DeepAI AI Chat
Log In Sign Up

Co-domain Symmetry for Complex-Valued Deep Learning

by   Utkarsh Singhal, et al.
berkeley college

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.


page 1

page 2

page 12


SurReal: Fréchet Mean and Distance Transform for Complex-Valued Deep Learning

We develop a novel deep learning architecture for naturally complex-valu...

Fully complex-valued deep learning model for visual perception

Deep learning models operating in the complex domain are used due to the...

Theory and Implementation of Complex-Valued Neural Networks

This work explains in detail the theory behind Complex-Valued Neural Net...

Adversarial Audio Synthesis with Complex-valued Polynomial Networks

Time-frequency (TF) representations in audio synthesis have been increas...

Massively Parallel Universal Linear Transformations using a Wavelength-Multiplexed Diffractive Optical Network

We report deep learning-based design of a massively parallel broadband d...

Can A Neural Network Hear the Shape of A Drum?

We have developed a deep neural network that reconstructs the shape of a...