Decomposition And Compression Of Tensor Networks And Their Applications

In recent years,Machine Learning and Big data have attracted widespread attention in the fields of physics,biological sciences and environmental ecology.Much interrelated big data can be organized into tensor networks.Tensor is an extension of matrix to high dimension and has become the core technology of many fields.Tensor network algorithms have become a key technology.In this paper we will introduce some tensor network algorithms,including regularization,decomposition and compression of one-dimensional tensor networks(such as matrix product state(MPS),matrix product operator(MPO),etc.).We will also introduce the technique for transforming two-dimensional square lattice tensor network(PEPS)into one-dimensional tensor networks.Furthermore,we will introduce the design and package of the tensor network algorithm.Finally,we will apply the algorithms of these software package to the following two areas.(1)Extraction of information entropy in MPO networks.We will firstly analyze the difficulties in extracting information entropy by the traditional density matrix renormalization group(DMRG)algorithm.In order to improve the algorithm,we will use the tensor-networkcompression algorithm to reduce the dimensionality of the one-dimensional tensor networks.Results show that the computational and stability of DMRG can be effectively improved by the compression algorithm.(2)The application of MPS network in face recognition.Generally,we save all the photos as a database.When the database is large,the efficiency of face recognition is particularly important.Database can be decomposed into a form of a one-dimensional tensor network by the MPS decomposition algorithm.The experimental results show that the images can be effectively compressed,and the amount of computation can be greatly reduced,and the efficiency of face recognition can be improved by this algorithm.