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Convolutional neural networks have been extremely successful in the image recognition domain because they ensure equivariance to translations.
Harmonic networks: Deep translation and rotation equivariance
Worrall, D. E., Garbin, S. J., Turmukhambetov, D., and Brostow, G. J · 1977
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Backpropagation applied to handwritten zip code recognition
LeCun, Y., Boser, B., Denker, J. S., Henderson, D., Howard, R. E., Hubbard, W., and Jackel, L. D · 1989
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Fourier analysis on finite groups and applications , volume 43 of London Mathematical Society Student Texts
Terras, A · 1999
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The Symmetric Group
Sagan, B. E · 2001
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Group invariant scattering
Mallat, S · 2012
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Convolutional networks on graphs for learning molecular fingerprints
Duvenaud, D., Maclaurin, D., Aguilera-Iparraguirre, J., Gomez-Bombarelli, R., Hirzel, T., Aspuru-Guzik, A., and Adams, R. P · 2015
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Geodesic convolutional neural networks on Riemannian manifolds
Masci, J., Boscaini, D., Bronstein, M. M., and Vandergheynst, P · 2015
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Group equivariant convolutional networks
Cohen, T. S. and Welling, M · 2016
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Defferrard, M., Bresson, X., and Vandergheynst, P · 2016
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Niepert, M., Ahmed, M., and Kutzkov, K · 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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Geometric deep learning on graphs and manifolds using mixture model cnns
Monti, F., Boscaini, D., Masci, J., Rodolà, E., Svoboda, J., and Bronstein, M. M · 2017
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Equivariance through parameter-sharing
Ravanbakhsh, S., Schneider, J., and Poczos, B · 2017
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Spherical CNNs
Cohen, T. S., Geiger, M., Köhler, J., and Welling, M · 2018
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N-body networks: a covariant hierarchical neural network architecture for learning atomic potentials
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Tensor field networks: Rotation- and translation-equivariant neural networks for 3D point clouds
Thomas, N., Smidt, T., Kearnes, S. M., Yang, L., Li, L., Kohlhoff, K., and Riley, P · 2018
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Marcos, D., Volpi, M., Komodakis, N., and Tuia, D · 2017
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3D steerable CNNs: Learning rotationally equivariant features in volumetric data
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