Neural Network Quantum Field Theory from Transformer Architectures
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , |
|---|---|
| Format: | Preprint |
| Publié: |
2026
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866911439247114240 |
|---|---|
| author | Ageev, Dmitry S. Ageeva, Yulia A. |
| author_facet | Ageev, Dmitry S. Ageeva, Yulia A. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_10209 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Neural Network Quantum Field Theory from Transformer Architectures Ageev, Dmitry S. Ageeva, Yulia A. Machine Learning Disordered Systems and Neural Networks High Energy Physics - Theory 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. |
| title | Neural Network Quantum Field Theory from Transformer Architectures |
| topic | Machine Learning Disordered Systems and Neural Networks High Energy Physics - Theory |
| url | https://arxiv.org/abs/2602.10209 |