Co-domain Symmetry for Complex-Valued Deep Learning

• URL: http://arxiv.org/abs/2112.01525v2
• Date: Tue, 22 Apr 2025 18:09:36 GMT
• Title: Co-domain Symmetry for Complex-Valued Deep Learning
• Authors: Utkarsh Singhal, Yifei Xing, Stella X. Yu,
• Abstract summary: We study complex-valued scaling as a type of symmetry natural and unique to complex-valued measurements and representations.<n>We analyze complex-valued scaling as a co-domain transformation and design novel equivariant and invariant neural network layer functions for this special transformation.<n>We also propose novel complex-valued representations of RGB images, where complex-valued scaling indicates hue shift or correlated changes across color channels.
• Score: 34.16793679479781
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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 takes a restrictive manifold view of complex numbers, adopting a distance metric to achieve complex-scaling invariance while losing rich complex-valued information. We analyze complex-valued scaling as a co-domain transformation and design novel equivariant and invariant neural network layer functions for this special transformation. 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, robustness to co-domain transformations, and lower model bias and variance than DCN and SurReal with far fewer parameters.

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