51–60 of 564 posts
Earlier quoted context omitted.
They're def gonna go after the Riemann hypothesis with this, hehe.
Guessing the context here is that the RH was recently translated into Lean. Would be very cool if they threw their compute on that
So I am extremely hyped about this, but it's not clear to me how much heavy lifting this sentence is doing: > First, the problems were manually translated into formal mathematical language for our systems to understand. The non-geometry problems which were solved were all of the form "Determine all X such that…", and the resulting theorem statements are all of the form "We show that the set of all X is {foo}". The do…
> While the problem statements were formalized into Lean by hand, the answers within the problem statements were generated and formalized by the agent.
However, it's unclear what initial format was given to the agents that allowed this step
So I am extremely hyped about this, but it's not clear to me how much heavy lifting this sentence is doing: > First, the problems were manually translated into formal mathematical language for our systems to understand. The non-geometry problems which were solved were all of the form "Determine all X such that…", and the resulting theorem statements are all of the form "We show that the set of all X is {foo}". The do…
The computer did find the answers itself. I.e., it found "even integers" for P1, "{1,1}" for P2, and "2" for P6. It then also provided provided a Lean proof in each case.
> First, the problems were manually translated into formal mathematical language for our systems to understand. In the official competition, students submit answers in two sessions of 4.5 hours each. Our systems solved one problem within minutes and took up to three days to solve the others. Three days is interesting... Not technically silver medal performance I guess, but let's be real I'd be okay waiting a month fo…
"three days" does not say anything about how much computational power is used to solve problems, maybe they have used 10% of all GCP :)
Also, for what it's worth, I'm pretty sure that I wouldn't have been able to solve it myself in three days, even if I had access to all of GCP, Azure and AWS (except if I could mine crypto to then pay actual IMO-level mathematicians to solve it for me).
So I am extremely hyped about this, but it's not clear to me how much heavy lifting this sentence is doing: > First, the problems were manually translated into formal mathematical language for our systems to understand. The non-geometry problems which were solved were all of the form "Determine all X such that…", and the resulting theorem statements are all of the form "We show that the set of all X is {foo}". The do…
What was the total energy consumption required to acheive this result (both training and running) And, how much CO2 was released into earths atmosphere?
Compared to all of the humans who compete at this level and their inputs and outputs for the trailing 5 years.
The result is (likely) net energy consumption, resulting in (likely) net CO2 emissions.
So, what was did it cost us for this achievement in AI?
EDIT TO ADD: It's fair to think that such a presser should not include answers to my questions. But, it's also fair to want that level of transparency given we are dealing with climate change.
> First, the problems were manually translated into formal mathematical language for our systems to understand. In the official competition, students submit answers in two sessions of 4.5 hours each. Our systems solved one problem within minutes and took up to three days to solve the others. Three days is interesting... Not technically silver medal performance I guess, but let's be real I'd be okay waiting a month fo…
How many cycles of guess-and-check did it take over the course of three days to get the right answer?
If the IMO contestants were allowed to use theorem provers and were given 3 days (even factoring in sleep) would AlphaProof still have gotten silver?
> let's be real I'd be okay waiting a month for the cure to cancer.
I don't think these results suggest that we're on the brink of knowledge coming at a substantially faster rate than before. Humans have been using theorem provers to advance our understanding for decades. Now an LLM has been wired up to one too, but it still took 8x as long to solve the problems as our best humans did without any computer assistance.
So I am extremely hyped about this, but it's not clear to me how much heavy lifting this sentence is doing: > First, the problems were manually translated into formal mathematical language for our systems to understand. The non-geometry problems which were solved were all of the form "Determine all X such that…", and the resulting theorem statements are all of the form "We show that the set of all X is {foo}". The do…
To me, this sounds like Alphaproof receives a "problem", whatever that is (how do you formalize "determine all X such that..."? One is asked to show that an abstract set is actually some easily understandable set...). Then it generates candidate Theorems, persumably in Lean. I.e. the set is {n: P(n)} for some formula or something. Then it searches for proofs.
I think if Alphaproof did not find {foo} but it was given then it would be very outrageous to claim that it solved the problem.
I am also very hyped.
Earlier quoted context omitted.
"three days" does not say anything about how much computational power is used to solve problems, maybe they have used 10% of all GCP :)
The thing is though, once we have a benchmark that we pass, it’s pretty typical to be able to bring down time required in short order through performance improvements and iterating on ideas. So if you knew you had GAI but it took 100% of all GCP for 3 years to give a result, within the next 5 years that would come down significantly (not least of which you’d build HW dedicated to accelerating the slow parts).
And there are good reasons to believe that theorem finding and proof generation are at least NP-hard problems.
> First, the problems were manually translated into formal mathematical language for our systems to understand. In the official competition, students submit answers in two sessions of 4.5 hours each. Our systems solved one problem within minutes and took up to three days to solve the others. Three days is interesting... Not technically silver medal performance I guess, but let's be real I'd be okay waiting a month fo…
It feels pretty disingenuous to claim silver-medal status when your machine played by significantly different rules. The article is light on details, but it says they wired it up to a theorem prover, presumably with feedback sent back to the AI model for re-evaluation. How many cycles of guess-and-check did it take over the course of three days to get the right answer? If the IMO contestants were allowed to use theor…
LLM/ML is fascinating tech that has a lot of legitimate applications, but it is not fucking intelligent, artificial or otherwise, and I am sick to death of people treating it like it is.