Gauge-covariant stochastic neural fields: Stability and finite-width effects

ArXi:2508.18948v2 Announce Type: replace-cross 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 Lyapuno exponent and the amplification factor for the edge of chaos.