中文

Neural Network Quantum Field Theory from Transformer Architectures

机器学习 2026-02-12 v1 无序系统与神经网络 高能物理 - 理论

摘要

We propose a neural-network construction of Euclidean scalar quantum field theories from transformer attention heads, defining nn-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 dkd_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/Nh1/N_h normalization suppresses connected non-Gaussian correlators as 1/Nh1/N_h, 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