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Equivariant neural networks, whose hidden features transform according to representations of a group G acting on the data, exhibit training efficiency and an improved generalisation performance.
General e ( 2 ) e(2) -equivariant steerable cnns
Weiler, M. and Cesa, G · 1911
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Convolutional networks for images, speech, and time series
LeCun, Y., Bengio, Y., et al · 1995
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Graph Matching and Similarity , pp. 281–304
Bunke, H. and Jiang, X · 2000
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A novel method for alignment of 3d models
Chaouch, M. and Verroust-Blondet, A · 2008
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Alignment of 3d models
Chaouch, M. and Verroust-Blondet, A · 2009
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Transforming auto-encoders
Hinton, G. E., Krizhevsky, A., and Wang, S. D · 2011
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Active co-analysis of a set of shapes
Wang, Y., Asafi, S., van Kaick, O. M., Zhang, H., Cohen-Or, D., and Chen, B · 2012
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Spectral networks and locally connected networks on graphs
Bruna, J., Zaremba, W., Szlam, A., and LeCun, Y · 2013
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Quantum chemistry structures and properties of 134 kilo molecules
Ramakrishnan, R., Dral, P. O., Rupp, M., and von Lilienfeld, O. A · 2014
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Shapenet: An information-rich 3d model repository
Chang, A. X., Funkhouser, T., Guibas, L., Hanrahan, P., Huang, Q., Li, Z., Savarese, S., Savva, M., Song, S., Su, H., et al · 2015
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Variational inference with normalizing flows
Rezende, D. and Mohamed, S · 2015
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Autocorrelation descriptor for efficient co-alignment of 3d shape collections
Averkiou, M., Kim, V. G., and Mitra, N. J · 2016
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Convolutional neural networks on graphs with fast localized spectral filtering
Defferrard, M., Bresson, X., and Vandergheynst, P · 2016
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Exploiting cyclic symmetry in convolutional neural networks
Dieleman, S., De Fauw, J., and Kavukcuoglu, K · 2016
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Semi-supervised classification with graph convolutional networks
Kipf, T. N. and Welling, M · 2016
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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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Dynamic routing between capsules
Sabour, S., Frosst, N., and Hinton, G. E · 2017
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Ani-1: an extensible neural network potential with dft accuracy at force field computational cost
Smith, J. S., Isayev, O., and Roitberg, A. E · 2017
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Attention is all you need
Vaswani, A., Shazeer, N., Parmar, N., Uszkoreit, J., Jones, L., Gomez, A. N., Kaiser, Ł., and Polosukhin, I · 2017
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Harmonic networks: Deep translation and rotation equivariance
Worrall, D. E., Garbin, S. J., Turmukhambetov, D., and Brostow, G. J · 2017
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Zaheer, M., Kottur, S., Ravanbakhsh, S., Poczos, B., Salakhutdinov, R., and Smola, A · 2017
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Roto-translation covariant convolutional networks for medical image analysis
Bekkers, E. J., Lafarge, M. W., Veta, M., Eppenhof, K. A., Pluim, J. P., and Duits, R · 2018
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A general theory of equivariant cnns on homogeneous spaces
Cohen, T., Geiger, M., and Weiler, M · 2018
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Towards a definition of disentangled representations
Higgins, I., Amos, D., Pfau, D., Racanière, S., Matthey, L., Rezende, D. J., and Lerchner, A · 2018
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Hoogeboom, E., Peters, J. W. T., Cohen, T., and Welling, M · 2018
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On the generalization of equivariance and convolution in neural networks to the action of compact groups
Kondor, R. and Trivedi, S · 2018
Cited alongside, same era.
Manifold learning in quotient spaces
Mehr, Ã., Lieutier, A., Bermudez, F. S., Guitteny, V., Thome, N., and Cord, M · 2018
Cited alongside, same era.
