Effective Certification of Monotone Deep Equilibrium Models

Abstract

Monotone Operator Equilibrium Models (monDEQs) represent a class of models combining the powerful deep equilibrium paradigm with convergence guarantees. Further, their inherent robustness to adversarial perturbations makes investigating their certifiability a promising research direction. Unfortunately, existing approaches are either imprecise or severely limited in scalability. In this work, we propose the first scalable and precise monDEQ verifier, based on two key ideas: (i) a novel convex relaxation enabling efficient inclusion checks, and (ii) non-trivial mathematical insights characterizing the fixpoint operations at the heart of monD-EQs on sets rather than concrete inputs. An extensive evaluation of our verifier on the challenging ∞ perturbations demonstrates that it exceeds state-of-the-art performance in terms of speed (two orders of magnitude) and scalability (an order of magnitude) while yielding 25% higher certified accuracies on the same networks.