How good is your explanation? Algorithmic stability measures to assess the qualityof explanations for deep neural networks

A plethora of methods have been proposed to explain howdeep neural networks reach a decision but comparativelylittle effort has been made to ensure that the explanationsproduced by these methods are objectively relevant. Whiledesirable properties for a good explanation are easy to come,objective measures have been harder to derive. Here, we pro-pose two new measures to evaluate explanations borrowedfrom the field of algorithmic stability: relative consistencyReCo and mean generalizability MeGe. We conduct severalexperiments on multiple image datasets and network archi-tectures to demonstrate the benefits of the proposed measuresover representative methods. We show that popular fidelitymeasures are not sufficient to guarantee good explanations.Finally, we show empirically that 1-Lipschitz networks pro-vide general and consistent explanations, regardless of theexplanation method used, making them a relevant directionfor explainability.