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In this paper, we present BERN-NN as an efficient tool to perform boundpropagation of Neural Networks (NNs). Bound propagation is a critical step inwide range of NN model checkers and reachability analysis tools. Given abounded input set, bound propagation algorithms aim to compute tight bounds onthe output of the NN. So far, linear and convex optimizations have been used toperform bound propagation. Since neural networks are highly non-convex,state-of-the-art bound propagation techniques suffer from introducing largeerrors. To circumvent such drawback, BERN-NN approximates the bounds of eachneuron using a class of polynomials called Bernstein polynomials. Bernsteinpolynomials enjoy several interesting properties that allow BERN-NN to obtaintighter bounds compared to those relying on linear and convex approximations.BERN-NN is efficiently parallelized on graphic processing units (GPUs).Extensive numerical results show that bounds obtained by BERN-NN are orders ofmagnitude tighter than those obtained by state-of-the-art verifiers such aslinear programming and linear interval arithmetic. Moreoveer, BERN-NN is bothfaster and produces tighter outputs compared to convex programming approacheslike alpha-CROWN.

BERN-NN: Tight Bound Propagation For Neural Networks Using Bernstein Polynomial Interval Arithmetic