Generalization bounds for neural ordinary differential equations and deep residual networks

• URL: http://arxiv.org/abs/2305.06648v2
• Date: Wed, 11 Oct 2023 21:32:57 GMT
• Title: Generalization bounds for neural ordinary differential equations and deep residual networks
• Authors: Pierre Marion
• Abstract summary: We consider a family of parameterized neural ordinary differential equations (neural ODEs) with continuous-in-time parameters. By leveraging the analogy between neural ODEs and deep residual networks, our approach yields a generalization bound for a class of deep residual networks.
• Score: 1.2328446298523066
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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