We show that the Rademacher complexity-based framework can establish non-vacuous generalization bounds for Convolutional Neural Networks (CNNs) in the context of classifying a small set of image classes. A key technical advancement is the formulation of novel contraction lemmas for high-dimensional mappings between vector spaces, specifically designed for general Lipschitz activation functions. These lemmas extend and refine the Talagrand contraction lemma across a broader range of scenarios. Our Rademacher complexity bound provides an enhancement over the results presented by Golowich et al. for ReLU-based Deep Neural Networks (DNNs). Moreover, while previous works utilizing Rademacher complexity have primarily focused on ReLU DNNs, our results generalize to a wider class of activation functions.

翻译：我们证明，在分类少量图像类别的任务中，基于Rademacher复杂度的理论框架能够为卷积神经网络（CNNs）建立非平凡的泛化界。关键技术进展在于提出了针对向量空间之间高维映射的新型收缩引理，这些引理专门为一般的Lipschitz激活函数设计。这些引理扩展并改进了Talagrand收缩引理在更广泛场景下的适用性。我们的Rademacher复杂度界改进了Golowich等人针对基于ReLU的深度神经网络（DNNs）所提出的结果。此外，以往基于Rademacher复杂度的研究主要集中于ReLU DNNs，而我们的结果可推广至更广泛的激活函数类别。