Web: http://arxiv.org/abs/2205.14612

Sept. 16, 2022, 1:13 a.m. | Michael E. Sander, Pierre Ablin, Gabriel Peyré

stat.ML updates on arXiv.org arxiv.org

Neural Ordinary Differential Equations (Neural ODEs) are the continuous
analog of Residual Neural Networks (ResNets). We investigate whether the
discrete dynamics defined by a ResNet are close to the continuous one of a
Neural ODE. We first quantify the distance between the ResNet's hidden state
trajectory and the solution of its corresponding Neural ODE. Our bound is tight
and, on the negative side, does not go to 0 with depth N if the residual
functions are not smooth with depth. …

arxiv networks neural networks ordinary

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