mlsanityData to 14 Oct 2026

Topological Effects in Neural Network Field Theory

arXiv 2604.02313 ↗First posted 2 Apr 2026hep-th cond-mat.dis-nn cs.LGcited by 2

Not on the map. Why?

Abstract (arXiv)

Neural network field theory formulates field theory as a statistical ensemble of fields defined by a network architecture and a density on its parameters. We extend the construction to topological settings via the inclusion of discrete parameters that label the topological quantum number. We recover the Berezinskii--Kosterlitz--Thouless transition, including the spin-wave critical line and the proliferation of vortices at high temperatures. We also verify the T-duality of the bosonic string, showing invariance under the exchange of momentum and winding on S1, the transformation of the sigma model couplings according to the Buscher rules on constant toroidal backgrounds, the enhancement of the current algebra at self-dual radius, and non-geometric T-fold transition functions.

Key facts. Cited by 2 papers in the map (data through 14 Oct 2026). Builds on 24 of its 51 references that are in the map. First posted on arXiv 2 Apr 2026.

Builds on

24 of 51 references.

References · 24

  1. 2017Attention Is All You Needcited by 60,361
  2. 2018Neural Tangent Kernel: Convergence and Generalization in Neural Networkscited by 2,621
  3. 2018Gaussian Process Behaviour in Wide Deep Neural Networkscited by 317
  4. 2021The Principles of Deep Learning Theorycited by 173
  5. 2018Bayesian Deep Convolutional Networks with Many Channels are Gaussian Processescited by 167
  6. 2019Tensor Programs I: Wide Feedforward or Recurrent Neural Networks of Any Architecture are Gaussian Processescited by 151
  7. 2020Tensor Programs II: Neural Tangent Kernel for Any Architecturecited by 143
  8. 2018Deep Convolutional Networks as shallow Gaussian Processescited by 138
  9. 2020Infinite attention: NNGP and NTK for deep attention networkscited by 121
  10. 2019Non-Gaussian processes and neural networks at finite widthscited by 78
  11. 2020Neural Networks and Quantum Field Theorycited by 61
  12. 2020Predicting the outputs of finite deep neural networks trained with noisy gradientscited by 31
12 more
  1. 2021Symmetry-via-Duality: Invariant Neural Network Densities from Parameter-Space Correlatorscited by 29
  2. 2021Building Quantum Field Theories Out of Neuronscited by 28
  3. 2023Neural Network Field Theories: Non-Gaussianity, Actions, and Localitycited by 22
  4. 2017A Correspondence Between Random Neural Networks and Statistical Field Theorycited by 14
  5. 2024Conformal Fields from Neural Networkscited by 11
  6. 2025Quantum Mechanics and Neural Networkscited by 7
  7. 2025Fermions and Supersymmetry in Neural Network Field Theoriescited by 6
  8. 2024TASI Lectures on Physics for Machine Learningcited by 5
  9. 2025Conformal Defects in Neural Network Field Theoriescited by 3
  10. 2025Virasoro Symmetry in Neural Network Field Theoriescited by 3
  11. 2025The neural networks with tensor weights and emergent fermionic Wick rules in the large-width limitcited by 2
  12. 2025Viability of perturbative expansion for quantum field theories on neuronscited by 2

Built on by

Cited by year (2026 to 14 Oct)

Citing papers per year: 2026: 2.

2 papers.

  1. 2026Spinning Conformal Correlators from Neural Networkscited by 1
  2. 2026Neural Network Field Theory at Finite Widthcited by 0