Neural Networks and Quantum Field Theory
| Autor: | Anindita Maiti, Keegan Stoner, James Halverson |
|---|---|
| Rok vydání: | 2020 |
| Předmět: |
High Energy Physics - Theory
FOS: Computer and information sciences Computer Science - Machine Learning Artificial neural network FOS: Physical sciences Machine Learning (stat.ML) Disordered Systems and Neural Networks (cond-mat.dis-nn) Condensed Matter - Disordered Systems and Neural Networks Renormalization group Machine Learning (cs.LG) Human-Computer Interaction symbols.namesake Naturalness High Energy Physics - Theory (hep-th) Statistics - Machine Learning Artificial Intelligence symbols Effective field theory Feynman diagram Limit (mathematics) Statistical physics Quantum field theory Gaussian process Software Mathematics |
| DOI: | 10.48550/arxiv.2008.08601 |
| Popis: | We propose a theoretical understanding of neural networks in terms of Wilsonian effective field theory. The correspondence relies on the fact that many asymptotic neural networks are drawn from Gaussian processes, the analog of non-interacting field theories. Moving away from the asymptotic limit yields a non-Gaussian process and corresponds to turning on particle interactions, allowing for the computation of correlation functions of neural network outputs with Feynman diagrams. Minimal non-Gaussian process likelihoods are determined by the most relevant non-Gaussian terms, according to the flow in their coefficients induced by the Wilsonian renormalization group. This yields a direct connection between overparameterization and simplicity of neural network likelihoods. Whether the coefficients are constants or functions may be understood in terms of GP limit symmetries, as expected from 't Hooft's technical naturalness. General theoretical calculations are matched to neural network experiments in the simplest class of models allowing the correspondence. Our formalism is valid for any of the many architectures that becomes a GP in an asymptotic limit, a property preserved under certain types of training. Comment: v2: published in Machine Learning: Science and Technology. Additions include study of N-scaling, a correction for examples, and new experimental tests. 53 pages, 7 figures, and appendices |
| Databáze: | OpenAIRE |
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