alt Hacker NewsSurely this implies these LLM generated proofs require the LLMs to have mathematical intuition . . . and honestly I don't think many people believe that, and rightly so, certainly not in the way Poincaré was on about.
Maybe it's been done, but I'd like to see an LLM recreate Euclid from questioning without having seen it during training.
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I think it's actually the opposite. Intuition is the only thing LLMs can do, which is why they are prone to hallucinating when they can't validate their intuition against reality.
There is an idea that human intuition, expertise, and critical thinking are largely pattern recognition. When you encounter a situation, your brain gives you a plausible starting point, based on what it has experienced before. You then continue with explicit reasoning, which is slow and inefficient, and try to validate your ideas. The more relevant the patterns you have learned are to the situation, the more likely you reach a useful conclusion.
LLMs are largely the same, except that they cannot learn from experience in normal usage. And except that they experience the world only through symbolic data, while the human brain has access to plenty of sensory data.
My hunch (or intuition, hah!) is that intuition is an instinctive mental shortcut required to navigate large problem spaces that can’t entirely fit into our heads.
Maybe LLMs do not need intuition because they can scale their “cognitive capacity” with hardware and brute force their way through these problem spaces.
>Surely this implies these LLM generated proofs require the LLMs to have mathematical intuition
Well yeah they do, obviously.
That has been done, like back in the 1960’s.
It does not imply that. He is talking about how people do math. Intuition is what you use when deciding what to try and how to think about things.
Proof is the rigorous outcome.
LLM running probabilistic loop is different kind of process.
LLMs have LLM intuition, not human intuition. (See the movie Her.)
LLM cannot reinvent Euclid from scratch, but a larger system including LLM might.
> Surely this implies these LLM generated proofs require the LLMs to have mathematical intuition . . . and honestly I don't think many people believe that
Yes, I believe that, it's part of what I was implying (I believe the LLM weights have some internal representation of math in the same way brains do that allow them to produce proofs)