Deep neural networks as lattice gauge theories
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 ...
| Authors | Ro Jefferson, Shradha Ramakrishnan |
|---|---|
| Primary category | hep-th |
| Published | 19 August 2026 |
| Last updated at source | 19 August 2026 |
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