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The Geometric Algebra Transformer (GATr) is a versatile architecture for geometric deep learning based on projective geometric algebra.
The quantum theory of the electron
Paul Adrien Maurice Dirac and Ralph Howard Fowler · 1928
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A new self-organizing neural network using geometric algebra
Eduardo Bayro-Corrochano, Sven Buchholz, and Gerald Sommer · 1996
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Geometric Algebra for Computer Science: An Object-oriented Approach to Geometry
Leo Dorst, Daniel Fontijne, and Stephen Mann · 2007
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Geometric Algebra for Computer Science
Leo Dorst, Stephen Mann, and Daniel Fontijne · 2009
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Group equivariant convolutional networks
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Attention is all you need
Ashish Vaswani, Noam Shazeer, Niki Parmar, Jakob Uszkoreit, Llion Jones, Aidan N Gomez, Łukasz Kaiser, and Illia Polosukhin · 2017
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Pointnet++: Deep hierarchical feature learning on point sets in a metric space
Charles Ruizhongtai Qi, Li Yi, Hao Su, and Leonidas J Guibas · 2017
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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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SE(3)-Transformers: 3D Roto-Translation equivariant attention networks
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Self-attention does not need O ( n 2 ) O(n^{2}) memory
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Highly accurate protein structure prediction with alphafold
John Jumper, Richard Evans, Alexander Pritzel, Tim Green, Michael Figurnov, Olaf Ronneberger, Kathryn Tunyasuvunakool, Russ Bates, Augustin Žídek, Anna Potapenko, et al · 2021
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Tri Dao, Dan Fu, Stefano Ermon, Atri Rudra, and Christopher Ré · 2022
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Equiformer: Equivariant graph attention transformer for 3d atomistic graphs
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Mesh neural networks for se (3)-equivariant hemodynamics estimation on the artery wall
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MACE: Higher order equivariant message passing neural networks for fast and accurate force fields
Ilyes Batatia, David Peter Kovacs, Gregor N C Simm, Christoph Ortner, and Gabor Csanyi · 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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Marc Finzi, Max Welling, and Andrew Gordon Wilson · 2021
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Gauge equivariant mesh CNNs: Anisotropic convolutions on geometric graphs
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E(n) equivariant graph neural networks
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Geometric and physical quantities improve E(3) equivariant message passing
Johannes Brandstetter, Rob Hesselink, Elise van der Pol, Erik J Bekkers, and Max Welling
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Die lineale Ausdehnungslehre
Hermann Grassmann
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Applications of Grassmann’s Extensive Algebra
William Kingdon Clifford
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Clifford neural layers for PDE modeling
Johannes Brandstetter, Rianne van den Berg, Max Welling, and Jayesh K Gupta
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So3krates: Equivariant attention for interactions on arbitrary length-scales in molecular systems
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Geometric algebra transformers
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A guided tour to the plane-based geometric algebra PGA
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