>you classify different pictures of digits that DID appear.

Are you implying models that classify hand-written digits don’t generalize and only work on training data?

No, that is false; a neural net trained on a decent set of handwritten digits will recognize a newly handwritten digit.

I'm saying that this is a strawman version of "not in the training data". The newly handwritten digit is squarely the same sort of stuff that is in the training data: an interpolation.

We are not surprised when we fit a curve to a bunch of points and then find points on the curve that are not exactly any of those points, but are located among the points.

Go too far outside of the cluster of points though and the curve is a hallucination.

This is the intuition behind interpolate vs extrapolate.

You're saying they don't use math textbooks and math forums to train LLMs, then?

The paper is evaluating how well an LLM can handle novelty, and on the paper's terms you need to calculate or otherwise somehow deduce the degree or type of novelty rather than simply describing your never published research as novel.

I don't even know that this is possible without seeing the training data. Hence the difficulty in describing how good at "reasoning" O3 Pro is.

The most novel problem would presumably be something only a martian could understand, written in an alien language, the least novel problem would be a basic question taught in preschool like what color is the sky.

Your research falls somewhere between those extremes.

LLMs don't learn reasoning. At all. They are statistical language models. Nothing else. If they get math right it's because correct math is more statistically probable given the training data, it can't actually do math. This should be pretty clear from all the "how many Rs are there in strawberry" type examples.