Learning to Convolve: A Generalized Weight-Tying Approach

Nichita Diaconu, Daniel Worrall
Proceedings of the 36th International Conference on Machine Learning, PMLR 97:1586-1595, 2019.

Abstract

Recent work (Cohen & Welling, 2016) has shown that generalizations of convolutions, based on group theory, provide powerful inductive biases for learning. In these generalizations, filters are not only translated but can also be rotated, flipped, etc. However, coming up with exact models of how to rotate a 3x3 filter on a square pixel-grid is difficult. In this paper, we learn how to transform filters for use in the group convolution, focussing on roto-translation. For this, we learn a filter basis and all rotated versions of that filter basis. Filters are then encoded by a set of rotation invariant coefficients. To rotate a filter, we switch the basis. We demonstrate we can produce feature maps with low sensitivity to input rotations, while achieving high performance on MNIST and CIFAR-10.

Cite this Paper

BibTeX
@InProceedings{pmlr-v97-diaconu19a, title = {Learning to Convolve: A Generalized Weight-Tying Approach}, author = {Diaconu, Nichita and Worrall, Daniel}, booktitle = {Proceedings of the 36th International Conference on Machine Learning}, pages = {1586--1595}, year = {2019}, editor = {Chaudhuri, Kamalika and Salakhutdinov, Ruslan}, volume = {97}, series = {Proceedings of Machine Learning Research}, month = {09--15 Jun}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v97/diaconu19a/diaconu19a.pdf}, url = {https://proceedings.mlr.press/v97/diaconu19a.html}, abstract = {Recent work (Cohen & Welling, 2016) has shown that generalizations of convolutions, based on group theory, provide powerful inductive biases for learning. In these generalizations, filters are not only translated but can also be rotated, flipped, etc. However, coming up with exact models of how to rotate a 3x3 filter on a square pixel-grid is difficult. In this paper, we learn how to transform filters for use in the group convolution, focussing on roto-translation. For this, we learn a filter basis and all rotated versions of that filter basis. Filters are then encoded by a set of rotation invariant coefficients. To rotate a filter, we switch the basis. We demonstrate we can produce feature maps with low sensitivity to input rotations, while achieving high performance on MNIST and CIFAR-10.} }
Endnote
%0 Conference Paper %T Learning to Convolve: A Generalized Weight-Tying Approach %A Nichita Diaconu %A Daniel Worrall %B Proceedings of the 36th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2019 %E Kamalika Chaudhuri %E Ruslan Salakhutdinov %F pmlr-v97-diaconu19a %I PMLR %P 1586--1595 %U https://proceedings.mlr.press/v97/diaconu19a.html %V 97 %X Recent work (Cohen & Welling, 2016) has shown that generalizations of convolutions, based on group theory, provide powerful inductive biases for learning. In these generalizations, filters are not only translated but can also be rotated, flipped, etc. However, coming up with exact models of how to rotate a 3x3 filter on a square pixel-grid is difficult. In this paper, we learn how to transform filters for use in the group convolution, focussing on roto-translation. For this, we learn a filter basis and all rotated versions of that filter basis. Filters are then encoded by a set of rotation invariant coefficients. To rotate a filter, we switch the basis. We demonstrate we can produce feature maps with low sensitivity to input rotations, while achieving high performance on MNIST and CIFAR-10.
APA
Diaconu, N. & Worrall, D.. (2019). Learning to Convolve: A Generalized Weight-Tying Approach. Proceedings of the 36th International Conference on Machine Learning, in Proceedings of Machine Learning Research 97:1586-1595 Available from https://proceedings.mlr.press/v97/diaconu19a.html.

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