Circular FC: Fast Fourier Transform Meets Fully Connected Layer for Convolutional Neural Network

The fully connected (FC) layer is generally located behind the global pooling layer in the convolutional neural network (CNN). Its essence is the weighted summation of the features extracted from the previous convolutional layers, that is, feature remapping. However, the FC layer with close internal correlation inevitably brings parameter redundancy. In order to alleviate this problem, in this paper, we propose a novel lightweight FC-like module, dubbed as Circular FC, by constructing weight parameters in a circular manner. Inspired by digital signal processing theories, we implement Circular FC by fast Fourier transform (FFT) based on the circular convolution theorem of discrete signals. Circular FC is designed to be a plug-and-play classification head and can be easily embedded into existing CNNs such as VGG, Xception, DenseNet, and ResNets. Extensive experiments on CIFAR-10, CIFAR-100, and ImageNet datasets illustrate that the above networks equipped with Circular FC reduce the number of parameters while maintaining comparable image classification performance.