Renormalization in the neural network-quantum field theory correspondence

2022/12/22 by Harold Erbin, Erbin, Harold, Vincent Lahoche +3 · 2 citations
Computer Science · Physics and Astronomy · #Disordered Systems and Neural Networks (cond-mat.dis-nn) #FOS: Computer and information sciences #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Model Reduction and Neural Networks #Neural Networks and Applications #Statistical Mechanics and Entropy

paper · pdf · doi:10.48550/arxiv.2212.11811

openalex publication_date 2022/12/22 · openalex created_date 2023/01/04 · openalex updated_date 2026/07/28

Abstract

A statistical ensemble of neural networks can be described in terms of a quantum field theory (NN-QFT correspondence). The infinite-width limit is mapped to a free field theory, while finite N corrections are mapped to interactions. After reviewing the correspondence, we will describe how to implement renormalization in this context and discuss preliminary numerical results for translation-invariant kernels. A major outcome is that changing the standard deviation of the neural network weight distribution corresponds to a renormalization flow in the space of networks.

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• The Neural Networks with Tensor Weights and the Corresponding Fermionic Quantum Field Theory
• Functional Renormalization for Signal Detection: Dimensional Analysis and Dimensional Phase Transition for Nearly Continuous Spectra Effective Field Theory

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