DCFNet: Deep Neural Network with Decomposed Convolutional Filters

TL;DR

This paper introduces DCFNet, a CNN architecture that decomposes filters into fixed bases with learned coefficients, reducing parameters and computation while maintaining accuracy, supported by theoretical stability analysis.

Contribution

The paper proposes a novel filter decomposition method in CNNs using fixed bases, which reduces parameters and computation while ensuring stability.

Findings

Maintains accuracy with fewer parameters.

Fourier-Bessel bases outperform random bases.

Theoretically proven stability under input variations.

Abstract

Filters in a Convolutional Neural Network (CNN) contain model parameters learned from enormous amounts of data. In this paper, we suggest to decompose convolutional filters in CNN as a truncated expansion with pre-fixed bases, namely the Decomposed Convolutional Filters network (DCFNet), where the expansion coefficients remain learned from data. Such a structure not only reduces the number of trainable parameters and computation, but also imposes filter regularity by bases truncation. Through extensive experiments, we consistently observe that DCFNet maintains accuracy for image classification tasks with a significant reduction of model parameters, particularly with Fourier-Bessel (FB) bases, and even with random bases. Theoretically, we analyze the representation stability of DCFNet with respect to input variations, and prove representation stability under generic assumptions on the expansion coefficients. The analysis is consistent with the empirical observations.