  The ubiquity of deep learning algorithms in various applications has
amplified the need for assuring their robustness against small input
perturbations such as those occurring in adversarial attacks. Existing complete
verification techniques offer provable guarantees for all robustness queries
but struggle to scale beyond small neural networks. To overcome this
computational intractability, incomplete verification methods often rely on
convex relaxation to over-approximate the nonlinearities in neural networks.
Progress in tighter approximations has been achieved for piecewise linear
functions. However, robustness verification of neural networks for general
activation functions (e.g., Sigmoid, Tanh) remains under-explored and poses new
challenges. Typically, these networks are verified using convex relaxation
techniques, which involve computing linear upper and lower bounds of the
nonlinear activation functions. In this work, we propose a novel parameter
search method to improve the quality of these linear approximations.
Specifically, we show that using a simple search method, carefully adapted to
the given verification problem through state-of-the-art algorithm configuration
techniques, improves the average global lower bound by 25% on average over the
current state of the art on several commonly used local robustness verification
benchmarks.
