Neural Network Field Theory at Finite Width

Abstract:Under mild assumptions, any quantum mechanical (QM) model or quantum field theory (QFT) admits a representation in terms of an ensemble of neural networks with countably many random parameters. We investigate the features of NN-QM and NN-FT models with finitely many parameters, such as a feedforward network of width $N < \infty$. We find that, generically, such models must violate one of the properties of conventional Euclidean QFTs, such as reflection positivity or cluster decomposition. We present several complementary ways of understanding which features can and cannot be preserved at finite $N$, both in QM and in QFT.

High Energy Physics - Theory (hep-th); Disordered Systems and Neural Networks (cond-mat.dis-nn); Machine Learning (cs.LG)

arXiv:2608.21588 [hep-th]

(or arXiv:2608.21588v1 [hep-th] for this version)

https://doi.org/10.48550/arXiv.2608.21588 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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