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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.
Advanced Linear Algebra
S. Roman · 2008
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Y. Kosmann-Schwarzbach and S. Singer · 2009
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E. Vinberg · 2010
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Linear Representations of Finite Groups
J. Serre · 2012
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Group equivariant convolutional networks
T. Cohen and M. Welling · 2016
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Neural message passing for quantum chemistry
J. Gilmer, S. S. Schoenholz, P. F. Riley, O. Vinyals, and G. E. Dahl · 2017
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Rotation equivariant vector field networks
D. Marcos, M. Volpi, N. Komodakis, and D. Tuia · 2017
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Attention is all you need
A. Vaswani, N. Shazeer, N. Parmar, J. Uszkoreit, L. Jones, A. N. Gomez, Ł. Kaiser, and I. Polosukhin · 2017
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T. S. Cohen, M. Geiger, J. Köhler, and M. Welling · 2018
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Tensor field networks: Rotation-and translation-equivariant neural networks for 3d point clouds
N. Thomas, T. Smidt, S. Kearnes, L. Yang, L. Li, K. Kohlhoff, and P. Riley · 2018
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3D steerable CNNs: Learning rotationally equivariant features in volumetric data
M. Weiler, M. Geiger, M. Welling, W. Boomsma, and T. S. Cohen · 2018
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Cormorant: Covariant molecular neural networks
B. Anderson, T. S. Hy, and R. Kondor · 2019
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Array programming with NumPy
C. R. Harris, K. J. Millman, S. J. Van Der Walt, R. Gommers, P. Virtanen, D. Cournapeau, E. Wieser, J. Taylor, S. Berg, N. J. Smith, et al · 2020
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Jax MD: a framework for differentiable physics
S. Schoenholz and E. D. Cubuk · 2020
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Equivariant message passing for the prediction of tensorial properties and molecular spectra
K. Schütt, O. Unke, and M. Gastegger · 2021
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E(3)-equivariant graph neural networks for data-efficient and accurate interatomic potentials
S. Batzner, A. Musaelian, L. Sun, M. Geiger, J. P. Mailoa, M. Kornbluth, N. Molinari, T. E. Smidt, and B. Kozinsky · 2022
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SE(3)-equivariant attention networks for shape reconstruction in function space
E. Chatzipantazis, S. Pertigkiozoglou, E. Dobriban, and K. Daniilidis · 2022
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A general theory of equivariant CNNs on homogeneous spaces
T. S. Cohen, M. Geiger, and M. Weiler · 2019
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SE(3)-transformers: 3D roto-translation equivariant attention networks
F. Fuchs, D. Worrall, V. Fischer, and M. Welling · 2020
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SE(3)-equivariant prediction of molecular wavefunctions and electronic densities
O. Unke, M. Bogojeski, M. Gastegger, M. Geiger, T. Smidt, and K.-R. Müller
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Spookynet: Learning force fields with electronic degrees of freedom and nonlocal effects
O. T. Unke, S. Chmiela, M. Gastegger, K. T. Schütt, H. E. Sauceda, and K.-R. Müller
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Flax: A neural network library and ecosystem for JAX, 2023
J. Heek, A. Levskaya, A. Oliver, M. Ritter, B. Rondepierre, A. Steiner, and M. van Zee · 2023
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