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Comment by reasonableklout | Hacker News Reader

I don't really understand this. Aren't LLMs already performing at near-expert level on "certain mathematical problem" benchmarks?

For example, over a year ago MINERVA from Google [1] got >50% on the MATH dataset, a set of competition math problems. These are not easy problems. From the MATH dataset paper:

> We also evaluated humans on MATH, and found that a computer science PhD student who does not especially like mathematics attained approximately 40% on MATH, while a three-time IMO gold medalist attained 90%, indicating that MATH can be challenging for humans as well.

[1] https://blog.research.google/2022/06/minerva-solving-quantit...

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No, they are completely awful at math. The way you can see that is that, whenever you ask it about known concepts, even hard ones, it will answer, making it look intelligent. But then if you create a small new theory or logical problem that is completely not in the internet, and ask SIMPLE questions about it - i.e., questions a 10 years old would be able to answer given the context - it will fail disgracefully.

Every example on that web page is a trivial textbook problem. That shows memorization of training set and textual pattern matching.

No, that shows only that the dataset is comprised of common problem patterns. The paper explicitly investigates whether memorization has overly impacted performance. From page 10 [1]:

> A central question in interpreting Minerva’s solutions is whether performance reflects genuine analytic capability or instead rote memorization. This is especially relevant as there has been much prior work indicating that language models often memorize some fraction of their training data ... In order to evaluate the degree to which our models solve problems by recalling information memorized from training data, we conduct three analyses on the MATH dataset ... Overall, we find little evidence that the model’s performance can be attributed to memorization.

[1] https://arxiv.org/pdf/2206.14858.pdf

in Appendix j.2. they say that accuracy degraded after modification, figure 11 shows that accuracy degraded in 15 out of 20 examples after large modification.

GPT-4 is also a lot better than Minerva.

I guess it depends on the size and what kind/quantity of data they fed it.

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