深度泛化机制的再思考:过参数化与高维噪声扰动下的一致收敛界重构

Deep neural net-works demonstrate both powerful expressive capabilities and exceptional generalization performance, •which fundamentally conflicts -with the classical statistical learning tenet that "model complexity harms generalization" , rendering the analysis of deep generalization mechanisms under traditional frameworks intractable. Classic uniform convergence theory,constrained by its reliance on parameter space dimensionality and neglect of algorithmic implicit bias,fails to directly align with the core characteristics of deep networks. To address this theoretical gap,this paper constructs a novel statistical learning framework that integrates key features of deep models,thereby redefining the explanatory paradigm of uniform convergence theory for deep generalization mechanisms. It derives the first effective uniform convergence bound for deep networks by introducing a surrogate linear model that preserves overparameterization and high-dimensional noise-perturbation features,which reveals a benign role of high-dimensional noise in improving generalization beyond classical low-dimensional theory. Building on this deep generalization mechanism, it further proposes a scale-sensitive regularized training scheme and shows that the bound and the generalization error decay with increasing sample complexity. Supported by both theoretical and empirical evidence, this work breaks through the adaptability bottleneck of uniform convergence bounds and reopens the door for uniform convergence theory to analyze the generalization of deep models.