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Title: Neural network field theories: non-Gaussianity, actions, and locality
Abstract Both the path integral measure in field theory (FT) and ensembles of neural networks (NN) describe distributions over functions. When the central limit theorem can be applied in the infinite-width (infinite-N) limit, the ensemble of networks corresponds to a free FT. Although an expansion in 1 / N corresponds to interactions in the FT, others, such as in a small breaking of the statistical independence of network parameters, can also lead to interacting theories. These other expansions can be advantageous over the 1 / N -expansion, for example by improved behavior with respect to the universal approximation theorem. Given the connected correlators of a FT, one can systematically reconstruct the action order-by-order in the expansion parameter, using a new Feynman diagram prescription whose vertices are the connected correlators. This method is motivated by the Edgeworth expansion and allows one to derive actions for NN FT. Conversely, the correspondence allows one to engineer architectures realizing a given FT by representing action deformations as deformations of NN parameter densities. As an example,φ4theory is realized as an infinite-NNN FT.  more » « less
Award ID(s):
1848089
PAR ID:
10485042
Author(s) / Creator(s):
; ; ; ;
Publisher / Repository:
IOP Publishing
Date Published:
Journal Name:
Machine Learning: Science and Technology
Volume:
5
Issue:
1
ISSN:
2632-2153
Format(s):
Medium: X Size: Article No. 015002
Size(s):
Article No. 015002
Sponsoring Org:
National Science Foundation
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