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It would be interesting to put this in perspective in regards to total energy savings.

Since so much of computation is matrix multiplication, how much computational power integrated over the next decade would we say that the exponent going from 3->2.3 has saved?

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None. Afaik, all practical implementations of matrix multiplication execute the naive n^3 algorithm because sub-cubic algorithms have too large constant overheads and/or are numerically unstable.

People definitely use the more sophisticated algorithms, it just depends on the size of the matrix. Usually exploring computer architecture is more important than the algo, but at a certain size MMM is definitely faster using state of the art algos.

Fascinating! I wonder if the instability could be kept small enough to be accurate enough for graphic applications (for power savings)… What if the constants were hardware stored in the silicon? :)

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