A Toolbox for Fast Interval Arithmetic in numpy with an Application to Formal Verification of Neural Network Controlled Systems

In this paper, we present a toolbox for interval analysis in \texttt{numpy}, with an application to formal verification of neural network controlled systems. Using the notion of natural inclusion functions, we systematically construct interval bounds for a general class of mappings. The toolbox offers efficient computation of natural inclusion functions using compiled C code, as well as a familiar interface in \texttt{numpy} with its canonical features, such as $n$-dimensional arrays, matrix/vector operations, and vectorization. We then use this toolbox in formal verification of dynamical systems with neural network controllers, through the composition of their inclusion functions.