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Previous work on symmetric group equivariant neural networks generally only considered the case where the group acts by permuting the elements of a single vector.
Funzione caratteristica di un fenomeno aleatorio, mem
De Finetti, B · 1930
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Linear Representations of Finite Groups , volume 42 of Graduate Texts in Mathamatics
Serre, J.-P · 1977
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Finite exchangeable sequences
Diaconis, P. and Freedman, D · 1980
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Fast generalized Fourier transforms
Clausen, M · 1989
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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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Representation Theory
Fulton, W. and Harris, J · 1991
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Separation of Variables and the Computation of Fourier Transforms on Finite Groups, I
Maslen, D. K. and Rockmore, D. N · 1997
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The Symmetric Group
Sagan, B. E · 2001
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Probabilistic Symmetries and Invariance Principles
Kallenberg, O · 2006
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Collective classification in network data
Sen, P., Namata, G. M., Bilgic, M., Getoor, L., Gallagher, B., , and Eliassi-Rad, T · 2008
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Glorot, X. and Bengio, Y · 2010
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Kingma, D. P. and Welling, M · 2013
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Bruna, J., Zaremba, W., Szlam, A., and LeCun, Y · 2014
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Bayesian models of graphs, arrays and other exchangeable random structures
Orbanz, P. and Roy, D. M · 2014
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Perozzi, B., Al-Rfou, R., and Skiena, S · 2014
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Cai, D., Campbell, T., and Broderick, T · 2016
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Cohen, T. and Welling, M · 2016
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Zaheer, M., Kottur, S., Ravanbakhsh, S., Poczos, B., Salakhutdinov, R. R., and Smola, A. J · 2017
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Spherical CNNs
Cohen, T. S., Geiger, M., Köhler, J., and Welling, M · 2018
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Predicting molecular properties with covariant compositional networks
Hy, T. S., Trivedi, S., Pan, H., Anderson, B. M., and Kondor, R · 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
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3D steerable CNNs: Learning rotationally equivariant features in volumetric data
Weiler, M., Geiger, M., Welling, M., Boomsma, W., and Cohen, T · 2018
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Universal approximations of invariant maps by neural networks
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Permutation-equivariant neural networks applied to dynamics prediction
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Kipf, T. N. and Welling, M · 2016
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You, J., Liu, B., Ying, Z., Pande, V., and Leskovec, J · 2018
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Universal approximations of permutation invariant/equivariant functions by deep neural networks
Sannai, A., Takai, Y., and Cordonnier, M · 2019
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Permutation equivariant models for compositional generalization in language
Gordon, J., Lopez-Paz, D., Baroni, M., and Bouchacourt, D · 2020
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