Phase Collapse in Neural Networks

TL;DR

This paper introduces the concept of phase collapse as a key mechanism in neural networks, showing it effectively reduces spatial variability and enhances class separation, unlike traditional sparsity-inducing nonlinearities.

Contribution

It demonstrates that phase collapse of wavelet coefficients is sufficient for high classification accuracy, offering a new perspective on neural network nonlinearities.

Findings

Phase collapse matches ResNet accuracy at similar depths.

Thresholding nonlinearities degrade performance compared to phase collapse.

Iterative phase collapse improves class separation progressively.

Abstract

Deep convolutional classifiers linearly separate image classes and improve accuracy as depth increases. They progressively reduce the spatial dimension whereas the number of channels grows with depth. Spatial variability is therefore transformed into variability along channels. A fundamental challenge is to understand the role of non-linearities together with convolutional filters in this transformation. ReLUs with biases are often interpreted as thresholding operators that improve discrimination through sparsity. This paper demonstrates that it is a different mechanism called phase collapse which eliminates spatial variability while linearly separating classes. We show that collapsing the phases of complex wavelet coefficients is sufficient to reach the classification accuracy of ResNets of similar depths. However, replacing the phase collapses with thresholding operators that enforce sparsity considerably degrades the performance. We explain these numerical results by showing that the iteration of phase collapses progressively improves separation of classes, as opposed to thresholding non-linearities.