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Generalization bounds for neural ordinary differential equations and deep residual networks

Pierre Marion · Pierre Marion

Great Hall & Hall B1+B2 (level 1) #1925
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Thu 14 Dec 8:45 a.m. PST — 10:45 a.m. PST


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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