alt Hacker Newsone of the early premises of how ai takeoff would go was that a system that could solve open problems in advanced mathematics would also discover novel advances in math and computer science that directly unlock drastically better software performance. we are seeing frontier level math breakthroughs (ie performance that would put it in the top 100 or 1000 mathematicians in the world if it were a human, meaning top .00001% or 800/8B). we are also seeing incredible advances in software performance. open ai announced like 15% improvement by fixing gpu kernel issues. these are clearly linked in the sense of scaling laws and generalization of intelligence: a huge model gets capabilities in both math and software engineering that isn't possible at smaller scales.
but it seems less likely to me than before that the types of math/science discoveries will explicitly unlock better software performance. in some sense this fits our intuitions. when top tech companies use math PhD type employees, they have them stop doing pure math research and instead focus on software engineering. these people are often very good at software engineering but not due to recent discoveries in academic mathematics, it's due to their general intelligence. to me, this is evidence that the models are getting better but does not make me think we are on the cusp of a foom style fast takeoff enabled by revolutions in frontier math (i also posted this on twitter @mlipman13)
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> but it seems less likely to me than before that the types of math/science discoveries will explicitly unlock better software performance.
You seem to overlook a simpler barrier. To make these advances, they have to be possible. A 15% improvement in GPU kernels doesn't evidence that significantly more improvement has been left on the table.
Correct me if I'm wrong, but all of the aforementioned advances were made in the last year? Until very recently few people had access to these tools. Most people still don't know how to use ChatGPT, and very few use tools like CC regularily. If in a few years these frontier tools become commonplace and people upskill we would should see a network effect?
This makes no sense. To believe this you have to think that the models are somehow being overfit explicitly on academic mathematics and it doesn’t carry over at all to more practical software engineering. I wouldn’t make that bet.
This will depend on the problem; I expect big algorithmic performance improvements in AI since the algorithms are still new, inefficent, and constantly being improved. But maybe not for sorting, fast fourier transforms, or other well-studied basic algorithms?
> we are also seeing incredible advances in software performance
Incredible?
> open ai announced like 15% improvement by fixing gpu kernel issue
That is... ordinary software optimization.
> novel advances in math
> we are seeing frontier level math breakthroughs (ie performance that would put it in the top 100 or 1000 mathematicians in the world if it were a human, meaning top .00001% or 800/8B)
i think you have misunderstanding of what mathematicians do
I don’t really like AI but let’s stop kidding ourselves, no human mathematician could make progress on a dozen major open problems in a week or two. If you’re measuring it against humans then it is by far the best mathematician to ever live.