{"ID":2878067,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2508.18948","arxiv_id":"2508.18948","title":"Gauge-covariant stochastic neural fields: Stability and finite-width effects","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.","short_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~Domini...","url_abs":"https://arxiv.org/abs/2508.18948","url_pdf":"https://arxiv.org/pdf/2508.18948v2","authors":"[\"Rodrigo Carmo Terin\"]","published":"2025-08-26T11:41:11Z","proceeding":"hep-th","tasks":"[\"hep-th\",\"cond-mat.dis-nn\",\"cs.LG\",\"stat.ML\"]","methods":"[]","has_code":false}