Learning Convolutional Neural Networks in the Frequency Domain

Convolutional neural network (CNN) achieves impressive success in the field of computer vision during the past few decades. As the core of CNNs, image convolution operation helps CNNs to achieve good performance on image-related tasks. However, image convolution is hard to be implemented and parallelized. In this paper, we propose a novel neural network model, namely CEMNet, that can be trained in frequency domain. The most important motivation of this research is that we can use the very simple element-wise multiplication operation to replace the image convolution in frequency domain based on Cross-Correlation Theorem. We further introduce Weight Fixation Mechanism to alleviate over-fitting, and analyze the working behavior of Batch Normalization, Leaky ReLU and Dropout in frequency domain to design their counterparts for CEMNet. Also, to deal with complex inputs brought by DFT, we design two branch network structure for CEMNet. Experimental results imply that CEMNet works well in frequency domain, and achieve good performance on MNIST and CIFAR-10 databases. To our knowledge, CEMNet is the first model trained in Fourier Domain that achieves more than 70\% validation accuracy on CIFAR-10 database.