标题： GINN框架：深度神经网络中稳定性和混沌的随机量子电动力学对应关系 显示英文标题

标题： The GINN framework: a stochastic QED correspondence for stability and chaos in deep neural networks

摘要： 一种将深度神经网络（DNN）映射到具有局部U(1)对称性的量子电动力学（QED）的欧几里得随机场论方法被提出。 神经激活和权重由费米物质场和规范场表示，一个虚构的Langevin时间使得规范固定协变。 这种映射将规范参数与宽DNN中的核设计选择相联系，将稳定性阈值与规范依赖的放大因子相关联。 有限宽度波动对应于QED中的环修正。 作为概念验证，我们通过标准多层感知器的数值模拟验证了理论预测，并同时提出了一种使用权重的幅度-相位参数化的规范不变神经网络（GINN）实现。 最后，展示了一种双复制副本方法，以统一计算随机QED和宽DNN中的最大李雅普诺夫指数。 显示英文摘要

摘要： The development of a Euclidean stochastic field-theoretic approach that maps deep neural networks (DNNs) to quantum electrodynamics (QED) with local U(1) symmetry is presented. Neural activations and weights are represented by fermionic matter and gauge fields, with a fictitious Langevin time enabling covariant gauge fixing. This mapping identifies the gauge parameter with kernel design choices in wide DNNs, relating stability thresholds to gauge-dependent amplification factors. Finite-width fluctuations correspond to loop corrections in QED. As a proof of concept, we validate the theoretical predictions through numerical simulations of standard multilayer perceptrons and, in parallel, propose a gauge-invariant neural network (GINN) implementation using magnitude--phase parameterization of weights. Finally, a double-copy replica approach is shown to unify the computation of the largest Lyapunov exponent in stochastic QED and wide DNNs.