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We describe generalizations of the universal approximation theorem for neural networks to maps invariant or equivariant with respect to linear representations of groups.
The classical groups: their invariants and representations
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Multilayer feedforward networks with a nonpolynomial activation function can approximate any function
Moshe Leshno, Vladimir Ya Lin, Allan Pinkus, and Shimon Schocken · 1993
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Zeros of equivariant vector fields: Algorithms for an invariant approach
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On invariance and selectivity in representation learning
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Convolutional rectifier networks as generalized tensor decompositions
Nadav Cohen and Amnon Shashua · 2016
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Group equivariant convolutional networks
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Exploiting cyclic symmetry in convolutional neural networks
Sander Dieleman, Jeffrey De Fauw, and Koray Kavukcuoglu · 2016
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Ian Goodfellow, Yoshua Bengio, and Aaron Courville · 2016
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Stéphane Mallat · 2012
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Linear representations of finite groups , volume 42
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Linear representations of groups
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Robert Gens and Pedro M Domingos · 2014
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Warped convolutions: Efficient invariance to spatial transformations
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Understanding deep convolutional networks
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Rotation equivariant vector field networks
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Analysis and design of convolutional networks via hierarchical tensor decompositions
Nadav Cohen, Or Sharir, Yoav Levine, Ronen Tamari, David Yakira, and Amnon Shashua · 2017
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Carlos Esteves, Christine Allen-Blanchette, Xiaowei Zhou, and Kostas Daniilidis · 2017
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Why and when can deep-but not shallow-networks avoid the curse of dimensionality: A review
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