mlsanityData to 7 Oct 2026

Generative Modeling via Hierarchical Tensor Sketching

arXiv 2304.05305 ↗First posted 11 Apr 2023math.NA cs.LG cs.NAcited by 8

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Abstract (arXiv)

We propose a hierarchical tensor-network approach for approximating high-dimensional probability density via empirical distribution. This leverages randomized singular value decomposition (SVD) techniques and involves solving linear equations for tensor cores in this tensor network. The complexity of the resulting algorithm scales linearly in the dimension of the high-dimensional density. An analysis of estimation error demonstrates the effectiveness of this method through several numerical experiments.

Key facts. Cited by 8 papers in the map (data through 7 Oct 2026). Builds on 18 of its 53 references that are in the map. First posted on arXiv 11 Apr 2023.

Builds on

18 of 53 references.

References · 18

  1. 2013Auto-Encoding Variational Bayescited by 3,980
  2. 2015Variational Inference with Normalizing Flowscited by 2,161
  3. 2016Density estimation using Real NVPcited by 2,029
  4. 2017Masked Autoregressive Flow for Density Estimationcited by 680
  5. 2015An Introduction to Matrix Concentration Inequalitiescited by 391
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  7. 2015Density Modeling of Images using a Generalized Normalization Transformationcited by 123
  8. 2016Neural Autoregressive Distribution Estimationcited by 94
  9. 2017Unsupervised Generative Modeling Using Matrix Product Statescited by 87
  10. 2017Efficient Low Rank Tensor Ring Completioncited by 45
  11. 2021Tensor-Train Density Estimationcited by 30
  12. 2019Modeling Sequences with Quantum States: A Look Under the Hoodcited by 19
6 more
  1. 2022Generative modeling via tensor train sketchingcited by 13
  2. 2018Scalable Gaussian Process Computations Using Hierarchical Matricescited by 8
  3. 2022Generative Modeling via Tree Tensor Network Statescited by 5
  4. 2020A Hierarchical Optimization Architecture for Large-Scale Power Networkscited by 1
  5. 2020Multiscale semidefinite programming approach to positioning problems with pairwise structurecited by 1
  6. 2022Error Analysis of Tensor-Train Cross Approximationcited by 1

Built on by

Cited by year (2026 to 7 Oct)

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

8 papers.

  1. 2024Ensemble-Based Annealed Importance Samplingcited by 4
  2. 2025Tensorization of neural networks for improved privacy and interpretabilitycited by 3
  3. 2025Plastic tensor networks for interpretable generative modelingcited by 1
  4. 2023Combining Monte Carlo and Tensor-network Methods for Partial Differential Equations via Sketchingcited by 0
  5. 2025Explaining Anomalies with Tensor Networkscited by 0
  6. 2025Optimization-Free Diffusion Model -- A Perturbation Theory Approachcited by 0
  7. 2025Optimal Bias-variance Tradeoff in Matrix and Tensor Estimationcited by 0
  8. 2026On the Approximation Complexity of Matrix Product Operator Born Machinescited by 0