A Kernel Perspective for Regularizing Deep Neural Networks
This work provides a theoretical framework for regularization in deep learning, potentially benefiting researchers and practitioners dealing with overfitting and robustness issues, though it appears incremental as it builds on existing principles.
The paper tackles the problem of regularizing deep neural networks by introducing a kernel perspective using reproducing kernel Hilbert space (RKHS) norms, which unifies existing methods and leads to new penalties, showing effectiveness in small datasets and adversarial robustness.
We propose a new point of view for regularizing deep neural networks by using the norm of a reproducing kernel Hilbert space (RKHS). Even though this norm cannot be computed, it admits upper and lower approximations leading to various practical strategies. Specifically, this perspective (i) provides a common umbrella for many existing regularization principles, including spectral norm and gradient penalties, or adversarial training, (ii) leads to new effective regularization penalties, and (iii) suggests hybrid strategies combining lower and upper bounds to get better approximations of the RKHS norm. We experimentally show this approach to be effective when learning on small datasets, or to obtain adversarially robust models.