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A duality connecting neural network and cosmological dynamics

Krippendorf, Sven; Spannowsky, Michael

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Sven Krippendorf


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.


Krippendorf, S., & Spannowsky, M. (2022). A duality connecting neural network and cosmological dynamics. Machine Learning: Science and Technology, 3(3),

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


Published Journal Article (Advance online version) (1.9 Mb)

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Copyright Statement
Advance online version Original content from this work may be used under the terms of the Creative Commons Attribution 4.0 license. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.

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