Need to let loose a primal scream without collecting footnotes first? Have a sneer percolating in your system but not enough time/energy to make a whole post about it? Go forth and be mid: Welcome to the Stubsack, your first port of call for learning fresh Awful youāll near-instantly regret.
Any awful.systems sub may be subsneered in this subthread, techtakes or no.
If your sneer seems higher quality than you thought, feel free to cutānāpaste it into its own post ā thereās no quota for posting and the bar really isnāt that high.
The post Xitter web has spawned soo many āesotericā right wing freaks, but thereās no appropriate sneer-space for them. Iām talking redscare-ish, reality challenged āculture criticsā who write about everything but understand nothing. Iām talking about reply-guys who make the same 6 tweets about the same 3 subjects. Theyāre inescapable at this point, yet I donāt see them mocked (as much as they should be)
Like, there was one dude a while back who insisted that women couldnāt be surgeons because they didnāt believe in the moon or in stars? I think each and every one of these guys is uniquely fucked up and if I canāt escape them, I would love to sneer at them.
(Credit and/or blame to David Gerard for starting this.)
I know r/singularity is like shooting fish in a barrel but it really pissed me off seeing them misinterpret the significance of a result in matrix multiplication: https://old.reddit.com/r/singularity/comments/1knem3r/i_dont_think_people_realize_just_how_insane_the/
Yeah, the record has stood for āFIFTY-SIX YEARSā if you donāt count all the times the record has been beaten since then. Indeed, ācountless brilliant mathematicians and computer scientists have worked on this problem for over half a century without successā if you donāt count all the successes that have happened since then. The really annoying part about all this is that the original announcement didnāt have to lie: if you look at just 4x4 matrices, you could say there technically hasnāt been an improvement since Strassenās algorithm. Wow! Itās really funny how these promptfans ignore all the enormous number of human achievements in an area when they decide to comment about how AI is totally gonna beat humans there.
How much does this actually improve upon Strassenās algorithm? The matrix multiplication exponent given by Strassenās algorithm is log4(49) (i.e. log2(7)), and this result would improve it to log4(48). In other words, it improves from 2.81 to 2.79. Truly revolutionary, AGI is gonna make mathematicians obsolete now. Ignore the handy dandy Wikipedia chart which shows that this exponent was ā¦ beaten in 1979.
I know far less about how matrix multiplication is done in practice, but from what Iāve seen, even Strassenās algorithm isnāt useful in applications because memory locality and parallelism are far more important. This AlphaEvolve result would represent a far smaller improvement (and I hope you enjoy the pain of dealing with a 4x4 block matrix instead of 2x2). If anyone does have knowledge about how this works, Iād be interested to know.
Yes - on the theoretical side, they do have an actual improvement, which is a non-asymptotic reduction in the number of multiplications required for the product of two 4x4 matrices over an arbitrary noncommutative ring. You are correct that the implied improvement to omega is moot since theoretical algorithms have long since reduced the exponent beyond that of Strassenās algorithm.
From a practical side, almost all applications use some version of the naive O(n^3) algorithm, since the asymptotically better ones tend to be slower in practice. However, occasionally Strassenās algorithm has been implemented and used - it is still reasonably simple after all. There is possibly some practical value to the 48-multiplications result then, in that it could replace uses of Strassenās algorithm.
Your understanding is correct. Itās worth knowing that the matrix-multiplication exponent actually controls multiple different algorithms. I stubbed a little list a while ago; important examples include several graph-theory algorithms as well as parsing for context-free languages. Thereās also a variant of P vs NP for this specific problem, because we can verify that a matrix is a product in quadratic time.
That Reddit discussion contains mostly idiots, though. We expect an iterative sequence of ever-more-complicated algorithms with ever-slightly-better exponents, approaching quadratic time in the infinite limit. We also expected a computer to be required to compute those iterates at some point; personally I think Strassenās approach only barely fits inside a brain and the larger approaches canāt be managed by humans alone.
Iām not sure what you mean by your last sentence. All of the actual improvements to omega were invented by humans; computers have still not made a contribution to this.
Oh, sorry. Weāre in agreement and my sentence was poorly constructed. The computation of a matrix multiplication usually requires at least pencil and paper, if not a computer. I canāt compute anything larger than a 2 Ć 2. But Iāll readily concede that Strassenās specific trick is simple enough that a mentalist could use it.