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.

翻译：神经网络是一类强大的非线性函数。然而，其黑箱特性使得解释其行为并验证其安全性变得困难。抽象技术通过将神经网络转化为更简单的过近似函数来应对这一挑战。遗憾的是，现有抽象技术存在松弛性，这限制了其对输入域中小局部区域的适用性。本文提出全局区间神经网络抽象与中心精确重建（GINNACER）。我们提出的新型抽象技术能够在整个输入域上生成可靠的过近似边界，同时保证对任意给定局部输入实现精确重建。实验表明，GINNACER的紧致性比现有最先进全局抽象技术高出多个数量级，同时与局部抽象技术具有竞争力。