  Convolutional neural network (CNN) has achieved impressive success in
computer vision during the past few decades. The image convolution operation
helps CNNs to get good performance on image-related tasks. However, the image
convolution has high computation complexity and hard to be implemented. This
paper proposes the 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,
which obviously reduces the computation complexity. 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.
