Formal Security Analysis of Neural Networks using Symbolic Intervals
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Due to the increasing deployment of Deep Neural Networks (DNNs) in real-world security-critical domains including autonomous vehicles and collision avoidance systems, formally checking security properties of DNNs, especially under different attacker capabilities, is becoming crucial. Most existing security testing techniques for DNNs try to find adversarial examples without providing any formal security guarantees about the non-existence of adversarial examples. Recently, several projects have used different types of Satisfiability Modulo Theory (SMT) solvers to formally check security properties of DNNs. However, all of these approaches are limited by the high overhead caused by the solver. In this paper, we present a new direction for formally checking security properties of DNNs without using SMT solvers. Instead, we leverage interval arithmetic to formally check security properties by computing rigorous bounds on the DNN outputs. Our approach, unlike existing solver-based approaches, is easily parallelizable. We further present symbolic interval analysis along with several other optimizations to minimize overestimations. We design, implement, and evaluate our approach as part of ReluVal, a system for formally checking security properties of Relu-based DNNs. Our extensive empirical results show that ReluVal outperforms Reluplex, a state-of-the-art solver-based system, by 200 times on average for the same security properties. ReluVal is able to prove a security property within 4 hours on a single 8-core machine without GPUs, while Reluplex deemed inconclusive due to timeout (more than 5 days). Our experiments demonstrate that symbolic interval analysis is a promising new direction towards rigorously analyzing different security properties of DNNs.
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