论文标题
一类神经差分方程的一般类别的可及性分析
Reachability Analysis of a General Class of Neural Ordinary Differential Equations
论文作者
论文摘要
在过去的几年中，连续的深度学习模型（称为神经普通微分方程（神经odes））受到了很大的关注。尽管它们的影响迅速，但这些系统缺乏正式的分析技术。在本文中，我们考虑了一类具有不同架构和层次的神经odes类，并引入了一种新颖的可及性框架，可以对其行为进行正式分析。用于神经ODE的可及性分析开发的方法是在一种名为NNVODE的新工具中实现的。具体而言，我们的工作扩展了现有的神经网络验证工具以支持神经ODE。我们通过分析包括用于分类的神经ODE的一组基准，以及控制和动态系统的一组基准来证明我们方法的功能和功效，包括评估我们方法在持续时间到达系统中现有软件工具的功效和能力，以便在可能的情况下进行。
Continuous deep learning models, referred to as Neural Ordinary Differential Equations (Neural ODEs), have received considerable attention over the last several years. Despite their burgeoning impact, there is a lack of formal analysis techniques for these systems. In this paper, we consider a general class of neural ODEs with varying architectures and layers, and introduce a novel reachability framework that allows for the formal analysis of their behavior. The methods developed for the reachability analysis of neural ODEs are implemented in a new tool called NNVODE. Specifically, our work extends an existing neural network verification tool to support neural ODEs. We demonstrate the capabilities and efficacy of our methods through the analysis of a set of benchmarks that include neural ODEs used for classification, and in control and dynamical systems, including an evaluation of the efficacy and capabilities of our approach with respect to existing software tools within the continuous-time systems reachability literature, when it is possible to do so.
