The comparison we make is to residual networks, which I think is valid. First, we do parameterize a theta that changes with time, using a hypernet. But this is equivalent to the way sampo wrote the equations above - you can just feed time as another input to the dynamics network to get dynamics that change with time.

Second, I agree that general feedforward nets allow dimension changes, but resnets don't. This model is a drop-in replacement for resnets, but not for any feedforward net. If we gave the wrong impression somewhere, please let us know.

We didn't make the analogy with RNNs, because I don't think it fits - standard input-output RNNs have to take in part of the data with every time step, while here the data only appears at the input (depth 0) layer of the network.