A Toolbox for Fast Interval Arithmetic in numpy with an Application to
  Formal Verification of Neural Network Controlled Systems
Akash Harapanahalli Saber Jafarpour Samuel Coogan
In this paper, we present a toolbox for interval analysis in 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 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.