Formal specification and SMT verification of quantized neural network for autonomous vehicles

The complexity of Autonomous Vehicles imposes significant challenges to their formal specification and verification, especially when incorporating AI controllers based on quantized neural networks (QNNs), which use fixed-point arithmetic to accommodate the limited computational capabilities of embedded systems. Despite the advantages of QNNs, verification of these networks, whether using integers or bit vectors, has proven to be PSPACE-hard.

Our approach focuses on exhaustively verifying abstract scenarios expressed as Satisfiability Modulo Theories (SMT) proof objectives. We propose a formal verification method for QNNs that involves analyzing a rational approximation of the network with perturbations to ensure that the output sets of the perturbed rational neural network include those of both the QNN and its rational neural network approximation.

The distance between these output sets is computed using the p-norm. To evaluate our methodology, we used the Highway-env autonomous vehicle simulator and z3 SMT solver.