データ内の因果関係を直接的にネットワーク構造として抽出可能なテンソルネットワークをベースとした新しい生成モデルの研究に関するプレスリリースを行いました。

Title

Plastic tensor networks for interpretable generative modeling

Author

Katsuya O. Akamatsu, Kenji Harada, Tsuyoshi Okubo, Naoki Kawashima

Abstract

A structural optimization scheme for a single-layer nonnegative adaptive tensor tree (NATT) that models a target probability distribution is proposed as an alternative paradigm for generative modeling. The NATT scheme, by construction, automatically searches for a tree structure that best fits a given discrete dataset whose features serve as inputs, and has the advantage that it is interpretable as a probabilistic graphical model. We consider the NATT scheme and a recently proposed Born machine ATT optimization scheme and demonstrate their effectiveness on a variety of generative modeling tasks where the objective is to infer the hidden structure of a provided dataset. Our results show that in terms of minimizing the negative log-likelihood, the single-layer scheme has model performance comparable to the Born machine scheme, though not better. The tasks include deducing the structure of binary bitwise operations, learning the internal structure of random Bayesian networks given only visible sites, and a real-world example related to hierarchical clustering where a cladogram is constructed from mitochondrial DNA sequences. In doing so, we also show the importance of the choice of network topology and the versatility of a least-mutual information criterion in selecting a candidate structure for a tensor tree, as well as discuss aspects of these tensor tree generative models including their information content and interpretability.

Comments

21 pages, 17 figures

Citation

Katsuya O. Akamatsu, Kenji Harada, Tsuyoshi Okubo, and Naoki Kawashima, Machine Learning: Science and Technology 7 015014(2026)

DOI

10.1088/2632-2153/ae3048

Code

Nonnegative Adaptive Tensor Tree Modeling

Date

December 15, 2025

Conference

Mini-workshop: Tensor Network algorithms and applications 2025 (Tainan, National Cheng Kung University, Taiwan)

Title

Structure-Optimized Tensor Network Generative Models for Data Distributions

Title

Improving the accuracy of the tree-tensor network approach by optimization of network structure

Author

Toshiya Hikihara, Hiroshi Ueda, Kouichi Okunishi, Kenji Harada, and Tomotoshi Nishino

Abstract

Numerical methods based on tensor networks have been extensively explored in the research of quantum many-body systems in recent years. It has been recognized that the ability of tensor networks to describe a quantum many-body state crucially depends on the spatial structure of the network. In the previous work [T. Hikihara et al., Phys. Rev. Res. 5, 013031 (2023)], we proposed an algorithm based on tree-tensor networks (TTNs) that automatically optimizes the structure of a TTN according to the spatial profile of entanglement in the state of interest. In this paper, we apply the algorithm to the random 𝑋𝑌 -exchange model under random magnetic fields and the Richardson model in order to analyze how the performance of the algorithm depends on the detailed updating schemes of the structural optimization. We then find that for the random 𝑋𝑌 model, on the one hand, the algorithm achieves improved accuracy, and the stochastic algorithm, which selects the local network structure probabilistically, is notably effective. For the Richardson model, on the other hand, the resulting numerical accuracy subtly depends on the initial TTN and the updating schemes. In particular, the algorithm without the stochastic updating scheme certainly improves the accuracy, while the one with the stochastic updates results in poor accuracy due to the effect of randomizing the network structure at the early stage of the calculation. These results indicate that the algorithm successfully improves the accuracy of the numerical calculations for quantum many-body states, while it is essential to appropriately choose the updating scheme as well as the initial TTN structure, depending on the systems treated.

Comments

19 pages, 17 figures, 2 tables

Citation

Toshiya Hikihara, Hiroshi Ueda, Kouichi Okunishi, Kenji Harada, Tomotoshi Nishino, ``Improving the accuracy of the tree-tensor network approach by optimization of network structure'', Phys. Rev. B 112, 134427 (2025)

DOI

10.1103/ljj8-tkpc

Code

Demo code

日本物理学会　2025年年次大会（広島大学）

日程: 2025年9月16日から9月19日

• 18pPS-90 "グラウバーダイナミクスにおける熱力学不確定性関係" (寺前実, 原田健自)
• 18pPS-103 "動的制約付きモデルの有限時間における動的相転移の直接的観測" (西川大凱, 原田健自)
• 18pSL101-13 "MPS表現を用いた確率過程の動的低ランク近似法" (皆川諒, 原田健自)
• 18pSL101-14 "生成モデリングのためのミニバッチアニーリングを組み込んだ適応的テンソルツリー法" (原田健自, 大久保毅, 川島直輝)

Dates

August 25-29, 2025

Conference

SQAI-NCTS Workshop on Quantum Technologies and Machine Learning (National Taiwan University, Taipei, Taiwan)

Title

Adaptive Tensor Tree Method with Annealing of Mini-batch Samples for Generative Modeling on Quantum Devices

Abstract

We proposed the Adaptive Tensor Tree (ATT) method, which uses the tensor tree network within the Born machine framework to construct a generative model. This method expresses the target distribution function as the squared amplitude of a quantum wave function represented by a tensor tree. The core concept of the ATT method involves dynamically optimizing the tree structure to minimize the bond mutual information. In this presentation, we introduce a new technique that utilizes an annealing process on mini-batch samples to enhance the performance of the ATT method. We will demonstrate the effectiveness of this new ATT approach using various datasets.

テンソルネットワークをベースとした生成モデルの新しい構築法を提案しその有効性を示した研究に関するプレスリリースを行いました。

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 amplitude of the quantum wave function 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 handwritten digits, (iii) Bayesian networks, and (iv) the pattern of stock price fluctuation pattern in S\&P500. In (i) and (ii), the 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

10 pages, 3 figures

Citation

Kenji Harada, Tsuyoshi Okubo, and Naoki Kawashima, Machine Learning: Science and Technology 6 025002(2025)

DOI

10.1088/2632-2153/adc2c7

Code

Adaptive Tensor Tree Generative Modeling

日本物理学会　2025年春季大会（オンライン）

日程: 2025年3月18日から3月21日

• 講演(18pL3-2) "ツリーテンソルネットワークを用いた生成モデルにおけるテンソル・ネットワーク最適化"（共同研究者：大久保毅、川島直輝）