Research
Gauge-covariant stochastic neural fields: Stability and finite-width effects
arXiv:2508.18948v2 Announce Type: replace-cross Abstract: We develop a gauge-covariant stochastic effective field theory for stability and finite-width effects in deep neural systems. The model uses c
arXiv:2508.18948v2 Announce Type: replace-cross 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.
Related
- Collective Kernel EFT for Pre-activation ResNets
- Random Matrix Theory for Deep Learning: Beyond Eigenvalues of Linear Models
- Stochastic Gradient Descent in the Saddle-to-Saddle Regime of Deep Linear Networks
- Asymptotic behavior of eigenvalues of large rank perturbations of large random matrices
Source: arXiv cs.LG | 2026-04-23