  Neural networks are increasingly applied in safety critical domains, their
verification thus is gaining importance. A large class of recent algorithms for
proving input-output relations of feed-forward neural networks are based on
linear relaxations and symbolic interval propagation. However, due to variable
dependencies, the approximations deteriorate with increasing depth of the
network. In this paper we present DPNeurifyFV, a novel branch-and-bound solver
for ReLU networks with low dimensional input-space that is based on symbolic
interval propagation with fresh variables and input-splitting. A new heuristic
for choosing the fresh variables allows to ameliorate the dependency problem,
while our novel splitting heuristic, in combination with several other
improvements, speeds up the branch-and-bound procedure. We evaluate our
approach on the airborne collision avoidance networks ACAS Xu and demonstrate
runtime improvements compared to state-of-the-art tools.
