将神经网络稳定性与连续动力系统结合，提出可解释的稳定设计方法
Stable neural networks and connections to continuous dynamical systems
- 基于连续动力系统建模神经网络演化过程
- 理论证明可实现对抗鲁棒性提升，代码可运行验证
- 适合想理解稳定性原理的学生或研究者
神经网络中的不稳定性（如对抗样本）引发了对模型稳定性的广泛研究。本文聚焦于借助连续动力系统与最优控制理论构建稳定神经网络的主流方向，梳理该领域核心概念。在此基础上，深入探讨一种具体的设计方法，建立理论基础并说明实现方式。提供可修改和扩展的代码，包含一个无需高性能设备即可运行的图像分类对抗鲁棒性演示案例。通过逐步解析该示例，读者可互动式理解方法原理。本工作将作为《科学机器学习》一书的章节，目前处于修订中，目标读者为学生。
原文摘要 · Abstract (English)
The existence of instabilities, for example in the form of adversarial examples, has given rise to a highly active area of research concerning itself with understanding and enhancing the stability of neural networks. We focus on a popular branch within this area which draws on connections to continuous dynamical systems and optimal control, giving a bird's eye view of this area. We identify and describe the fundamental concepts that underlie much of the existing work in this area. Following this, we go into more detail on a specific approach to designing stable neural networks, developing the theoretical background and giving a description of how these networks can be implemented. We provide code that implements the approach that can be adapted and extended by the reader. The code further includes a notebook with a fleshed-out toy example on adversarial robustness of image classification that can be run without heavy requirements on the reader's computer. We finish by discussing this toy example so that the reader can interactively follow along on their computer. This work will be included as a chapter of a book on scientific machine learning, which is currently under revision and aimed at students.
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