On the building of efficient Fourier Convolutional Neural Networks

In computer vision tasks, Convolutional Neural Networks (CNN) have been the cornerstone to implement numerous models with outstanding results. Nevertheless, its high computational cost hinders its full potential when working with low-end devices. To overcome this drawback, various models have been proposed to take advantage of the properties of the convolution theorem to reduce calculations in CNN architectures. However, the use of the Fourier domain incurs in an increment of the number of weights of the kernels because they are defined using complex variable. In this work, we present a strategy to reduce such numbers by defining a reduced representation, which considers a limited amount of components to keep the parameter count comparable to that of a standard CNN. In deed, we introduce a novel layer, called Linear Transform, that learns to identify the most essential components of a frequency representation, building an appropriate reduced representation. Our experiments on image classification using databases MNIST, Fashion-MNIST, CIFAR-10 and CIFAR-100 showed that our proposal contains fewer parameters and floating point operations, in comparison with both conventional and Fourier CNN architectures. Moreover, the Linear Transform layer produced an improvement in the accuracy in several cases. Cases where accuracy decreases are also analyzed.