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Thanks for posting it!
It should be possible to get large speedups on CPUs, but the trick will be gradually approximating each of the layers in the model (see my reply to sibling comment). It's not conceptually difficult, but will require a fair amount of C++ work to port the code to GPUs* for training; and it will probably go slower than dense ops on modern GPUs due to tensor cores not supporting our memory layout.
I think of this paper as the first in a two-part series, where the next one takes these fast ops and gets them working in full neural nets. (If anyone wants to do this project, happy to coadvise you / talk about it whenever; I won't have bandwidth to do it myself for the foreseeable future).
*Someone recently started doing this as part of their master's thesis: https://github.com/joennlae/halutmatmul
This master's thesis sort of does it, but it doesn't have any fine-tuning yet so it completely wrecks the accuracy: https://github.com/joennlae/halutmatmul.
If someone worked on contributing this to Composer [1] I'd be down to help out. I can't justify building it all on my own right now since we're 100% focused on training speedup, but I could definitely meet and talk through it, help code tricky parts, review PRs, etc.
[1] https://github.com/mosaicml/composer