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Title
Tensor tree learns hidden relational structures in data to construct generative models
Author
Kenji Harada, Tsuyoshi Okubo, Naoki Kawashima
Abstract
Based on the tensor tree network with the Born machine framework, we propose a general method for constructing a generative model by expressing the target distribution function as the quantum wave function amplitude represented by a tensor tree. The key idea is dynamically optimizing the tree structure that minimizes the bond mutual information. The proposed method offers enhanced performance and uncovers hidden relational structures in the target data. We illustrate potential practical applications with four examples: (i) random patterns, (ii) QMNIST hand-written digits, (iii) Bayesian networks, and (iv) the stock price fluctuation pattern in S&P500. In (i) and (ii), strongly correlated variables were concentrated near the center of the network; in (iii), the causality pattern was identified; and, in (iv), a structure corresponding to the eleven sectors emerged.
Comments
9 pages, 3 figures
Preprint
arXiv:2408.10669
Code
Adaptive Tensor Tree Generative Modeling

Dates
March 25-29, 2024
Conference
SQAI-NCTS Workshop on Tensor Network and Quantum Embedding (Hongo Campus, The University of Tokyo)
Title
Optimizing the structure of tree tensor network for quantum generative modeling using mutual information-based approach
Abstract
Generative modeling is a crucial task in the field of machine learning. Recently, there have been several proposals for generative models on quantum devices. We can efficiently optimize generative models defined by tensor network states, but their performance largely depends on the geometrical structure of the tensor network. To tackle this issue, we have proposed an optimization method for the network structure in the tree tensor network class, based on the least mutual information principle. Generative modeling with an optimized network structure has better performance than a fixed network structure. Moreover, by embedding data dependencies into the tree structure based on the least mutual information principle, we can geometrically represent the correlations in the data.

Book title
Advanced Mathematical Science for Mobility Society
Editors
Kazushi Ikeda, Yoshiumi Kawamura, Kazuhisa Makino, Satoshi Tsujimoto, Nobuo Yamashita, Shintaro Yoshizawa, Hanna Sumita
Publisher
Springer Singapore
Reference
ISBN 978-981-99-9771-8 ISBN 978-981-99-9772-5 (eBook)
Title
Chapter 5 "Application of Tensor Network Formalism for Processing Tensor Data"
Authors
Kenji Harada, Hiroaki Matsueda, and Tsuyoshi Okubo
Web page
Open access

Date
Jan 26, 2024
Conference
2024 Annual Meeting of the Physical Society of Taiwan, Topical Symposia:Many-body systems and advanced numerical methods
Title
Optimizing tensor network structure

Date
Jan 22, 2024
Conference
Mini-workshop: Tensor Network algorithms and applications 2024 (Taipei, Taiwan)
Title
Optimizing tensor network structure

Date
Aug 22, 2023
Conference
Tensor Network States: Algorithms and Applications 2023 (Shanghai, China)
Title
Tensor network study of one-dimensional stochastic processes

TOPICS

Toolkit of Bayesian Scaling Analysis

Reference application software of a new scaling analysis method of critical phenomena based on Bayesian inference.

To demo To details
Toolkit of Adaptive Tensor Tree Generative Modeling

Reference application software of adaptive tensor tree generative modeling.

To GitHub
Monte Carlo simulations

This demonstration shows a Monte Carlo simulation of the two-dimensional Ising model by three algorithms: Metropolis, Swendsen-Wang, and Wolff algorithms.

To demo

ABOUT

Kenji Harada

Kenji Harada ( 原田健自 )
Assistant Professor, Graduate School of Informatics, Kyoto University, Japan.
harada.kenji.8e@kyoto-u.ac.jp
Room 203, Research Bldg. No.8, Yoshida Campus, Kyoto Univ., Kyoto, 606-8501, Japan. Map (No.59)

LINKS