Data is the wrong approach to develop reasoning. You we don't want LLM's to simply memorize 3x3 = 9 we want them to understand that 3 + 3 + 3 = 9 therefore 3x3 = 9 (obviously a trivial example). If they have developed reasoning very few examples should be needed.
The way I see it reasoning is actually the ability of the model to design and train smaller models that can learn with very few examples.
> If they have developed reasoning very few examples should be needed.
Yes, once the modules for reasoning have converged, it will take very few examples for it to update to new types of reasoning. But to develop those modules from scratch requires large amounts of examples that overtax its ability to memorize. We see this pattern in the "grokking" papers. Memorization happens first, then "grokking" (god I hate that word).
It's not like humans bootstrap reasoning out of nothing. We have a billion years of evolution that encoded the right inductive biases in our developmental pathways to quickly converge on the structures for reasoning. Training an LLM from scratch is like recapitulating the entire history of evolution in a few months.
The way I see it reasoning is actually the ability of the model to design and train smaller models that can learn with very few examples.