Co-Domain Symmetry for Complex-Valued Deep Learning

Utkarsh Singhal, Yifei Xing, Stella X. Yu; Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), 2022, pp. 681-690


We study complex-valued scaling as a type of symmetry natural and unique to complex-valued measurements and representations. Deep Complex Networks (DCN) extends real-valued algebra to the complex domain without addressing complex-valued scaling. SurReal extends manifold learning to the complex plane, achieving scaling invariance using distances that discard phase information. Treating complex-valued scaling as a co-domain transformation, we design novel equivariant/invariant neural network layer functions and construct architectures that exploit co-domain symmetry. We also propose novel complex-valued representations of RGB images, where complex-valued scaling indicates hue shift or correlated changes across color channels. Benchmarked on MSTAR, CIFAR10, CIFAR100, and SVHN, our co-domain symmetric (CDS) classifiers deliver higher accuracy, better generalization, more robustness to co-domain transformations, and lower model bias and variance than DCN and SurReal with far fewer parameters.

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@InProceedings{Singhal_2022_CVPR, author = {Singhal, Utkarsh and Xing, Yifei and Yu, Stella X.}, title = {Co-Domain Symmetry for Complex-Valued Deep Learning}, booktitle = {Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR)}, month = {June}, year = {2022}, pages = {681-690} }