Deep neural networks as lattice gauge theories

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.

High Energy Physics - Theory (hep-th); Disordered Systems and Neural Networks (cond-mat.dis-nn); Machine Learning (cs.LG)

arXiv:2608.19331 [hep-th]

(or arXiv:2608.19331v1 [hep-th] for this version)

https://doi.org/10.48550/arXiv.2608.19331 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.

Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.

Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.