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Equivariant neural networks (ENNs) have been shown to be extremely effective in applications involving underlying symmetries.
Xcv. symmetry changes in barium titanate at low temperatures and their relation to its ferroelectric properties
Herbert Frederick Kay and P Vousden · 1949
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Broken symmetries and the masses of gauge bosons
Peter W Higgs · 1964
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International tables for crystallography , volume 1
Theo Hahn, Uri Shmueli, and JC Wilson Arthur · 1983
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On the symmetry breaking instability leading to vortex shedding
Shaojie Tang and Nadine Aubry · 1997
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Octahedral tilting in perovskites. i. geometrical considerations
Patrick M Woodward · 1997
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Introduction to the Theory of Ferromagnetism , volume 109
Amikam Aharoni · 2000
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Algebraic Topology
Allen Hatcher · 2002
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On the meaning of symmetry breaking
Elena Castellani et al · 2003
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Abstract algebra , volume 3
David Steven Dummit and Richard M Foote · 2004
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An algebraic approach to symmetry detection
Yosi Keller and Yoel Shkolnisky · 2004
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The theory of finite groups: an introduction , volume 1
Hans Kurzweil and Bernd Stellmacher · 2004
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Normalizers of point groups
E Koch and W Fischer · 2006
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Partial and approximate symmetry detection for 3d geometry
Niloy J Mitra, Leonidas J Guibas, and Mark Pauly · 2006
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Group theory: application to the physics of condensed matter
Mildred S Dresselhaus, Gene Dresselhaus, and Ado Jorio · 2007
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Symmetry detection using feature lines
Martin Bokeloh, Alexander Berner, Michael Wand, H-P Seidel, and Andreas Schilling · 2009
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Symmetrizer: algorithmic determination of point groups in nearly symmetric molecules
R Jeffrey Largent, William F Polik, and JR Schmidt · 2012
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Commentary: The materials project: A materials genome approach to accelerating materials innovation
Anubhav Jain, Shyue Ping Ong, Geoffroy Hautier, Wei Chen, William Davidson Richards, Stephen Dacek, Shreyas Cholia, Dan Gunter, David Skinner, Gerbrand Ceder, et al · 2013
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On implementing 2d rectangular assignment algorithms
David F Crouse · 2016
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Spherical cnns
Taco S Cohen, Mario Geiger, Jonas Köhler, and Max Welling · 2018
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On the generalization of equivariance and convolution in neural networks to the action of compact groups
Risi Kondor and Shubhendu Trivedi · 2018
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Tensor field networks: Rotation-and translation-equivariant neural networks for 3d point clouds
Nathaniel Thomas, Tess Smidt, Steven Kearnes, Lusann Yang, Li Li, Kai Kohlhoff, and Patrick Riley · 2018
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Finding symmetry breaking order parameters with euclidean neural networks
Tess E Smidt, Mario Geiger, and Benjamin Kurt Miller · 2021
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Breaking the symmetry: Resolving symmetry ambiguities in equivariant neural networks
Sidhika Balachandar, Adrien Poulenard, Congyue Deng, and Leonidas Guibas · 2022
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Mace: Higher order equivariant message passing neural networks for fast and accurate force fields
Ilyes Batatia, David P Kovacs, Gregor Simm, Christoph Ortner, and Gábor Csányi · 2022
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E (3)-equivariant graph neural networks for data-efficient and accurate interatomic potentials
Simon Batzner, Albert Musaelian, Lixin Sun, Mario Geiger, Jonathan P Mailoa, Mordechai Kornbluth, Nicola Molinari, Tess E Smidt, and Boris Kozinsky · 2022
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GAP – Groups, Algorithms, and Programming, Version 4.12.2
GAP · 2022
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3d steerable cnns: Learning rotationally equivariant features in volumetric data
Maurice Weiler, Mario Geiger, Max Welling, Wouter Boomsma, and Taco S Cohen · 2018
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An introduction to spontaneous symmetry breaking
Aron Beekman, Louk Rademaker, and Jasper van Wezel · 2019
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A general theory of equivariant cnns on homogeneous spaces
Taco S Cohen, Mario Geiger, and Maurice Weiler · 2019
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Applying a machine learning interatomic potential to unravel the effects of local lattice distortion on the elastic properties of multi-principal element alloys
Mehdi Jafary-Zadeh, Khoong Hong Khoo, Robert Laskowski, Paulo S Branicio, and Alexander V Shapeev · 2019
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Graph normalizing flows
Jenny Liu, Aviral Kumar, Jimmy Ba, Jamie Kiros, and Kevin Swersky · 2019
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Generalizing convolutional neural networks for equivariance to lie groups on arbitrary continuous data
Marc Finzi, Samuel Stanton, Pavel Izmailov, and Andrew Gordon Wilson · 2020
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Pushing the limit of molecular dynamics with ab initio accuracy to 100 million atoms with machine learning
Weile Jia, Han Wang, Mohan Chen, Denghui Lu, Lin Lin, Roberto Car, E Weinan, and Linfeng Zhang · 2020
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Mario Geiger and Tess Smidt · 2022
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Equivariant diffusion for molecule generation in 3d
Emiel Hoogeboom, Vıctor Garcia Satorras, Clément Vignac, and Max Welling · 2022
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Equiformer: Equivariant graph attention transformer for 3d atomistic graphs
Yi-Lun Liao and Tess Smidt · 2022
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Multi-scale rotation-equivariant graph neural networks for unsteady eulerian fluid dynamics
Mario Lino, Stathi Fotiadis, Anil A Bharath, and Chris D Cantwell · 2022
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Relaxing equivariance constraints with non-stationary continuous filters
Tycho van der Ouderaa, David W Romero, and Mark van der Wilk · 2022
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Symphony: Symmetry-equivariant point-centered spherical harmonics for molecule generation
Ameya Daigavane, Song Kim, Mario Geiger, and Tess Smidt · 2023
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Approximately equivariant graph networks
Ningyuan Teresa Huang, Ron Levie, and Soledad Villar · 2023
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Symmetry breaking and equivariant neural networks
Sékou-Oumar Kaba and Siamak Ravanbakhsh · 2023
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Equivariance with learned canonicalization functions
Sékou-Oumar Kaba, Arnab Kumar Mondal, Yan Zhang, Yoshua Bengio, and Siamak Ravanbakhsh · 2023
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Relaxed octahedral group convolution for learning symmetry breaking in 3d physical systems
Rui Wang, Robin Walters, and Tess Smidt · 2023
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Improved machine learning algorithm for predicting ground state properties
Laura Lewis, Hsin-Yuan Huang, Viet T Tran, Sebastian Lehner, Richard Kueng, and John Preskill · 2024
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