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The rapid growth of deep learning applications in real life is accompanied bysevere safety concerns. To mitigate this uneasy phenomenon, much research hasbeen done providing reliable evaluations of the fragility level in differentdeep neural networks. Apart from devising adversarial attacks, quantifiers thatcertify safeguarded regions have also been designed in the past five years. Thesummarizing work of Salman et al. unifies a family of existing verifiers undera convex relaxation framework. We draw inspiration from such work and furtherdemonstrate the optimality of deterministic CROWN (Zhang et al. 2018) solutionsin a given linear programming problem under mild constraints. Given thistheoretical result, the computationally expensive linear programming basedmethod is shown to be unnecessary. We then propose an optimization-basedapproach \textit{FROWN} (\textbf{F}astened C\textbf{ROWN}): a general algorithmto tighten robustness certificates for neural networks. Extensive experimentson various networks trained individually verify the effectiveness of FROWN insafeguarding larger robust regions.

Fastened CROWN: Tightened Neural Network Robustness Certificates