Uniform convergence does not effectively account for generalization within the domain of deep learning.

本研究意义：揭示基于统一收敛（u.c.）的界限存在局限性，质疑统一收敛界限在解释深度学习泛化能力方面的有效性。

1. 强调阐明泛化误差对训练集规模的依赖性，显然与阐明其对参数数量的依赖性同样具有复杂性。
2. 展示在某些情况下，无论如何巧妙地应用所有统一收敛界限，这些界限都将变得毫无意义。

Development of generalisation bound

stage 1：conventional u.c. bound

\text{generalisation gap} \leq O\Big(\sqrt{\frac{\text{representational complexity of whole hypothesis class}}{\text{training set size}}}\Big)
con: representational complexity \propto depth\timeswidth – too vacuous for deep networks

精炼U.C.界：考虑SGD隐含偏差

$\text{generalisation gap} \leq O\Big(\sqrt{\frac{\text{representational complexity of 'relevant' subse