End-to-End Training of Deep Neural Networks in the Fourier Domain

Convolutional networks are commonly used in various machine learning tasks, and they are more and more popularly used in the embedded domain with devices such as smart cameras and mobile phones. The operation of convolution can be substituted by point-wise multiplication in the Fourier domain, which can save operation, but usually, it is applied with a Fourier transform before and an inverse Fourier transform after the multiplication, since other operations in neural networks cannot be implemented efficiently in the Fourier domain. In this paper, we will present a method for implementing neural network completely in the Fourier domain, and by this, saving multiplications and the operations of inverse Fourier transformations. Our method can decrease the number of operations by four times the number of pixels in the convolutional kernel with only a minor decrease in accuracy, for example, 4% on the MNIST and 2% on the HADB datasets.