Neural ordinary differential equations (neural ODEs) are a popular family of continuous-depth deep learning models. In this work, we consider a large family of parameterized ODEs with continuous-in-time parameters, which include time-dependent neural ODEs. We derive a generalization bound for this class by a Lipschitz-based argument. By leveraging the analogy between neural ODEs and deep residual networks, our approach yields in particular a generalization bound for a class of deep residual networks. The bound involves the magnitude of the difference between successive weight matrices. We illustrate numerically how this quantity affects the generalization capability of neural networks.

翻译：神经常微分方程（neural ODEs）是一类流行的连续深度深度学习模型。本文考虑一大类含连续时间参数的参数化常微分方程，其中包含时间依赖型神经ODE。我们通过基于Lipschitz条件的论证推导了该类模型的泛化界。利用神经ODE与深度残差网络之间的类比关系，我们的方法特别为某类深度残差网络给出了泛化界。该界涉及相邻权重矩阵之间的差值大小。我们通过数值实验展示了该量如何影响神经网络的泛化能力。