Scaling-up Diverse Orthogonal Convolutional Networks by a Paraunitary Framework

Jiahao Su, Wonmin Byeon, Furong Huang
Proceedings of the 39th International Conference on Machine Learning, PMLR 162:20546-20579, 2022.

Abstract

Enforcing orthogonality in convolutional neural networks is a remedy for gradient vanishing/exploding problems and sensitivity to perturbation. Many previous approaches for orthogonal convolutions enforce orthogonality on its flattened kernel, which, however, do not lead to the orthogonality of the operation. Some recent approaches consider orthogonality for standard convolutional layers and propose specific classes of their realizations. In this work, we propose a theoretical framework that establishes the equivalence between diverse orthogonal convolutional layers in the spatial domain and the paraunitary systems in the spectral domain. Since 1D paraunitary systems admit a complete factorization, we can parameterize any separable orthogonal convolution as a composition of spatial filters. As a result, our framework endows high expressive power to various convolutional layers while maintaining their exact orthogonality. Furthermore, our layers are memory and computationally efficient for deep networks compared to previous designs. Our versatile framework, for the first time, enables the study of architectural designs for deep orthogonal networks, such as choices of skip connection, initialization, stride, and dilation. Consequently, we scale up orthogonal networks to deep architectures, including ResNet and ShuffleNet, substantially outperforming their shallower counterparts. Finally, we show how to construct residual flows, a flow-based generative model that requires strict Lipschitzness, using our orthogonal networks. Our code will be publicly available at https://github.com/umd-huang-lab/ortho-conv

Cite this Paper

BibTeX
@InProceedings{pmlr-v162-su22a, title = {Scaling-up Diverse Orthogonal Convolutional Networks by a Paraunitary Framework}, author = {Su, Jiahao and Byeon, Wonmin and Huang, Furong}, booktitle = {Proceedings of the 39th International Conference on Machine Learning}, pages = {20546--20579}, year = {2022}, editor = {Chaudhuri, Kamalika and Jegelka, Stefanie and Song, Le and Szepesvari, Csaba and Niu, Gang and Sabato, Sivan}, volume = {162}, series = {Proceedings of Machine Learning Research}, month = {17--23 Jul}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v162/su22a/su22a.pdf}, url = {https://proceedings.mlr.press/v162/su22a.html}, abstract = {Enforcing orthogonality in convolutional neural networks is a remedy for gradient vanishing/exploding problems and sensitivity to perturbation. Many previous approaches for orthogonal convolutions enforce orthogonality on its flattened kernel, which, however, do not lead to the orthogonality of the operation. Some recent approaches consider orthogonality for standard convolutional layers and propose specific classes of their realizations. In this work, we propose a theoretical framework that establishes the equivalence between diverse orthogonal convolutional layers in the spatial domain and the paraunitary systems in the spectral domain. Since 1D paraunitary systems admit a complete factorization, we can parameterize any separable orthogonal convolution as a composition of spatial filters. As a result, our framework endows high expressive power to various convolutional layers while maintaining their exact orthogonality. Furthermore, our layers are memory and computationally efficient for deep networks compared to previous designs. Our versatile framework, for the first time, enables the study of architectural designs for deep orthogonal networks, such as choices of skip connection, initialization, stride, and dilation. Consequently, we scale up orthogonal networks to deep architectures, including ResNet and ShuffleNet, substantially outperforming their shallower counterparts. Finally, we show how to construct residual flows, a flow-based generative model that requires strict Lipschitzness, using our orthogonal networks. Our code will be publicly available at https://github.com/umd-huang-lab/ortho-conv} }
Endnote
%0 Conference Paper %T Scaling-up Diverse Orthogonal Convolutional Networks by a Paraunitary Framework %A Jiahao Su %A Wonmin Byeon %A Furong Huang %B Proceedings of the 39th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2022 %E Kamalika Chaudhuri %E Stefanie Jegelka %E Le Song %E Csaba Szepesvari %E Gang Niu %E Sivan Sabato %F pmlr-v162-su22a %I PMLR %P 20546--20579 %U https://proceedings.mlr.press/v162/su22a.html %V 162 %X Enforcing orthogonality in convolutional neural networks is a remedy for gradient vanishing/exploding problems and sensitivity to perturbation. Many previous approaches for orthogonal convolutions enforce orthogonality on its flattened kernel, which, however, do not lead to the orthogonality of the operation. Some recent approaches consider orthogonality for standard convolutional layers and propose specific classes of their realizations. In this work, we propose a theoretical framework that establishes the equivalence between diverse orthogonal convolutional layers in the spatial domain and the paraunitary systems in the spectral domain. Since 1D paraunitary systems admit a complete factorization, we can parameterize any separable orthogonal convolution as a composition of spatial filters. As a result, our framework endows high expressive power to various convolutional layers while maintaining their exact orthogonality. Furthermore, our layers are memory and computationally efficient for deep networks compared to previous designs. Our versatile framework, for the first time, enables the study of architectural designs for deep orthogonal networks, such as choices of skip connection, initialization, stride, and dilation. Consequently, we scale up orthogonal networks to deep architectures, including ResNet and ShuffleNet, substantially outperforming their shallower counterparts. Finally, we show how to construct residual flows, a flow-based generative model that requires strict Lipschitzness, using our orthogonal networks. Our code will be publicly available at https://github.com/umd-huang-lab/ortho-conv
APA
Su, J., Byeon, W. & Huang, F.. (2022). Scaling-up Diverse Orthogonal Convolutional Networks by a Paraunitary Framework. Proceedings of the 39th International Conference on Machine Learning, in Proceedings of Machine Learning Research 162:20546-20579 Available from https://proceedings.mlr.press/v162/su22a.html.

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