leonidas J. Guibas CVPR 2017 paper  Deep Sets
Manzil Zaheer, Satwik Kottur, Siamak Ravanbakhsh, Barnabas Poczos, Ruslan Salakhutdinov, Alexander Smola NeurIPS 2017 paper  Invariant and Equivariant Graph Networks
Haggai Maron, Heli BenHamu, Nadav Shamir, Yaron Lipman ICLR 2019 paper  Provably Powerful Graph Networks
Haggai Maron, Heli BenHamu, Hadar Serviansky, Yaron Lipman NeurIPS 2019 paper  Universal Invariant and Equivariant Graph Neural Networks
Nicolas Keriven, Gabriel Peyré NeurIPS 2019 paper  On Learning Sets of Symmetric Elements
Haggai Maron, Or Litany, Gal Chechik, Ethan Fetaya ICML 2020 best paper  On the Universality of Invariant Networks
Haggai Maron, Ethan Fetaya, Nimrod Segol, Yaron Lipman paper
Talk and Tutorial
IAS: Graph Nets: The Next Generation  Max Welling  YouTube
Equivariance and Data Augmentation workshop: many nice talks
IPAM: E(3) Equivariant Neural Network Tutorial
IPAM: Risi Kondor: “Fourier space neural networks”
NeurIPS 2020 tutorial: Equivariant Networks
Yaron Lipman  Deep Learning of Irregular and Geometric Data  YouTube
MathML: Erik J Bekkers: Group Equivariant CNNs beyond RotoTranslations: BSpline CNNs on Lie Groups
Background
I am by no means an expert in this field. Here are books and articles suggest by Taco Cohen when asked references to learn group theory and representation theory.

Carter, Visual Group Theory
Note: very basic intro to group theory 
Theoretical Aspects of Group Equivariant Neural Networks
Carlos Esteves
Note: covers all the math you need for equivariant nets in a fairly compact and accessible manner. 
Serre, Linear Representations of Finite Groups
Note: classic text on representations of finite groups. First few chapters are relevant to equivariant nets. 
G B Folland. A Course in Abstract Harmonic Analysis
Note: covers representations of locally compact groups; induced representations. 
Mark Hamilton. Mathematical Gauge Theory: With Applications to the Standard Model of Particle Physics
Note: covers fiber bundles, useful for understanding homogeneous GCNNs and Gauge CNNs.
TO READ
There are many paper I haven’t read carefully yet.
 Making Convolutional Networks ShiftInvariant Again
Richard Zhang ICML 2019 paper  Probabilistic symmetries and invariant neural networks
Benjamin BloemReddy, Yee Whye Teh JMLR paper  On Representing (Anti)Symmetric Functions
Marcus Hutter paper  PDEbased Group Equivariant Convolutional Neural Networks
Bart M.N. Smets, Jim Portegies, Erik J. Bekkers, Remco Duits paper