

Old McDonald had a startup, iyo io o[4-mini].
It’s funny how just today in a completely unrelated context a generative ai enthusiast used an example of OpenAI getting sued by NYT as a reason why they wouldn’t commit some other malfeasance because they’d get caught if they did.
One thing that I couldn’t easily figure out is what is the constant factor. If the constant factor is significantly worse than for Strassen, then it would be much slower than Strassen except for very large matrices.
Let’s say the constant factor is k.
N should be large enough that N^((log(49)-log(48))/log(4)) > k where k is the constant factor. Let’s say the difference in exponents is x, then
N^x > k
log(N)*x > log(k)
N > exp(log(k)/x)
N > k^(1/x)
So lets say x is 0.01487367169 , then we’re talking [constant factor]^67 for how big the matrix has to be?
So, 2^67 sized matrix (2^134 entries in it) if Google’s is 2x greater constant than Strassen.
That don’t even sound right, but I double checked, (k^67) ^ 0.01487367169 is approximately k.
edit: I’m not sure what the cross over points would be if you use Google’s then Strassen’s then O( n^3 )
Also, Strassen’s algorithm works on reals (and of course, on complex numbers), while the new “improvement” reduces by 1 the number of real multiplications required for a product of two 4x4 complex-valued matrices.