mlsanityData to 7 Oct 2026

Generative modeling with projected entangled-pair states

arXiv 2202.08177 ↗First posted 16 Feb 2022quant-ph cond-mat.stat-mech cs.CVcited by 14

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Abstract (arXiv)

We argue and demonstrate that projected entangled-pair states (PEPS) outperform matrix product states significantly for the task of generative modeling of datasets with an intrinsic two-dimensional structure such as images. Our approach builds on a recently introduced algorithm for sampling PEPS, which allows for the efficient optimization and sampling of the distributions.

Key facts. Cited by 14 papers in the map (data through 7 Oct 2026). Builds on 20 of its 41 references that are in the map. First posted on arXiv 16 Feb 2022.

Builds on

20 of 41 references.

References · 20

  1. 2018UMAP: Uniform Manifold Approximation and Projection for Dimension Reductioncited by 2,841
  2. 2016Pixel Recurrent Neural Networkscited by 814
  3. 2017Unsupervised Generative Modeling Using Matrix Product Statescited by 87
  4. 2019Tree Tensor Networks for Generative Modelingcited by 63
  5. 2019Expressive power of tensor-network factorizations for probabilistic modeling, with applications from hidden Markov models to quantum machine learningcited by 55
  6. 2017Learning Relevant Features of Data with Multi-scale Tensor Networkscited by 50
  7. 2017Information Perspective to Probabilistic Modeling: Boltzmann Machines versus Born Machinescited by 33
  8. 2018From probabilistic graphical models to generalized tensor networks for supervised learningcited by 31
  9. 2020Supervised Learning with Projected Entangled Pair Statescited by 30
  10. 2020Locally Masked Convolution for Autoregressive Modelscited by 22
  11. 2021Tensor networks for unsupervised machine learningcited by 20
  12. 2019Modeling Sequences with Quantum States: A Look Under the Hoodcited by 19
8 more
  1. 2020Entanglement and Tensor Networks for Supervised Image Classificationcited by 18
  2. 2020Hybrid Tensor Decomposition in Neural Network Compressioncited by 15
  3. 2021Tensor networks and efficient descriptions of classical datacited by 13
  4. 2019Probabilistic Modeling with Matrix Product Statescited by 11
  5. 2021Boltzmann machines as two-dimensional tensor networkscited by 7
  6. 2015Matrix Product State for Feature Extraction of Higher-Order Tensorscited by 6
  7. 2016Matrix Product State for Higher-Order Tensor Compression and Classificationcited by 6
  8. 2014Iterative Neural Autoregressive Distribution Estimator (NADE-k)cited by 1

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2022: 2; 2023: 5; 2024: 4; 2025: 2; 2026: 1.

14 papers.

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  1. 2023Trainability barriers and opportunities in quantum generative modelingcited by 35
  2. 2023Machine learning with tree tensor networks, CP rank constraints, and tensor dropoutcited by 14
  3. 2023Quantum-Inspired Machine Learning: a Surveycited by 11
  4. 2023TensorKrowch: Smooth integration of tensor networks in machine learningcited by 5
  5. 2024A Matrix Product State Model for Simultaneous Classification and Generationcited by 5
  6. 2022High-dimensional density estimation with tensorizing flowcited by 4
  7. 2025Tensorization of neural networks for improved privacy and interpretabilitycited by 3
  8. 2024Quantum-inspired Techniques in Tensor Networks for Industrial Contextscited by 2
  9. 2022Stack operation of tensor networkscited by 0
  10. 2023Intelligent diagnostic scheme for lung cancer screening with Raman spectra data by tensor network machine learningcited by 0
  11. 2024T'ecnicas Quantum-Inspired en Tensor Networks para Contextos Industrialescited by 0
  12. 2024No-Free-Lunch Theories for Tensor-Network Machine Learning Modelscited by 0
2 more
  1. 2025Efficient Probabilistic Tensor Networkscited by 0
  2. 2026Efficient Generative Modeling with Unitary Matrix Product States Using Riemannian Optimizationcited by 0