mlsanityData to 7 Oct 2026

Tensor network to learn the wavefunction of data

arXiv 2111.08014 ↗First posted 15 Nov 2021quant-ph cs.LGcited by 4

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Abstract (arXiv)

How many different ways are there to handwrite digit 3? To quantify this question imagine extending a dataset of handwritten digits MNIST by sampling additional images until they start repeating. We call the collection of all resulting images of digit 3 the "full set." To study the properties of the full set we introduce a tensor network architecture which simultaneously accomplishes both classification (discrimination) and sampling tasks. Qualitatively, our trained network represents the indicator function of the full set. It therefore can be used to characterize the data itself. We illustrate that by studying the full sets associated with the digits of MNIST. Using quantum mechanical interpretation of our network we characterize the full set by calculating its entanglement entropy. We also study its geometric properties such as mean Hamming distance, effective dimension, and size. The latter answers the question above -- the total number of black and white threes written MNIST style is 272.

Key facts. Cited by 4 papers in the map (data through 7 Oct 2026). Builds on 20 of its 31 references that are in the map. First posted on arXiv 15 Nov 2021.

Builds on

20 of 31 references.

References · 20

  1. 2020Scaling Laws for Neural Language Modelscited by 6,411
  2. 2016Understanding deep learning requires rethinking generalizationcited by 1,657
  3. 2017Exploring Generalization in Deep Learningcited by 595
  4. 2021Explaining Neural Scaling Lawscited by 353
  5. 2018Estimating the intrinsic dimension of datasets by a minimal neighborhood informationcited by 246
  6. 2017Generalization in Deep Learningcited by 146
  7. 2017Unsupervised Generative Modeling Using Matrix Product Statescited by 87
  8. 2019Tree Tensor Networks for Generative Modelingcited by 63
  9. 2019Cold Case: The Lost MNIST Digitscited by 61
  10. 2019Expressive power of tensor-network factorizations for probabilistic modeling, with applications from hidden Markov models to quantum machine learningcited by 55
  11. 2018Quantum Entanglement in Deep Learning Architecturescited by 49
  12. 2020A Neural Scaling Law from the Dimension of the Data Manifoldcited by 48
8 more
  1. 2019TensorNetwork for Machine Learningcited by 29
  2. 2017Deep Learning and Quantum Entanglement: Fundamental Connections with Implications to Network Designcited by 22
  3. 2020Entanglement and Tensor Networks for Supervised Image Classificationcited by 18
  4. 2021Tensor networks and efficient descriptions of classical datacited by 13
  5. 2017Tensor network language modelcited by 9
  6. 2017Language as a matrix product statecited by 7
  7. 2020Tangent-Space Gradient Optimization of Tensor Network for Machine Learningcited by 6
  8. 2021Entangled q-Convolutional Neural Netscited by 4

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Cited by year

Citing papers per year: 2022: 2; 2023: 2.

4 papers.

  1. 2022Grokking phase transitions in learning local rules with gradient descentcited by 28
  2. 2023Machine learning with tree tensor networks, CP rank constraints, and tensor dropoutcited by 14
  3. 2023What Makes Data Suitable for a Locally Connected Neural Network? A Necessary and Sufficient Condition Based on Quantum Entanglementcited by 4
  4. 2022Deep tensor networks with matrix product operatorscited by 2