Dynamic and Scalable Deep Neural Network Verification Algorithm

Deep neural networks have widely used for dealing with complex real-world problems. However, a major concern in applying them to safety-critical systems is the great difficulty in providing formal guarantees about their behavior. Verifying its behavior means study the evolution of its outputs depending on the variation of its inputs. This verification is crucial in an uncertain environment where neural network inputs are noisy. In this paper, we propose an efficient technique for verifying feed-forward neural networks properties. In order to quantify the behavior of the proposed algorithm, we introduce different neural network scenarios to highlight the robustness according to predefined metrics and constraints. The proposed technique is based on the linearization of the non-convex Rectified Linear Unit (ReLU) activation function using the Big-M optimization approach. Moreover, we contribute by an iterative process to find the largest input range verifying (and then defining) the neural network proprieties of neural networks.