I believe that it may be misguided to focus on compute that much, and it would be more instructive to consider the effort that went into curating the training set. The easiest way of solving math problems with an LLM is to make sure that very similar problems are included in the training set. Many of the AI achievements would probably look a lot less miraculous if one could check the training data. The most crass example is OpenAI paying off the FrontierMath creators last year to get exclusive secret access to the problems before the evaluation [1]. Even without resorting to cheating, competition formats are vulnerable to this. It is extremely difficult to come up with truly original questions, so by spending significant resources on re-hashing all kinds of permutations of previous question, one will probably end up very close to the actual competition set. The first rule I learned about training neural networks is to make damn sure there is no overlap between the training and validation sets. It it interesting that this rule has gone completely out of the window in the age of LLMs.

[1] https://www.lesswrong.com/posts/8ZgLYwBmB3vLavjKE/some-lesso...

> The easiest way of solving math problems with an LLM is to make sure that very similar problems are included in the training set. Many of the AI achievements would probably look a lot less miraculous if one could check the training data

I'm fairly certain this phenomenon is responsible for LLM capabilities on GeoGuesser type games. They have unreasonably good performance. For example, being able to identify obscure locations from featureless/foggy pictures of a bench. GeoGuesser's entire dataset, including GPS metadata, is definitely included in all of the frontier model training datasets - so it should be unsurprising that they have excellent performance in that domain.

> It is extremely difficult to come up with truly original questions, [...]

No, that's actually really easy. What's hard is coming up with original questions of a specific level of difficulty. And that's what you need for a competition.

To elaborate: it's really easy to find lots and lots of elementary, unsolved questions. But it's not clear whether you can actually solve them or how hard solving them is, so it's hard to judge the performance of LLMs on them.

> It it interesting that this rule has gone completely out of the window in the age of LLMs.

No, it hasn't.

> The easiest way of solving math problems with an LLM is to make sure that very similar problems are included in the training set.

An irony here is that math blogs like Tao's might not be in LLM training data, for the same reason they aren't accessible to screen readers - they're full of math, and the math is rendered as images, so it's nonsense if you can't read the images.

(The images on his blog do have alt text, but it's just the LaTeX code, which isn't much better.)

Language modeling is compression, whittle down graph to reduce duplication and data with little relationship: https://arxiv.org/abs/2309.10668

Let’s say everyone agrees to refer to one hosted copy of a token “cat”, and instead generate a unique vector to represent their reference to “cat”.

Blam. Endless unique vectors which are nice and precise for parsing. No endless copies of arbitrary text like “cat”.

Now make that your globally distributed data base to bootstrap AI chips from. The data driven programming dream where other machines on the network feed new machines boot strap.

American tech industry is IBM now. Stuck on recent success of web SaaS and way behind the plans of AI.