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Due to the increasing deployment of Deep Neural Networks (DNNs) in real-worldsecurity-critical domains including autonomous vehicles and collision avoidancesystems, formally checking security properties of DNNs, especially underdifferent attacker capabilities, is becoming crucial. Most existing securitytesting techniques for DNNs try to find adversarial examples without providingany formal security guarantees about the non-existence of such adversarialexamples. Recently, several projects have used different types ofSatisfiability Modulo Theory (SMT) solvers to formally check securityproperties of DNNs. However, all of these approaches are limited by the highoverhead caused by the solver.  In this paper, we present a new direction for formally checking securityproperties of DNNs without using SMT solvers. Instead, we leverage intervalarithmetic to compute rigorous bounds on the DNN outputs. Our approach, unlikeexisting solver-based approaches, is easily parallelizable. We further presentsymbolic interval analysis along with several other optimizations to minimizeoverestimations of output bounds.  We design, implement, and evaluate our approach as part of ReluVal, a systemfor formally checking security properties of Relu-based DNNs. Our extensiveempirical results show that ReluVal outperforms Reluplex, a state-of-the-artsolver-based system, by 200 times on average. On a single 8-core machinewithout GPUs, within 4 hours, ReluVal is able to verify a security propertythat Reluplex deemed inconclusive due to timeout after running for more than 5days. Our experiments demonstrate that symbolic interval analysis is apromising new direction towards rigorously analyzing different securityproperties of DNNs.

Formal Security Analysis of Neural Networks using Symbolic Intervals