Year: 2026
Type: article
Abstract: We develop a gauge-covariant stochastic effective field theory for stability and finite-width effects in deep neural systems. The model uses classical commuting fields: a complex matter field, a real Abelian connection field, and a fictitious stochastic depth variable. Using the Martin–Siggia–Rose–Janssen–de Dominicis formalism, we derive its functional representation and a two-replica linear-response construction defining the maximal Lyapunov exponent and the amplification factor for the edge of chaos. Finite-width effects appear as perturbative corrections to dressed kernels, and the marginality condition remains unchanged at the order considered for fixed kernel geometry. Numerically, finite-width multilayer perceptrons follow the mean-field instability threshold, and a linear stochastic effective sector reproduces the predicted low-frequency spectral deformation.
Source: Scientific Reports
Author: Rodrigo Carmo Terin
Institution: Universidad Rey Juan Carlos
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $2,690
OpenAlex ID: W7150751607