The coupling effect of Lipschitz regularization in deep neural networks
This addresses robustness issues in neural networks for applications sensitive to input noise, but it is incremental as it builds on existing regularization techniques.
The paper investigates how Lipschitz regularization affects robustness in deep neural networks under input uncertainties, showing that it creates a coupling effect across layers that leads to a tradeoff between robustness and expressiveness, with evidence provided on a dataset.
We investigate robustness of deep feed-forward neural networks when input data are subject to random uncertainties. More specifically, we consider regularization of the network by its Lipschitz constant and emphasize its role. We highlight the fact that this regularization is not only a way to control the magnitude of the weights but has also a coupling effect on the network weights accross the layers. We claim and show evidence on a dataset that this coupling effect brings a tradeoff between robustness and expressiveness of the network. This suggests that Lipschitz regularization should be carefully implemented so as to maintain coupling accross layers.