1-Lipschitz Layers Compared: Memory, Speed, and Certifiable Robustness
Bernd Prach Fabio Brau Giorgio Buttazzo Christoph H. Lampert
The robustness of neural networks against input perturbations with bounded
magnitude represents a serious concern in the deployment of deep learning
models in safety-critical systems. Recently, the scientific community has
focused on enhancing certifiable robustness guarantees by crafting 1-Lipschitz
neural networks that leverage Lipschitz bounded dense and convolutional layers.
Although different methods have been proposed in the literature to achieve this
goal, understanding the performance of such methods is not straightforward,
since different metrics can be relevant (e.g., training time, memory usage,
accuracy, certifiable robustness) for different applications. For this reason,
this work provides a thorough theoretical and empirical comparison between
methods by evaluating them in terms of memory usage, speed, and certifiable
robust accuracy. The paper also provides some guidelines and recommendations to
support the user in selecting the methods that work best depending on the
available resources. We provide code at
https://github.com/berndprach/1LipschitzLayersCompared.