Formal Monotony Analysis of Neural Networks with Mixed Inputs: An Asset for Certification

Abstract

The use of ML technology to design safety-critical systems requires a complete understanding of the neural network's properties. Among the relevant properties in an industrial context, the verification of partial monotony may become mandatory. This paper proposes a method to evaluate the monotony property using a Mixed Integer Linear Programming (MILP) solver. Contrary to the existing literature, this monotony analysis provides a lower and upper bound of the space volume where the property does not hold, that we denote "Non-Monotonic Space Coverage". This work has several advantages: (i) our formulation of the monotony property works on discrete inputs, (ii) the iterative nature of our algorithm allows for refining the analysis as needed, and (iii) from an industrial point of view, the results of this evaluation are valuable to the aeronautical domain where it can support the certification demonstration. We applied this method to an avionic case study (braking distance estimation using a neural network) where the verification of the monotony property is of paramount interest from a safety perspective.