Source-linked AI summary
Machine Learning by Unitary Tensor Network of Hierarchical Tree Structure
Ding Liu, Shi-Ju Ran, Peter Wittek, Cheng Peng, Raul Blázquez García, Gang Su, Maciej Lewenstein
TL;DR
Because images are two-dimensional, the paper develops a hierarchical tensor-network approach suited to their structure. It trains unitary TTNs with a MERA-inspired algorithm and finds that quantum-state fidelity and entanglement characterize image classes and classification tasks.
Problem
The paper addresses how tensor networks can represent images in a hierarchy suited to their two-dimensional structure.
Source: p. 1Method
It maps image pixels to vectors and trains unitary hierarchical TTNs with a MERA-inspired algorithm to predict image classes and define class-encoding quantum states.
Source: pp. 1, 3Results
The authors find that fidelity indicates pairwise classification difficulty, while moderate entanglement entropies (S ∼ O(1)) indicate classifiers represented as slightly-entangled states.
Source: p. 2Takeaways & Limitations
The results show that quantum properties such as fidelity and entanglement can characterize classical image data and machine-learning tasks.
Source: p. 5The training-sample vectors are assumed to have total squared norm N.
Source: p. 2
Abstract
from arXiv · showhide
The resemblance between the methods used in quantum-many body physics and in machine learning has drawn considerable attention. In particular, tensor networks (TNs) and deep learning architectures bear striking similarities to the extent that TNs can be used for machine learning. Previous results used one-dimensional TNs in image recognition, showing limited scalability and flexibilities. In this work, we train two-dimensional hierarchical TNs to solve image recognition problems, using a training algorithm derived from the multi-scale entanglement renormalization ansatz. This approach introduces mathematical connections among quantum many-body physics, quantum information theory, and machine learning. While keeping the TN unitary in the training phase, TN states are defined, which encode classes of images into quantum many-body states. We study the quantum features of the TN states, including quantum entanglement and fidelity. We find these quantities could be properties that characterize the image classes, as well as the machine learning tasks.