A Multi-Scale Tensor Network Architecture for Classification and\n Regression

Abstract

We present an algorithm for supervised learning using tensor networks,\nemploying a step of preprocessing the data by coarse-graining through a\nsequence of wavelet transformations. We represent these transformations as a\nset of tensor network layers identical to those in a multi-scale entanglement\nrenormalization ansatz (MERA) tensor network, and perform supervised learning\nand regression tasks through a model based on a matrix product state (MPS)\ntensor network acting on the coarse-grained data. Because the entire model\nconsists of tensor contractions (apart from the initial non-linear feature\nmap), we can adaptively fine-grain the optimized MPS model backwards through\nthe layers with essentially no loss in performance. The MPS itself is trained\nusing an adaptive algorithm based on the density matrix renormalization group\n(DMRG) algorithm. We test our methods by performing a classification task on\naudio data and a regression task on temperature time-series data, studying the\ndependence of training accuracy on the number of coarse-graining layers and\nshowing how fine-graining through the network may be used to initialize models\nwith access to finer-scale features.\n