Robustness Verification of Swish Neural Networks Embedded in Autonomous Driving Systems

With the applications of deep learning in safety-critical domains such as autonomous driving systems gaining ground, it demands rigorous verification to guarantee the safety and reliability of corresponding systems. As the intelligent component in such systems, neural networks (NNs) must be robust in that their outputs are not affected by minor perturbation to inputs. Many research studies have shown that formal methods are effective ways to the robustness verification of NNs. However, most of the existing approaches are focused on NNs that contain monotonic activation functions, such as ReLU, Tanh, and Sigmoid. In this work, we propose an approach to verify the robustness of NNs with the nonmonotonic activation function called Swish. Such networks have been proved to have a better performance on image classification than other NNs. In our approach, we turn the robustness verification problem into a constraint-solving problem using the linear approximation technique. We first model the affine function of an NN into a linear constraint model. Then, for nonlinear activation functions, we leverage an efficient approximation strategy to linearly approximate them. Finally, we utilize the constraint solver gurobi to solve the model, which reveals that the model satisfies the robustness property. We develop a prototype tool and evaluate it with open-sourced NNs. Experimental results showed the effectiveness and efficiency of our approach.