Reviews: Efficient and Accurate Estimation of Lipschitz Constants for Deep Neural Networks

Even though other optimization-based certification of Lipschitz constants have been proposed before, the theoretical result leading to the SDP formulation (Theorem 1) is novel. The multiple variants of the main algorithm aim to provide a more scalable method and in part succeeds at doing so (evaluated networks are still relatively simple), and despite the loss in accuracy the less-complex version of the methodology can achieve better or competitive estimation of the constant. On the other hand the authors overplay the fact that any method that estimates a Lipschitz constant on a multilayer network can be trivially parallelized by splitting the network into "chunks". This is not a particular advantage of their method and so I think the claims about the parallel version should be toned down. Even from the trivial upper bound on the Lipschitz constant, given by the product of the layer-wise constants, it is clear that such methods can be easily parallelized.