Learning Convolutional Neural Networks in the Frequency Domain

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