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
6/27/2023
eess.SYcs.LGmath.OC

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Abstract

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.

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Cite this paper

@article{harapanahalli2023toolbox,
  title  = {A Toolbox for Fast Interval Arithmetic in numpy with an Application to Formal Verification of Neural Network Controlled Systems},
  author = {Akash Harapanahalli and Saber Jafarpour and Samuel Coogan},
  year   = {2023},
  eprint = {2306.15340},
  archivePrefix = {arXiv},
  url    = {http://arxiv.org/abs/2306.15340v1}
}

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