I skipped to the table at the end. The gains don't seem enormous. Is there a kind of problem where we would expect quaternions to perform dramatically better than other kinds of numbers?
Not to mention that it appears they're comparing against networks of the same architecture. If you build your quaternion components with with same number types as your reals you effectively have 4 times the number of parameters, which could be most of the benefit. They should also benchmark against similar architectures with equivalent parameter counts.
Hi I'm one of the authors of this paper. Sorry if it unclear, but we reduce the number of filters per layer to account for this. The quaternion networks actually have fewer parameters.
Can you provide some technical details on what you do? Do you divide the number of channels on each real layered network by 4? I don't see anything describing this in the paper.
Yes that is exactly what we do.
This paper was mostly to lay out the framework and give out the Keras layers for others to use. We expect that the biggest improvements will come from segmentation where the gains may come from treating each color channel as an imaginary axis. And from architectures like PointNet https://arxiv.org/abs/1612.00593.