Neuro-evolutionary stochastic architectures in gauge-covariant neural fields

TL;DR

This paper introduces a gauge-covariant stochastic neural-field framework with an evolutionary scheme that uses symmetry constraints to guide architecture search, demonstrating robustness in approaching marginal regimes.

Contribution

It extends neural-field models with architecture-level stochastic parameters and develops a symmetry-constrained evolutionary scheme for neural architecture optimization.

Findings

Symmetry-constrained models robustly approach near-marginal regimes.

The fully symmetry-constrained Ginibre U(1) model reproduces spectral behavior.

Effective stability diagnostics can guide stochastic architecture search.

Abstract

We extend our gauge-covariant stochastic neural-field framework by promoting architecture-level parameters to slow stochastic variables evolving in function space. Our effective theory is formulated in terms of classical commuting fields and provides symmetry-constrained diagnostics of marginality and finite-width effects through the maximal Lyapunov exponent, the amplification factor, and dressed spectral kernels. On top of this dynamics, we introduce a Markovian evolutionary scheme compatible with the local $U(1)$ structure of the effective model. By using a minimal implementation, the genotype is reduced to the weight-variance parameter $\sigma_w^2$, and the fitness functional combines spectral agreement, marginal stability, and a symmetry-constrained critical anchor. Comparing three evolutionary models, we find that only the fully symmetry-constrained Ginibre $U(1)$ version robustly approaches a narrow near-marginal regime and reproduces the predicted low-frequency finite-width spectral behavior. These results support the use of symmetry-guided effective stability diagnostics as practical principles for stochastic architecture search in controlled settings.