  Neural Networks are used today in numerous security- and safety-relevant
domains and are, as such, a popular target of attacks that subvert their
classification capabilities, by manipulating the network parameters. Prior work
has introduced sensitive samples -- inputs highly sensitive to parameter
changes -- to detect such manipulations, and proposed a gradient ascent-based
approach to compute them. In this paper we offer an alternative, using symbolic
constraint solvers. We model the network and a formal specification of a
sensitive sample in the language of the solver and ask for a solution. This
approach supports a rich class of queries, corresponding, for instance, to the
presence of certain types of attacks. Unlike earlier techniques, our approach
does not depend on convex search domains, or on the suitability of a starting
point for the search. We address the performance limitations of constraint
solvers by partitioning the search space for the solver, and exploring the
partitions according to a balanced schedule that still retains completeness of
the search. We demonstrate the impact of the use of solvers in terms of
functionality and search efficiency, using a case study for the detection of
Trojan attacks on Neural Networks.
