  Neural networks are a powerful class of non-linear functions. However, their
black-box nature makes it difficult to explain their behaviour and certify
their safety. Abstraction techniques address this challenge by transforming the
neural network into a simpler, over-approximated function. Unfortunately,
existing abstraction techniques are slack, which limits their applicability to
small local regions of the input domain. In this paper, we propose Global
Interval Neural Network Abstractions with Center-Exact Reconstruction
(GINNACER). Our novel abstraction technique produces sound over-approximation
bounds over the whole input domain while guaranteeing exact reconstructions for
any given local input. Our experiments show that GINNACER is several orders of
magnitude tighter than state-of-the-art global abstraction techniques, while
being competitive with local ones.
