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If the data is synthetic and covers a limited class of problems I would imagine what it's doing mostly reduces to some basic search pattern heuristics which would be of more value to understand than just being told it can solve a few problems in three days.
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Or the simultaneous discovery of thousands of cryptographic exploits...
Still waiting for the first one. I'm not holding my breath - just like fuzzing found a lot of vulnerabilities in low-level software, I expect novel automated analysis approaches will yield some vulnerabilities - but that won't be a catastrophic event just like fuzzing wasn't.
EDIT - I hope if that new class of bug exists that it is found. I hope that new class of bug doesn't exist.
IMO problems aren't fundamentally different from chess or other games, in that the answer is already known.
I really don't understand what you mean by this. 1) it's not known whether chess is a win for White or not. 2) IMO problems, such as 2024 problem 1 which the system solved, are often phrased as "Determine all X such that…".
Competition problems are designed to be actually solvable by contestants. In particular, the problems should be solvable using a reasonable collection of techniques and many "prep courses" will teach you many techniques, tools and algorithms and a good starting point is to throw that stuff at any given problem. So just like chess openings putting in lots of leg work will give you some good results for that part. You might very well lose in mid and late game, just like this AI might struggle with "actual problems"
It is of course still very impressive, but that is an important point.
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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.
formal definition of first theorem already contain answer of the problem "{α : ℝ | ∃ k : ℤ, Even k ∧ α = k}" (which mean set of even real numbers).if they say that they have translated first problem into formal definition then it is very interesting how they initially formalized problem without including answer in it
{Formal description of the set in question} = ?
And then Alphaproof has to find candidate descriptions of this set and prove a theorem that they are equal to the above.
I doubt they would claim to solve the problem if they provided half of the answer.
Earlier quoted context omitted.
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.
formal definition of first theorem already contain answer of the problem "{α : ℝ | ∃ k : ℤ, Even k ∧ α = k}" (which mean set of even real numbers).if they say that they have translated first problem into formal definition then it is very interesting how they initially formalized problem without including answer in it
Earlier quoted context omitted.
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.
formal definition of first theorem already contain answer of the problem "{α : ℝ | ∃ k : ℤ, Even k ∧ α = k}" (which mean set of even real numbers).if they say that they have translated first problem into formal definition then it is very interesting how they initially formalized problem without including answer in it
What was the total energy consumption required to acheive this result (both training and running) And, how much CO2 was released into earths atmosphere?
There's no energy limit in the IMO rules.
It's that we are living in a period of time where there are very real consequences of nearly a century of unchecked CO2 due to human industry.
And AI (like crypto before it) requires considerable energy consumption. Because of which, I believe we (people who believe in AI) need to hold companies accountable by very transparently disclosing those energy costs.
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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…
I am so exhausted of the AI hype nonsense. LLMs are not fucking curing cancer. Not now, not in five years, not in a hundred years. That's not what they do. 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.
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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).
That's patently false for many classes of problems. We know exactly how to solve the traveling salesman problem, and have for decades, but we're nowhere close to solving a random 1000 city case (note: there are approximate methods that can find good, but not optimal, results on millions of cities). Edit: I should say 1,000,000 city problem, as there are some solutions for 30-60k cities from the 2000s. And there are g…