We show that the Rademacher complexity-based approach can generate non-vacuous generalisation bounds on Convolutional Neural Networks (CNNs) for classifying a small number of classes of images. The development of new contraction lemmas for high-dimensional mappings between vector spaces for general Lipschitz activation functions is a key technical contribution. These lemmas extend and improve the Talagrand contraction lemma in a variety of cases. Our generalisation bound can improve Golowich et al. for ReLU DNNs. Furthermore, while prior works that use the Rademacher complexity-based approach primarily focus on ReLU DNNs, our results extend to a broader class of activation functions.

翻译：我们证明，基于Rademacher复杂度的方法能够为卷积神经网络（CNN）在少量图像类别分类任务上生成非平凡的泛化界。本研究的关键技术贡献在于：针对一般Lipschitz激活函数，建立了向量空间之间高维映射的新收缩引理。这些引理在多类情形下扩展并改进了Talagrand收缩引理。我们的泛化界能够改进Golowich等人针对ReLU深度神经网络的研究结果。此外，现有基于Rademacher复杂度的研究主要集中于ReLU深度神经网络，而我们的结果可扩展至更广泛的激活函数类别。