3D Discrete Matrix‐Product Operation and Its Generalization

Two‐dimensional (2D) discrete matrix‐product operation (DMPO) and its corresponding matrix‐product neural networks (MPNNs) are the substitutions of 2D discrete convolutional operation and its corresponding convolutional neural networks (CNNs), respectively. MPNNs not only achieve the better performance in comparison with CNNs, but also the calculation amount of MPNNs is less than that of CNNs. Therefore, the DMPO occupies an important position in deep learning. However, there is no research on three‐dimensional (3D) and higher dimensional DMPO. Therefore, the paper presents 3D and n ‐dimensional (n‐D) DMPO based on 2D DMPO. The paper first presents the definition, properties, and matrix‐product theorem of 3D DMPO and then presents the definition, properties, and matrix‐product theorem of n‐D DMPO, which provides enough theoretical support for the realization of 3D or n‐D MPNN.