mlsanityData to 7 Oct 2026

Learning Relevant Features of Data with Multi-scale Tensor Networks

arXiv 1801.00315 ↗First posted 31 Dec 2017stat.ML cond-mat.stat-mech cond-mat.str-elcited by 50

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Abstract (arXiv)

Inspired by coarse-graining approaches used in physics, we show how similar algorithms can be adapted for data. The resulting algorithms are based on layered tree tensor networks and scale linearly with both the dimension of the input and the training set size. Computing most of the layers with an unsupervised algorithm, then optimizing just the top layer for supervised classification of the MNIST and fashion-MNIST data sets gives very good results. We also discuss mixing a prior guess for supervised weights together with an unsupervised representation of the data, yielding a smaller number of features nevertheless able to give good performance.

Key facts. Cited by 50 papers in the map (data through 7 Oct 2026). First posted on arXiv 31 Dec 2017.

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 11; 2022: 12; 2023: 10; 2024: 3; 2025: 5; 2026: 9.

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  1. 2021Variational Quantum Reinforcement Learning via Evolutionary Optimizationcited by 50
  2. 2021Enhancing Generative Models via Quantum Correlationscited by 40
  3. 2022Grokking phase transitions in learning local rules with gradient descentcited by 28
  4. 2022Implicit Regularization in Hierarchical Tensor Factorization and Deep Convolutional Neural Networkscited by 27
  5. 2021Tensor networks for unsupervised machine learningcited by 20
  6. 2023Tensor networks for quantum machine learningcited by 16
  7. 2023Tensor networks for interpretable and efficient quantum-inspired machine learningcited by 16
  8. 2022Generative modeling with projected entangled-pair statescited by 14
  9. 2023Machine learning with tree tensor networks, CP rank constraints, and tensor dropoutcited by 14
  10. 2021Tensor networks and efficient descriptions of classical datacited by 13
  11. 2022On the Ability of Graph Neural Networks to Model Interactions Between Verticescited by 12
  12. 2022Quantum-Inspired Tensor Neural Networks for Partial Differential Equationscited by 9
38 more
  1. 2022Privacy-preserving machine learning with tensor networkscited by 8
  2. 2021Explainable Natural Language Processing with Matrix Product Statescited by 7
  3. 2021Probabilistic Graphical Models and Tensor Networks: A Hybrid Frameworkcited by 5
  4. 2021Entangled q-Convolutional Neural Netscited by 4
  5. 2022Interaction Decompositions for Tensor Network Regressioncited by 4
  6. 2022Combining Reinforcement Learning and Tensor Networks, with an Application to Dynamical Large Deviationscited by 4
  7. 2023What Makes Data Suitable for a Locally Connected Neural Network? A Necessary and Sufficient Condition Based on Quantum Entanglementcited by 4
  8. 2024Ultra-low latency quantum-inspired machine learning predictors implemented on FPGAcited by 4
  9. 2022Positive unlabeled learning with tensor networkscited by 3
  10. 2025Riemannian Optimization on Tree Tensor Networks with Application in Machine Learningcited by 3
  11. 2025DisCoCLIP: A Distributional Compositional Tensor Network Encoder for Vision-Language Understandingcited by 3
  12. 2021Infinitely Wide Tensor Networks as Gaussian Processcited by 2
  13. 2022Deep tensor networks with matrix product operatorscited by 2
  14. 2023Quantum-inspired tensor network for Earth sciencecited by 2
  15. 2023Boosting Defect Detection in Manufacturing using Tensor Convolutional Neural Networkscited by 2
  16. 2024Tensor-Networks-based Learning of Probabilistic Cellular Automata Dynamicscited by 2
  17. 2026Towards Tensor Network Models for Low-Latency Jet Tagging on FPGAscited by 2
  18. 2021Lower and Upper Bounds on the VC-Dimension of Tensor Network Modelscited by 1
  19. 2021Rademacher Random Projections with Tensor Networkscited by 1
  20. 2021Neural Tangent Kernel of Matrix Product States: Convergence and Applicationscited by 1
  21. 2022Quantum-Inspired Tensor Neural Networks for Option Pricingcited by 1
  22. 2023The cross-sectional stock return predictions via quantum neural network and tensor networkcited by 1
  23. 2023Minimal Effective Theory for Phonotactic Memory: Capturing Local Correlations due to Errors in Speechcited by 1
  24. 2023Tensor Ring Optimized Quantum-Enhanced Tensor Neural Networkscited by 1
  25. 2024Cons-training Tensor Networks: Embedding and Optimization Over Discrete Linear Constraintscited by 1
  26. 2026Natural Riemannian gradient for learning functional tensor networkscited by 1
  27. 2026Quantum-Inspired Robust and Scalable SAR Object Classificationcited by 1
  28. 2022Stack operation of tensor networkscited by 0
  29. 2023Application of Tensor Neural Networks to Pricing Bermudan Swaptionscited by 0
  30. 2025HMAE: Self-Supervised Few-Shot Learning for Quantum Spin Systemscited by 0
  31. 2025Explaining Anomalies with Tensor Networkscited by 0
  32. 2025On computing and the complexity of computing higher-order U-statistics, exactlycited by 0
  33. 2026Quantum-Inspired Tensor Network Autoencoders for Anomaly Detection: A MERA-Based Approachcited by 0
  34. 2026Tensor-Augmented Convolutional Neural Networks: Enhancing Expressivity with Generic Tensor Kernelscited by 0
  35. 2026Quantum-inspired tensor networks in machine learning modelscited by 0
  36. 2026Entanglement is Half the Story: Post-Selection vs. Partial Tracescited by 0
  37. 2026Stochastic Optimization of Tree Tensor Networkscited by 0
  38. 2026Benign Loss Landscapes Can Coexist with Worst-Case Hardnesscited by 0