Neural Network Field Theory at Finite Width

• URL: http://arxiv.org/abs/2608.21588v1
• Date: Fri, 21 Aug 2026 19:43:46 GMT
• Title: Neural Network Field Theory at Finite Width
• Abstract summary: We investigate the features of NN-QM and NN-FT models with finitely many parameters, such as a feedforward network of width $N infty$.<n>We find that, generically, such models must violate one of the properties of conventional Euclidean QFTs, such as positivity or cluster decomposition.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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