Matrix-product neural network based on sequence block matrix product

Convolution neural networks (CNNs) based on the discrete convolutional operation have achieved great success in image processing, voice and audio processing, natural language processing and other fields. However, it is still an open problem how to develop new models instead of CNNs. Using the idea of the sequence block matrix product, we propose a novel operation and its corresponding neural network, namely two-dimensional discrete matrix-product operation (TDDMPO) and matrix-product neural network (MPNN). We present the definition of the TDDMPO, a series of its properties and matrix-product theorem in detail, and then construct its corresponding MPNN. Experimental results on Fashion-MNIST, SVHN, FLOWER17 and FLOWER102 datasets show that MPNNs obtain 1.65–13.04% relative performance improvement in comparison with the corresponding CNNs, and the amount of calculation of matrix-product layers of MPNNs obtains 41× to 57× reduction in comparison with the corresponding convolutional layers of CNNs. Hence, it is a potential model that may open some new directions for deep neural networks, particularly alternatives to CNNs.