A duality connecting neural network and cosmological dynamics

Krippendorf, Sven; Spannowsky, Michael

doi:10.1088/2632-2153/ac87e9

A duality connecting neural network and cosmological dynamics

Krippendorf, Sven; Spannowsky, Michael

Authors

Sven Krippendorf

Professor Michael Spannowsky michael.spannowsky@durham.ac.uk
Director

Abstract

We demonstrate that the dynamics of neural networks (NNs) 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 NN dynamics and new ways of simulating and describing early Universe models. Working in the continuous-time limit of NNs, 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 NN. As a result of this duality, the cosmological constant is matched inversely to the learning rate in the gradient descent update.

Citation

Krippendorf, S., & Spannowsky, M. (2022). A duality connecting neural network and cosmological dynamics. Machine Learning: Science and Technology, 3(3), https://doi.org/10.1088/2632-2153/ac87e9

Journal Article Type	Article
Acceptance Date	Aug 8, 2022
Online Publication Date	Aug 30, 2022
Publication Date	2022
Deposit Date	Sep 28, 2022
Publicly Available Date	Sep 29, 2022
Journal	Machine Learning: Science and Technology
Print ISSN	2632-2153
Publisher	IOP Publishing
Peer Reviewed	Peer Reviewed
Volume	3
Issue	3
DOI	https://doi.org/10.1088/2632-2153/ac87e9

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