Title: DCFNet: Deep Neural Network with Decomposed Convolutional Filters,
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.