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Equivariance to permutations and rigid motions is an important inductive bias for various 3D learning problems.
C ∞ C^{\infty} -differentiable spaces , volume 1824
González, J. A. N. and de Salas, J. B. S · 2003
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Shape matching and anisotropy
Kazhdan, M., Funkhouser, T., and Rusinkiewicz, S · 2004
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U-net: Convolutional networks for biomedical image segmentation
Ronneberger, O., Fischer, P., and Brox, T · 2015
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3d shapenets: A deep representation for volumetric shapes
Wu, Z., Song, S., Khosla, A., Yu, F., Zhang, L., Tang, X., and Xiao, J · 2015
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Graph isomorphism in quasipolynomial time
Babai, L · 2016
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Exact recovery with symmetries for procrustes matching
Dym, N. and Lipman, Y · 2017
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Neural message passing for quantum chemistry
Gilmer, J., Schoenholz, S. S., Riley, P. F., Vinyals, O., and Dahl, G. E · 2017
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Pointnet: Deep learning on point sets for 3d classification and segmentation
Qi, C. R., Su, H., Mo, K., and Guibas, L. J · 2017
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Deep sets
Zaheer, M., Kottur, S., Ravanbakhsh, S., Poczos, B., Salakhutdinov, R. R., and Smola, A. J · 2017
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Covariant compositional networks for learning graphs
Kondor, R., Son, H. T., Pan, H., Anderson, B., and Trivedi, S · 2018
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Invariant and equivariant graph networks
Maron, H., Ben-Hamu, H., Shamir, N., and Lipman, Y · 2018
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Tensor field networks: Rotation-and translation-equivariant neural networks for 3d point clouds
Thomas, N., Smidt, T., Kearnes, S., Yang, L., Li, L., Kohlhoff, K., and Riley, P · 2018
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How powerful are graph neural networks?
Xu, K., Hu, W., Leskovec, J., and Jegelka, S · 2018
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Clusternet: Deep hierarchical cluster network with rigorously rotation-invariant representation for point cloud analysis
Chen, C., Li, G., Xu, R., Chen, T., Wang, M., and Lin, L · 2019
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Weisfeiler and leman go neural: Higher-order graph neural networks
Morris, C., Ritzert, M., Fey, M., Hamilton, W. L., Lenssen, J. E., Rattan, G., and Grohe, M · 2019
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Effective rotation-invariant point cnn with spherical harmonics kernels, 2019
Poulenard, A., Rakotosaona, M.-J., Ponty, Y., and Ovsjanikov, M · 2019
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Spherical fractal convolutional neural networks for point cloud recognition
Rao, Y., Lu, J., and Zhou, J · 2019
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Universal equivariant multilayer perceptrons
Ravanbakhsh, S · 2020
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Global context aware convolutions for 3d point cloud understanding, 2020
Zhang, Z., Hua, B.-S., Chen, W., Tian, Y., and Yeung, S.-K · 2020
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Zz-net: A universal rotation equivariant architecture for 2d point clouds
Bökman, G., Kahl, F., and Flinth, A · 2021
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Vector neurons: A general framework for so (3)-equivariant networks
Deng, C., Litany, O., Duan, Y., Poulenard, A., Tagliasacchi, A., and Guibas, L. J · 2021
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Gemnet: Universal directional graph neural networks for molecules
Klicpera, J., Becker, F., and Günnemann, S · 2021
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A rotation-invariant framework for deep point cloud analysis
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Dynamic graph cnn for learning on point clouds
Wang, Y., Sun, Y., Liu, Z., Sarma, S. E., Bronstein, M. M., and Solomon, J. M · 2019
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Rotation invariant convolutions for 3d point clouds deep learning, 2019
Zhang, Z., Hua, B.-S., Rosen, D. W., and Yeung, S.-K · 2019
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Lorentz group equivariant neural network for particle physics
Bogatskiy, A., Anderson, B., Offermann, J., Roussi, M., Miller, D., and Kondor, R · 2020
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On the universality of rotation equivariant point cloud networks
Dym, N. and Maron, H · 2020
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Se (3)-transformers: 3d roto-translation equivariant attention networks
Fuchs, F., Worrall, D., Fischer, V., and Welling, M · 2020
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On learning sets of symmetric elements
Maron, H., Litany, O., Chechik, G., and Fetaya, E · 2020
Cited alongside, same era.
Provably powerful graph networks
Maron, H., Ben-Hamu, H., Serviansky, H., and Lipman, Y
Cited in the paper.
Li, X., Li, R., Chen, G., Fu, C.-W., Cohen-Or, D., and Heng, P.-A · 2021
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Weisfeiler and leman go machine learning: The story so far
Morris, C., Lipman, Y., Maron, H., Rieck, B., Kriege, N. M., Grohe, M., Fey, M., and Borgwardt, K · 2021
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Frame averaging for invariant and equivariant network design
Puny, O., Atzmon, M., Ben-Hamu, H., Smith, E. J., Misra, I., Grover, A., and Lipman, Y · 2021
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E (n) equivariant graph neural networks
Satorras, V. G., Hoogeboom, E., and Welling, M · 2021
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Scalars are universal: Equivariant machine learning, structured like classical physics
Villar, S., Hogg, D. W., Storey-Fisher, K., Yao, W., and Blum-Smith, B · 2021
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Universal approximations of invariant maps by neural networks
Yarotsky, D · 2022
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