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Concept-based explanations for convolutional neural networks (CNNs) aim toexplain model behavior and outputs using a pre-defined set of semantic concepts(e.g., the model recognizes scene class ``bedroom'' based on the presence ofconcepts ``bed'' and ``pillow''). However, they often do not faithfully (i.e.,accurately) characterize the model's behavior and can be too complex for peopleto understand. Further, little is known about how faithful and understandabledifferent explanation methods are, and how to control these two properties. Inthis work, we propose UFO, a unified method for controlling Understandabilityand Faithfulness Objectives in concept-based explanations. UFO formalizesunderstandability and faithfulness as mathematical objectives and unifies mostexisting concept-based explanations methods for CNNs. Using UFO, wesystematically investigate how explanations change as we turn the knobs offaithfulness and understandability. Our experiments demonstrate afaithfulness-vs-understandability tradeoff: increasing understandabilityreduces faithfulness. We also provide insights into the ``disagreementproblem'' in explainable machine learning, by analyzing when and howconcept-based explanations disagree with each other.

UFO: A unified method for controlling Understandability and Faithfulness Objectives in concept-based explanations for CNNs