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 $σ_w^2$, 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.

翻译：我们将架构层级参数提升为在函数空间中演化的慢速随机变量，从而拓展了规范协变随机神经场框架。我们提出的有效理论以经典对易场形式表述，并通过最大李雅普诺夫指数、放大因子和修饰谱核，提供受对称性约束的边缘性与有限宽度效应诊断。在此动力学基础上，我们引入一种与有效模型局部$U(1)$结构相容的马尔可夫演化方案。通过最小化实现，基因型简化为权重方差参数$\sigma_w^2$，而适应度泛函则融合了谱一致性、边缘稳定性以及受对称性约束的临界锚点。比较三种演化模型后，我们发现仅完全受对称性约束的Ginibre $U(1)$版本能稳健逼近窄边缘区域，并再现预测的低频有限宽度谱行为。这些结果支持将对称性引导的有效稳定性诊断作为受控环境下随机架构搜索的实用原则。