Equivariant flows: exact likelihood generative learning for symmetric densities
Köhler, J., Klein, L., and Noé, F · 2020
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Rate-invariant autoencoding of time-series
Koneripalli, K., Lohit, S., Anirudh, R., and Turaga, P. K · 2020
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On the benefits of invariance in neural networks
Lyle, C., van der Wilk, M., Kwiatkowska, M. Z., Gal, Y., and Bloem-Reddy, B · 2020
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Relevance of rotationally equivariant convolutions for predicting molecular properties
Miller, B. K., Geiger, M., Smidt, T. E., and Noé, F · 2020
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Disentangling by subspace diffusion
Pfau, D., Higgins, I., Botev, A., and Racanière, S · 2020
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Schnet–a deep learning architecture for molecules and materials
Schütt, K. T., Sauceda, H. E., Kindermans, P.-J., Tkatchenko, A., and Müller, K.-R · 2018
Cited alongside, same era.
Deforming autoencoders: Unsupervised disentangling of shape and appearance
Shu, Z., Sahasrabudhe, M., Güler, R. A., Samaras, D., Paragios, N., and Kokkinos, I · 2018
Cited alongside, same era.
Tensor field networks: Rotation- and translation-equivariant neural networks for 3d point clouds, 2018
Thomas, N., Smidt, T., Kearnes, S., Yang, L., Li, L., Kohlhoff, K., and Riley, P · 2018
Cited alongside, same era.
Cormorant: Covariant molecular neural networks
Anderson, B., Hy, T.-S., and Kondor, R · 2019
Cited alongside, same era.
Invariant-equivariant representation learning for multi-class data, 2019
Feige, I · 2019
Cited alongside, same era.
Stochastic optimization of sorting networks via continuous relaxations
Grover, A., Wang, E., Zweig, A., and Ermon, S · 2019
Cited alongside, same era.
Affine equivariant autoencoder
Guo, X., Zhu, E., Liu, X., and Yin, J · 2019
Cited alongside, same era.
Softsort: A continuous relaxation for the argsort operator
Prillo, S. and Eisenschlos, J · 2020
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Group equivariant stand-alone self-attention for vision
Romero, D. W. and Cordonnier, J.-B · 2020
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Romero, D. W. and Hoogendoorn, M · 2020
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Attentive group equivariant convolutional networks
Romero, D. W., Bekkers, E. J., Tomczak, J. M., and Hoogendoorn, M · 2020
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Euclidean symmetry and equivariance in machine learning
Smidt, T · 2020
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https://sites.google.com/a/lisa.iro.umontreal.ca/public_static_twiki/variations-on-the-mnist-digits
Rotated MNIST · 2021
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GEOM, 2021
Axelrod, S. and Gomez-Bombarelli, R · 2021
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Sampling using su (n) gauge equivariant flows
Boyda, D., Kanwar, G., Racanière, S., Rezende, D. J., Albergo, M. S., Cranmer, K., Hackett, D. C., and Shanahan, P. E · 2021
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Geometric deep learning: Grids, groups, graphs, geodesics, and gauges
Bronstein, M. M., Bruna, J., Cohen, T., and Veličković, P · 2021
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Lietransformer: Equivariant self-attention for lie groups
Hutchinson, M. J., Le Lan, C., Zaidi, S., Dupont, E., Teh, Y. W., and Kim, H · 2021
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Frame averaging for invariant and equivariant network design, 2021
Puny, O., Atzmon, M., Ben-Hamu, H., Misra, I., Grover, A., Smith, E. J., and Lipman, Y · 2021
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E(n) equivariant graph neural networks, 2021
Satorras, V. G., Hoogeboom, E., and Welling, M · 2021
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Equivariant message passing for the prediction of tensorial properties and molecular spectra, 2021
Schütt, K. T., Unke, O. T., and Gastegger, M · 2021
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Permutation-invariant variational autoencoder for graph-level representation learning
Winter, R., Noé, F., and Clevert, D.-A · 2021
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Group equivariant subsampling, 2021
Xu, J., Kim, H., Rainforth, T., and Teh, Y. W · 2021
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Homomorphism autoencoder - learning group structured representations from observed transitions
Keurti, H., Pan, H.-R., Besserve, M., Grewe, B. F., and Scholkopf, B · 2022
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