[mlthoughts2018]

This paper is explicit that it only applies to sequences of ResNet layers, which happen to have the property that the input and output dimensionalities are equal.

It’s a property of the functional form of stacked ResNet layers that allows the ODE layer to be used instead.

You are right that many networks will require at least some (and usually many) layers that change dimensionality. So ODE layers are not going to wholesale replace anything, apart from possibly submodules of a bigger network where the submodule is made up just of sequences of ResNet layers.

ODE layers will also have new applications, such as for irregularly spaced sequential inputs or outputs.