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A plethora of methods have been proposed to explain how deep neural networksreach their decisions but comparatively, little effort has been made to ensurethat the explanations produced by these methods are objectively relevant. Whileseveral desirable properties for trustworthy explanations have been formulated,objective measures have been harder to derive. Here, we propose two newmeasures to evaluate explanations borrowed from the field of algorithmicstability: mean generalizability MeGe and relative consistency ReCo. We conductextensive experiments on different network architectures, common explainabilitymethods, and several image datasets to demonstrate the benefits of the proposedmeasures.In comparison to ours, popular fidelity measures are not sufficient toguarantee trustworthy explanations.Finally, we found that 1-Lipschitz networksproduce explanations with higher MeGe and ReCo than common neural networkswhile reaching similar accuracy. This suggests that 1-Lipschitz networks are arelevant direction towards predictors that are more explainable andtrustworthy.

How Good is your Explanation? Algorithmic Stability Measures to Assess the Quality of Explanations for Deep Neural Networks