Neural Network Quantum Field Theory from Transformer Architectures

• URL: http://arxiv.org/abs/2602.10209v1
• Date: Tue, 10 Feb 2026 19:02:03 GMT
• Title: Neural Network Quantum Field Theory from Transformer Architectures
• Authors: Dmitry S. Ageev, Yulia A. Ageeva,
• Abstract summary: We propose a neural-network construction of Euclidean scalar quantum field theories from transformer attention heads.<n>For a single attention head, shared random softmax weights couple different width coordinates and induce non-Gaussian field statistics.<n>We show that summing many independent heads with standard $1/N_h$ normalization suppresses connected non-Gaussian correlators as $1/N_h$, yielding a Gaussian NN-QFT in the large-head limit.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We propose a neural-network construction of Euclidean scalar quantum field theories from transformer attention heads, defining $n$-point correlators by averaging over random network parameters in the NN-QFT framework. For a single attention head, shared random softmax weights couple different width coordinates and induce non-Gaussian field statistics that persist in the infinite-width limit $d_k\to\infty$. We compute the two-point function in an attention-weight representation and show how Euclidean-invariant kernels can be engineered via random-feature token embeddings. We then analyze the connected four-point function and identify an "independence-breaking" contribution, expressible as a covariance over query-key weights, which remains finite at infinite width. Finally, we show that summing many independent heads with standard $1/N_h$ normalization suppresses connected non-Gaussian correlators as $1/N_h$, yielding a Gaussian NN-QFT in the large-head limit.

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