fdej · HackerTrans

If you don't want to allow division by 2 then there is Winograd's algorithm from 1967 which works over any commutative ring and uses 48 multiplications for 4 x 4.

fdej

tahun laludiscuss

> From the paper, "Notably, for multiplying two 4 × 4 matrices, applying the algorithm of Strassen recursively results in an algorithm with 49 multiplications, which works over any field...AlphaEvolve is the first method to find an algorithm to multiply two 4 × 4 complex-valued matrices using 48 multiplications."

...but Waksman's algorithm from 1970 [1] multiplies two 4 x 4 complex-valued matrices using only 46 multiplications (indeed, it works in any ring admitting division by 2).

Sloppy by DeepMind and by Nature to publish such a claim - did they not ask someone knowledgeable about matrix multiplication to review the work?

[1] https://doi.org/10.1109/T-C.1970.222926

fdej

tahun laludiscuss

Just check for the existence of at least one odd digit mod 10^B for some well chosen B.

Here is a C program that does the verification up to 2^(10^10) in 30 seconds: https://gist.github.com/fredrik-johansson/8924e10e5d74e39109...

Edit: made it multithreaded, goes up to 2^(10^12) in nine minutes on 8 cores.

fdej

2 tahun yang laludiscuss

There's no a priori reason why the expected success rate of research projects should be 50% and not, say, 1% or 99%.

fdej

13 tahun yang laludiscuss

Every time you add a new property to Player, wouldn't you be forced to update all such functions to pass along the extra properties?

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