Before revision:  While several methods were designed to partially mitigate this issue, the underlying causes are poorly understood. In this work we investigate the above phenomenon and show that tightness  may not be the determining factor for reduced certified robustness . Concretely, we identify two key features of relaxations that impact training dynamics: continuity and sensitivity.
After revision:  The poor understanding of this paradox has forced recent state-of-the-art certified defenses to focus on designing various heuristics in order to mitigate its effects. In contrast, in this paper we study the underlying causes and show that tightness may not be the determining factor for reduced certified robustness . Concretely, we identify two key features of relaxations that impact training dynamics: continuity and sensitivity.