mlsanityData to 14 Oct 2026

Infinite Neural Network Quantum States: Entanglement and Training Dynamics

arXiv 2112.00723 ↗First posted 1 Dec 2021quant-ph cond-mat.dis-nn cs.LGcited by 4

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Abstract (arXiv)

We study infinite limits of neural network quantum states (∞-NNQS), which exhibit representation power through ensemble statistics, and also tractable gradient descent dynamics. Ensemble averages of Renyi entropies are expressed in terms of neural network correlators, and architectures that exhibit volume-law entanglement are presented. A general framework is developed for studying the gradient descent dynamics of neural network quantum states (NNQS), using a quantum state neural tangent kernel (QS-NTK). For ∞-NNQS the training dynamics is simplified, since the QS-NTK becomes deterministic and constant. An analytic solution is derived for quantum state supervised learning, which allows an ∞-NNQS to recover any target wavefunction. Numerical experiments on finite and infinite NNQS in the transverse field Ising model and Fermi Hubbard model demonstrate excellent agreement with theory. ∞-NNQS opens up new opportunities for studying entanglement and training dynamics in other physics applications, such as in finding ground states.

Key facts. Cited by 4 papers in the map (data through 14 Oct 2026). Builds on 22 of its 55 references that are in the map. First posted on arXiv 1 Dec 2021.

Builds on

22 of 55 references.

References · 22

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10 more
  1. 2020Neural Networks and Quantum Field Theorycited by 61
  2. 2021Tensor Programs IIb: Architectural Universality of Neural Tangent Kernel Training Dynamicscited by 57
  3. 2021Representation Learning via Quantum Neural Tangent Kernelscited by 40
  4. 2021Symmetry-via-Duality: Invariant Neural Network Densities from Parameter-Space Correlatorscited by 29
  5. 2020Gauge equivariant neural networks for quantum lattice gauge theoriescited by 28
  6. 2021Neural tensor contractions and the expressive power of deep neural quantum statescited by 21
  7. 2021Quantum tangent kernelcited by 14
  8. 2021Spacetime Neural Network for High Dimensional Quantum Dynamicscited by 9
  9. 2021A quantum algorithm for training wide and deep classical neural networkscited by 7
  10. 2020Any Target Function Exists in a Neighborhood of Any Sufficiently Wide Random Network: A Geometrical Perspectivecited by 5

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Cited by year

Citing papers per year: 2022: 1; 2023: 3.

4 papers.

  1. 2023Expressibility-induced Concentration of Quantum Neural Tangent Kernelscited by 7
  2. 2022Quantum Lazy Trainingcited by 4
  3. 2023Learning ground states of gapped quantum Hamiltonians with Kernel Methodscited by 2
  4. 2023Artificial intelligence for artificial materials: moir'e atomcited by 1