Deep neural networks as lattice gauge theories

2026-08-19

AI Summary

本文通过将神经网络与量子场论结合，构建了一个格点规范理论模型，用以分析深度神经网络中的信息传播和统计波动问题。

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.

Problem

• Deep neural networks
• Lattice gauge theories
• Layer variance
• Information propagation

Innovation

• lattice gauge theory
• neuron-neuron propagator
• Feynman diagrams
• perturbative expansion
• scattering amplitudes