Deep Cyclic Group Networks

Zhe-Cheng Fan, Tak-Shing Chan, Yi-Hsuan Yang, Jyh-Shing Roger Jang

Abstract: We propose a new network architecture called deep cyclic group network (DCGN) that uses the cyclic group algebra for convolutional vector-neuron learning. The input to DCGN is a three-way tensor, where the mode-3 dimension corresponds to the dimensionality of the input data, e.g., three for RGB images. To handle vector-valued inputs, we replace scalar multiplication with circular convolution for the feedforward and backpropagation processes. As a result, every feature map and kernel map is a three-way tensor with the same mode-3 dimension as the input data. This way, DCGN may capture more of the relations among different data dimensions, especially for regression tasks where the target output has the same dimensionality as the input data. Moreover, DCGN can deal with input data of arbitrary dimensions, a property that existing architectures such as deep complex networks and deep quaternion networks (DQN) lack. Experiments show that DCGN indeed performs better than convolutional neural networks and DQN for two regression tasks, namely color image inpainting and multispectral image denoising.