Verification of piecewise deep neural networks: a star set approach with zonotope pre-filter

Abstract Verification has emerged as a means to provide formal guarantees on learning-based systems incorporating neural network before using them in safety-critical applications. This paper proposes new verification approach for deep networks (DNNs) with piecewise linear activation functions reachability analysis. The core of our is collection algorithms star sets (or shortly, stars), an effective symbolic representation high-dimensional polytopes. star-based compute the output reachable given input set verification. For functions, can construct both exact and over-approximate network. To enhance scalability approach, equipped outer-zonotope (a zonotope over-approximation set) quickly estimate lower upper bounds at specific neuron determine if splitting occurs that neuron. pre-filtering step reduces significantly number programming optimization problems must be solved analysis, leads reduction computation time, which enhances approach. Our are implemented software prototype called tool, applied analyzing robustness machine learning methods, such safety DNNs. experiments show achieve runtimes twenty 1400 times faster than Reluplex, satisfiability modulo theory-based also less conservative other recent abstract domain approaches.