Prioritizing Corners in OoD Detectors via Symbolic String Manipulation

For safety assurance of deep neural networks (DNNs), out-of-distribution (OoD) monitoring techniques are essential as they filter spurious input that is distant from the training dataset. This paper studies the problem of systematically testing OoD monitors to avoid cases where an input data point is tested as in-distribution by the monitor, but the DNN produces spurious output predictions. We consider the definition of "in-distribution" characterized in the feature space by a union of hyperrectangles learned from the training dataset. Thus the testing is reduced to finding corners in hyperrectangles distant from the available training data in the feature space. Concretely, we encode the abstract location of every data point as a finite-length binary string, and the union of all binary strings is stored compactly using binary decision diagrams (BDDs). We demonstrate how to use BDDs to symbolically extract corners distant from all data points within the training set. Apart from test case generation, we explain how to use the proposed corners to fine-tune the DNN to ensure that it does not predict overly confidently. The result is evaluated over examples such as number and traffic sign recognition.