Neural Network Quantum Field Theory from Transformer Architectures
摘要
We propose a neural-network construction of Euclidean scalar quantum field theories from transformer attention heads, defining -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 . 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 normalization suppresses connected non-Gaussian correlators as , yielding a Gaussian NN-QFT in the large-head limit.
关键词
引用
@article{arxiv.2602.10209,
title = {Neural Network Quantum Field Theory from Transformer Architectures},
author = {Dmitry S. Ageev and Yulia A. Ageeva},
journal= {arXiv preprint arXiv:2602.10209},
year = {2026}
}
备注
14 pages; comments are welcome