Generalization bounds for neural ordinary differential equations and deep residual networks

Pierre Marion

Keywords: residual neural networks, neural ODEs, generalization bound

TL;DR: We provide generalization bounds for a class of neural ODEs and of deep residual networks.

Abstract: 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.

Submission Number: 4211