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A bit of a shallow point, but will anyone ever actually implement this algorithm?

I'm having trouble seeing the value of such a paper -- the size of matrices required for this result to have a clear advantage is significant, and that is completely ignoring constant factors, real world performance and parallelization considerations.

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No, these algorithms are impractical, but their utility is in shedding more light on the matrix multiplication problem. So it enables further study, which could lead to more practical advances.

Right, from what I can tell the Strassen algorithm has been implemented but the others are typically pseudocode only...

http://stackoverflow.com/questions/1920031/strassens-algorit...

Yes, Strassen is straightforward to implement and makes a huge difference. Another practical algorithm applicable over small Galois fields is the "method of the four Russions" (none of whom are Russian). It's often used as a basecase for Strassen when multiplying matrices over GF2, which has a number of applications in the real world, including crypto research.

Not sure what sizes apply here, but there are cases (many ML algos use large matrices) where this can be useful. Agree on the parallelization considerations, though.

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