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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 i
by duvenaud 8y ago
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.
- joe_the_user 8y agoHasn't there been similar work to this in the past? I don't see a "related work" section in your paper.
- duvenaud 8y agoSection 7 is titled "Related Work".
- joe_the_user 8y agoThanks, Apologies for not looking harder
- soVeryTired 8y agoYou're absolutely right - sorry, somehow I managed to miss the explicit time parameter in your equation two, and didn't read carefully enough to see that you were restricting the discussion to resnets and normalising flows. You might be able to make a better connection to RNNs by having the input data as a 'forcing' function in your ODE. But you probably need some regularity conditions on the input data to make sure the result is nicely behaved.
- im3w1l 8y ago> standard input-output RNNs have to take in part of the data with every time step Well they can but I don't see they why they have to. And couldn't your network also take input and give output for all times? > First, we do parameterize a theta that changes with time, using a hypernet. Ah I see. Did you end up using it in the final model? I don't see that in the mnist example, but I could be missing it as I only skimmed the code.