Deep neural networks as lattice gauge theories

• URL: http://arxiv.org/abs/2608.19331v1
• Date: Wed, 19 Aug 2026 18:00:13 GMT
• Title: Deep neural networks as lattice gauge theories
• Abstract summary: We compute the tree-level neuron-neuron propagator which describes the evolution of layer variance in the network.<n>We present a preliminary analysis of neuron scattering amplitudes that contribute order-by-order in $1/N$, which provides a field-theoretic framework for studying higher-point correlations.
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We modify the NN/QFT duality [1] to incorporate the layerwise permutation symmetry of the network, resulting in a $(0\!+\!1)$-dimensional lattice gauge theory, in which each layer of $N$ neurons acts as an $N$-component lattice site, and the weight matrices play the role of gauge fields living on the links. In this framework, we compute the tree-level neuron-neuron propagator which describes the evolution of layer variance in the network, and develop the Feynman diagram machinery to compute interactions in the perturbative expansion in $1/N$. In particular, we obtain a recursive expression for all corrections to the exact propagator at $O(1)$, representing statistical fluctuations in the ensemble of networks, including infinitely-many loop diagrams mediating the interactions from previous layers. We also present a preliminary analysis of neuron scattering amplitudes that contribute order-by-order in $1/N$, which provides a field-theoretic framework for studying higher-point correlations, and by extension information propagation, in deep networks. We remark on some interesting directions for future work at the intersection of neural networks and quantum field theory.

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