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With the increasing adoption of Deep Learning (DL) for critical tasks, suchas autonomous driving, the evaluation of the quality of systems that rely on DLhas become crucial. Once trained, DL systems produce an output for anyarbitrary numeric vector provided as input, regardless of whether it is withinor outside the validity domain of the system under test. Hence, the quality ofsuch systems is determined by the intersection between their validity domainand the regions where their outputs exhibit a misbehaviour. In this paper, weintroduce the notion of frontier of behaviours, i.e., the inputs at which theDL system starts to misbehave. If the frontier of misbehaviours is outside thevalidity domain of the system, the quality check is passed. Otherwise, theinputs at the intersection represent quality deficiencies of the system. Wedeveloped DeepJanus, a search-based tool that generates frontier inputs for DLsystems. The experimental results obtained for the lane keeping component of aself-driving car show that the frontier of a well trained system containsalmost exclusively unrealistic roads that violate the best practices of civilengineering, while the frontier of a poorly trained one includes many validinputs that point to serious deficiencies of the system.

Model-based Exploration of the Frontier of Behaviours for Deep Learning System Testing