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One major drawback of deep convolutional neural networks (CNNs) for use insafety critical applications is their black-box nature. This makes it hard toverify or monitor complex, symbolic requirements on already trained computervision CNNs. In this work, we present a simple, yet effective, approach toverify that a CNN complies with symbolic predicate logic rules which relatevisual concepts. It is the first that (1) does not modify the CNN, (2) may usevisual concepts that are no CNN in- or output feature, and (3) can leveragecontinuous CNN confidence outputs. To achieve this, we newly combine methodsfrom explainable artificial intelligence and logic: First, using supervisedconcept embedding analysis, the output of a CNN is post-hoc enriched by conceptoutputs. Second, rules from prior knowledge are modelled as truth functionsthat accept the CNN outputs, and can be evaluated with little computationaloverhead. We here investigate the use of fuzzy logic, i.e., continuous truthvalues, and of proper output calibration, which both theoretically andpractically show slight benefits. Applicability is demonstrated onstate-of-the-art object detectors for three verification use-cases, wheremonitoring of rule breaches can reveal detection errors.

Enabling Verification of Deep Neural Networks in Perception Tasks Using Fuzzy Logic and Concept Embeddings