Despite their success, deep neural networks suffer from several drawbacks: they lack robustness to small changes of input data known as "adversarial examples" and training them with small amounts of annotated data is challenging. In this work, we study the connection between regularization and robustness by viewing neural networks as elements of a reproducing kernel Hilbert space (RKHS) of functions and by regularizing them using the RKHS norm. Even though this norm cannot be computed, we consider various approximations based on upper and lower bounds. These approximations lead to new strategies for regularization, but also to existing ones such as spectral norm penalties or constraints, gradient penalties, or adversarial training. Besides, the kernel framework allows us to obtain margin-based bounds on adversarial generalization. We study the obtained algorithms for learning on small datasets, learning adversarially robust models, and discuss implications for learning implicit generative models.

通过使用再生核希尔伯特空间的范数作为正则化深度神经网络的新视角来提高学习效果，并提出了一些新的有效的正则化策略，实验结果表明这种方法在小数据集或对抗鲁棒性较高的模型上都取得了很好的效果。

深度神经网络正则化的核视角