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2020

Universal Approximation Theorem for Equivariant Maps by Group CNNs

Kumagai, Wataru, Sannai, Akiyoshi

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Group symmetry is inherent in a wide variety of data distributions.

Data processing that preserves symmetry is described as an equivariant map and often effective in achieving high performance.
Convolutional neural networks (CNNs) have been known as models with equivariance and shown to approximate equivariant maps for some specific groups.
However, universal approximation theorems for CNNs have been separately derived with individual techniques according to each group and setting.

Universal Approximation Theorem for Equivariant Maps by Group CNNs · Around

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Similar

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[23] S. Ravanbakhsh (2020) “Universal Equivariant Multilayer Perceptrons,” arXiv preprint arXiv:2002.02912
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Then

[21] M. Nickel and D. Kiela (2017) “Poincaré embeddings for learning hierarchical representations,” in Advances in neural information processing systems
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[18] H. Maron, E. Fetaya, N. Segol, and Y. Lipman (2019b) “On the Universality of Invariant Networks,” Proceedings of the 36th International Conference on Machine Learning

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[2] T. S. Cohen, M. Geiger, and M. Weiler (2019) “A general theory of equivariant cnns on homogeneous spaces,” in Advances in Neural Information Processing Systems

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[11] N. Keriven and G. Peyré (2019) “Universal invariant and equivariant graph neural networks,” in Advances in Neural Information Processing Systems

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[22] P. Petersen and F. Voigtlaender (2020) “Equivalence of approximation by convolutional neural networks and fully-connected networks,” Proceedings of the American Mathematical Society

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