mlsanityData to 7 Oct 2026

Tensor tree learns hidden relational structures in data to construct generative models

arXiv 2408.10669 ↗First posted 20 Aug 2024cs.LG cond-mat.stat-mech cs.AIcited by 3

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Abstract (arXiv)

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.

Key facts. Cited by 3 papers in the map (data through 7 Oct 2026). Builds on 12 of its 36 references that are in the map. First posted on arXiv 20 Aug 2024.

Builds on

12 of 36 references.

References · 12

  1. 2015Learning both Weights and Connections for Efficient Neural Networkscited by 1,998
  2. 2015Tensorizing Neural Networkscited by 246
  3. 2018Differentiable Learning of Quantum Circuit Born Machinecited by 90
  4. 2017Unsupervised Generative Modeling Using Matrix Product Statescited by 87
  5. 2019The Born Supremacy: Quantum Advantage and Training of an Ising Born Machinecited by 75
  6. 2019Tree Tensor Networks for Generative Modelingcited by 63
  7. 2019Cold Case: The Lost MNIST Digitscited by 61
  8. 2013The Recovery of Causal Poly-Trees from Statistical Datacited by 19
  9. 2021Variational inference with a quantum computercited by 18
  10. 2023A Framework for Demonstrating Practical Quantum Advantage: Racing Quantum against Classical Generative Modelscited by 15
  11. 2021Probabilistic Graphical Models and Tensor Networks: A Hybrid Frameworkcited by 5
  12. 2022Combining Reinforcement Learning and Tensor Networks, with an Application to Dynamical Large Deviationscited by 4

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2025: 2; 2026: 1.

3 papers.

  1. 2025Plastic tensor networks for interpretable generative modelingcited by 1
  2. 2025Trainable Quantum Neural Network for Multiclass Image Classification with the Power of Pre-trained Tree Tensor Networkscited by 0
  3. 2026Entanglement is Half the Story: Post-Selection vs. Partial Tracescited by 0