Neural networks are increasingly applied in safety critical domains, their verification thus is gaining importance. A large class of recent algorithms for proving input-output relations of feed-forward neural networks are based on linear relaxations and symbolic interval propagation. However, due to variable dependencies, the approximations deteriorate with increasing depth of the network. In this paper we present DPNeurifyFV, a novel branch-and-bound solver for ReLU networks with low dimensional input-space that is based on symbolic interval propagation with fresh variables and input-splitting. A new heuristic for choosing the fresh variables allows to ameliorate the dependency problem, while our novel splitting heuristic, in combination with several other improvements, speeds up the branch-and-bound procedure. We evaluate our approach on the airborne collision avoidance networks ACAS Xu and demonstrate runtime improvements compared to state-of-the-art tools.
翻译:神经网络越来越多地应用于安全关键领域,因此其核查越来越重要。 证明进向神经网络投入-输出关系的一大批最新算法以线性放松和象征性间隔传播为基础。 但是,由于网络的相互依存性各异,近似随着网络深度的日益加深而恶化。 在本文中,我们介绍了DPneurifyFV, 这是一种新型的分机和开机求解器, 用于使用低维输入空间的ReLU网络, 其基础是象征性的间隔, 以新的变量和输入分割为基础。 选择新变量的新习惯有助于缓解依赖性问题, 而我们的新颖的分机求灵, 结合其他几项改进, 加快了分机程序。 我们评估了ACAS Xu 空中避免碰撞网络的方法, 并展示了与最新工具相比的运行时间改进。