An exploration of parameter redundancy in deep networks with circulant projections

TL;DR

This paper investigates replacing traditional fully-connected layer projections with circulant projections in deep neural networks, significantly reducing memory and computation costs while maintaining comparable accuracy.

Contribution

It introduces a circulant projection method that decreases complexity and memory usage in neural networks, with efficient gradient computation and minimal accuracy loss.

Findings

Reduces time complexity from O(d^2) to O(dlogd)

Reduces space complexity from O(d^2) to O(d)

Maintains similar error rates with significant efficiency gains

Abstract

We explore the redundancy of parameters in deep neural networks by replacing the conventional linear projection in fully-connected layers with the circulant projection. The circulant structure substantially reduces memory footprint and enables the use of the Fast Fourier Transform to speed up the computation. Considering a fully-connected neural network layer with d input nodes, and d output nodes, this method improves the time complexity from O(d^2) to O(dlogd) and space complexity from O(d^2) to O(d). The space savings are particularly important for modern deep convolutional neural network architectures, where fully-connected layers typically contain more than 90% of the network parameters. We further show that the gradient computation and optimization of the circulant projections can be performed very efficiently. Our experiments on three standard datasets show that the proposed approach achieves this significant gain in storage and efficiency with minimal increase in error rate compared to neural networks with unstructured projections.