mlsanityData to 7 Oct 2026

A duality connecting neural network and cosmological dynamics

arXiv 2202.11104 ↗First posted 22 Feb 2022gr-qc astro-ph.CO cs.LGcited by 10

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Abstract (arXiv)

We demonstrate that the dynamics of neural networks trained with gradient descent and the dynamics of scalar fields in a flat, vacuum energy dominated Universe are structurally profoundly related. This duality provides the framework for synergies between these systems, to understand and explain neural network dynamics and new ways of simulating and describing early Universe models. Working in the continuous-time limit of neural networks, we analytically match the dynamics of the mean background and the dynamics of small perturbations around the mean field, highlighting potential differences in separate limits. We perform empirical tests of this analytic description and quantitatively show the dependence of the effective field theory parameters on hyperparameters of the neural network. As a result of this duality, the cosmological constant is matched inversely to the learning rate in the gradient descent update.

Key facts. Cited by 10 papers in the map (data through 7 Oct 2026). Builds on 22 of its 45 references that are in the map. First posted on arXiv 22 Feb 2022.

Builds on

22 of 45 references.

References · 22

  1. 2018Neural Tangent Kernel: Convergence and Generalization in Neural Networkscited by 2,597
  2. 2019Wide Neural Networks of Any Depth Evolve as Linear Models Under Gradient Descentcited by 732
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10 more
  1. 2018Deep Convolutional Networks as shallow Gaussian Processescited by 137
  2. 2019Asymptotics of Wide Networks from Feynman Diagramscited by 77
  3. 2020Neural Networks and Quantum Field Theorycited by 58
  4. 2020Tensor Programs III: Neural Matrix Lawscited by 47
  5. 2021Representation Learning via Quantum Neural Tangent Kernelscited by 40
  6. 2021Symmetry-via-Duality: Invariant Neural Network Densities from Parameter-Space Correlatorscited by 28
  7. 2021Building Quantum Field Theories Out of Neuronscited by 27
  8. 2021Nonperturbative renormalization for the neural network-QFT correspondencecited by 24
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  10. 2022Born-Infeld (BI) for AI: Energy-Conserving Descent (ECD) for Optimizationcited by 10

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2023: 3; 2024: 4; 2025: 2; 2026: 1.

10 papers.

  1. 2023Neural Network Field Theories: Non-Gaussianity, Actions, and Localitycited by 21
  2. 2024Rigor with Machine Learning from Field Theory to the Poincar'e Conjecturecited by 12
  3. 2024On learning higher-order cumulants in diffusion modelscited by 10
  4. 2023Towards a Phenomenological Understanding of Neural Networks: Datacited by 4
  5. 2023Environmental effects on emergent strategy in micro-scale multi-agent reinforcement learningcited by 3
  6. 2024Collective variables of neural networks: empirical time evolution and scaling lawscited by 3
  7. 2025Beyond Scaling Curves: Internal Dynamics of Neural Networks Through the NTK Lenscited by 2
  8. 2024Learning 3-Manifold Triangulationscited by 1
  9. 2026Spectral Reach: Understanding Neural Scaling as Progress into the Spectral Tailcited by 1
  10. 2025Bulk-boundary decomposition of neural networkscited by 0