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AI solves International Math Olympiad problems at silver medal level

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Re: AI solves International Math Olympiad problems at silver medal level

#201

Post by Davidzheng »

cs702 wrote: post #177

In 1997, machines defeated a World Chess Champion for the first time, using brute-force "dumb search." Critics noted that while "dumb search" worked for chess, it might not necessarily be a general strategy applicable to other cognitive tasks.[a] In 2016, machines defeated a World Go Champion for the first time, using a clever form of "dumb search" that leverages compute, DNNs, reinforcement learning (RL), and self-p…

By its nature hard math problems do not have fast algorithmic solutions--you can only solve them by search or clever search. Mathematicians have heuristics on helping us decide intuitively what's going to work what can make progress. But in the end--there is only search

Re: AI solves International Math Olympiad problems at silver medal level

#202

Post by password54321 »

balls187 wrote: post #67
amelius wrote: post #48

Earlier quoted context omitted.

There's no energy limit in the IMO rules.

The point isn't 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.

> need to hold companies accountable by very transparently disclosing those energy costs.

And if they do, then what? If it is "too high" do we delay research because we need to keep the world how it is for you? What about all the other problems others face that could be solved by doubling down on compute for AI research?

Re: AI solves International Math Olympiad problems at silver medal level

#203

Post by Davidzheng »

jerb wrote: post #191

Is the score of 28 comparable to the score of 29 here? https://www.kaggle.com/competitions/ai-mathematical-olympiad...

No. I would say it is more impressive than 50/50 there. (Source: I used to do math comps back in the day sorry it's not a great source)

Re: AI solves International Math Olympiad problems at silver medal level

#206

Post by gowld »

visarga wrote: post #106
golol wrote: post #33

This is the real deal. AlphaGeometry solved a very limited set of problems with a lot of brute force search. This is a much broader method that I believe will have a great impact on the way we do mathematics. They are really implementing a self-feeding pipeling from natural language mathematics to formalized mathematics where they can train both formalization and proving. In principle this pipeline can also learn bas…

> a lot of brute force search Don't dismiss search, it might be brute force but it goes beyond human level in Go and silver at IMO. Search is also what powers evolution which created us, also by a lot of brute forcing, and is at the core of scientific method (re)search.

What makes solving IMO problems hard is usually the limits of human memory, pattern-matching, and search, not creativity. After all, these are problems that are already solved, and it is expected that many people can solve the problems in about 1 hour's time.

That makes it, in principle, similar or even easier than a champsionship-level chess move, which often take more than 1 hour for a professional human (with more training than an IMO high school student) to solve.

Another interesting concern is that when posing a problem to humans, it's fine to pose an "easy" brute-forceable problem, but humans, being slow brute-searchers, need to find more clever solutions. But if you give such a problem to a computer, it can trivialize it. So to test a computer, you need to pose non- easily-brute-forceable problems, which are harder for the computer than the others, but equally difficult for the humans as the other problems are.

Re: AI solves International Math Olympiad problems at silver medal level

#207

Post by Probiotic6081 »

cs702 wrote: post #177

In 1997, machines defeated a World Chess Champion for the first time, using brute-force "dumb search." Critics noted that while "dumb search" worked for chess, it might not necessarily be a general strategy applicable to other cognitive tasks.[a] In 2016, machines defeated a World Go Champion for the first time, using a clever form of "dumb search" that leverages compute, DNNs, reinforcement learning (RL), and self-p…

[dead]

Re: AI solves International Math Olympiad problems at silver medal level

#209

Post by netcan »

cs702 wrote: post #177

In 1997, machines defeated a World Chess Champion for the first time, using brute-force "dumb search." Critics noted that while "dumb search" worked for chess, it might not necessarily be a general strategy applicable to other cognitive tasks.[a] In 2016, machines defeated a World Go Champion for the first time, using a clever form of "dumb search" that leverages compute, DNNs, reinforcement learning (RL), and self-p…

Well written.

It kinda had to be this way, I think. There's a something from nothing problem. Douglas Adams brilliantly starts at this point.

We don't understand something from nothing. We don't even have the language to describe it. Concepts like "complexity" are frustratingly resistant to formalization.

"There is no free will." Has recently resurged as a philosophical position... like it did in response to Newton's mechanics.

Matter from void. Life from minerals. Consciousness from electrons. Free will from deterministic components. Smart reasoning & intelligent rationalisation from dumb search, computation, DNNs and such.

I don't think this debate was supposed to be ended by anything short of empirical demonstration.

Endnote: deep blue's victory over Gary was a bunch of preprogrammed bulls--t. Rematch!

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