2021/12/02 by Utkarsh Singhal, Singhal, Utkarsh, Yifei Xing +3 · 2 citations
Biochemistry, Genetics and Molecular Biology · Computer Science · Mathematics · #Algorithm #Artificial Intelligence (cs.AI) #Artificial intelligence #Cell Image Analysis Techniques #Combinatorics #Complex network #Computer Vision and Pattern Recognition (cs.CV) #Computer science #Deep learning #Digital Imaging for Blood Diseases #Domain (mathematical analysis) #Domain Adaptation and Few-Shot Learning #Equivariant map #FOS: Computer and information sciences #Generalization #Geometry #Invariant (physics) #Machine Learning (cs.LG) #Mathematical analysis #Mathematics #Pure mathematics #RGB color model #Robustness (evolution) #Scaling #Transformation (genetics)
paper · pdf · doi:10.48550/arxiv.2112.01525
openalex publication_date 2021/12/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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.