Neural Network Quantum Field Theory from Transformer Architectures

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 dk→∞. 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/Nh normalization suppresses connected non-Gaussian correlators as 1/Nh, yielding a Gaussian NN-QFT in the large-head limit.