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Title: Non-perturbative renormalization for the neural network-QFT correspondence
Abstract

In a recent work (Halversonet al2021Mach. Learn.: Sci. Technol.2035002), Halverson, Maiti and Stoner proposed a description of neural networks (NNs) in terms of a Wilsonian effective field theory. The infinite-width limit is mapped to a free field theory while finiteNcorrections are taken into account by interactions (non-Gaussian terms in the action). In this paper, we study two related aspects of this correspondence. First, we comment on the concepts of locality and power-counting in this context. Indeed, these usual space-time notions may not hold for NNs (since inputs can be arbitrary), however, the renormalization group (RG) provides natural notions of locality and scaling. Moreover, we comment on several subtleties, for example, that data components may not have a permutation symmetry: in that case, we argue that random tensor field theories could provide a natural generalization. Second, we improve the perturbative Wilsonian renormalization from Halversonet al(2021Mach. Learn.: Sci. Technol.2035002) by providing an analysis in terms of the non-perturbative RG using the Wetterich-Morris equation. An important difference with usual non-perturbative RG analysis is that only the effective infrared 2-point function is known, which requires setting the problem with care. Our aim is to provide a useful formalism to investigate NNs behavior beyond the large-width limit (i.e. far from Gaussian limit) in a non-perturbative fashion. A major result of our analysis is that changing the standard deviation of the NN weight distribution can be interpreted as a renormalization flow in the space of networks. We focus on translations invariant kernels and provide preliminary numerical results.

 
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Award ID(s):
2019786
NSF-PAR ID:
10363314
Author(s) / Creator(s):
; ;
Publisher / Repository:
IOP Publishing
Date Published:
Journal Name:
Machine Learning: Science and Technology
Volume:
3
Issue:
1
ISSN:
2632-2153
Page Range / eLocation ID:
Article No. 015027
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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