mlsanityData to 14 Oct 2026

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

arXiv 2508.18948 ↗First posted 26 Aug 2025hep-th cond-mat.dis-nn cs.LGcited by 3

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Abstract (arXiv)

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.

Key facts. Cited by 3 papers in the map (data through 14 Oct 2026). Builds on 18 of its 52 references that are in the map. First posted on arXiv 26 Aug 2025.

Builds on

18 of 52 references.

References · 18

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6 more
  1. 2021The edge of chaos: quantum field theory and deep neural networkscited by 24
  2. 2022Gauge Equivariant Neural Networks for 2+1D U(1) Gauge Theory Simulations in Hamiltonian Formulationcited by 11
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Cited by year (2026 to 14 Oct)

Citing papers per year: 2025: 1; 2026: 2.

3 papers.

  1. 2026Scale redundancy and soft gauge fixing in positively homogeneous neural networkscited by 2
  2. 2025Spectral functions in Minkowski quantum electrodynamics from neural reconstructioncited by 1
  3. 2026Spinning Conformal Correlators from Neural Networkscited by 1