Comparison of Fourier Bases and Asymmetric Network Bases in the Bio-Inspired Networks

Machine learning, deep learning and neural networks are extensively developed in many fields, in which neural network architectures have shown a variety of applications. However, there is a need for explainable fundamentals in complex neural networks. In this paper, it is shown that bio-inspired networks are useful for the explanation of network functions. First, the asymmetric network is created based on the bio-inspired retinal network. They have orthogonal bases which correspond to the Fourier bases. Second, the classification performance of the asymmetric network is compared to the conventional symmetric network. Further, the asymmetric network is extended to the layered networks, which generate higher dimensional orthogonal bases. Their replacement operation is shown to be useful in the classification. These higher dimensional bases preserve the independence of patterns in their layered networks. Finally, it is shown that the sparse codes made of the higher dimensional bases are applied to the classification of real-world data.