[igravious]

"using human-like reasoning (in a brute-force way)"

that's self-contradictory -- what brute force means is doing an exhaustive search of a search space (brute forcing it)

using human-like(?) reasoning means cutting down the search space by having some sort of insight or intuition which allows you to prune branches from the entire tree

[YeGoblynQueenne]

LLMs don't search trees. They generate plausible proofs and a human has to check it's true. Repeat until.

[tptacek]

That's not what happened here. This isn't a proof; it's a counterexample. The model was perfectly capable of verifying its correctness. You could have verified it by hand if you wanted; the verification is trivial. Finding it was the hard part.

[YeGoblynQueenne]

>> The model was perfectly capable of verifying its correctness.

It's an LLM. It can't do that.

[tptacek]

Are you doing the "LLMs don't know how many R's are in 'Raspberry'" thing here?

A bunch of people on the original thread about the Conjecture were like "we need to wait and see if real mathematicians verify this proof it's probably just LLM psychosis", because they don't understand that the counterexample is a trivial calculation. Checking it isn't hard; any AP calc student can do it quickly. It's finding the counterexample that's the challenge.

It's as if someone presented a SHA-2 collision, which anyone could just feed to `openssl sha256` to see, and then naysayers were like "we need to wait for independent verification because the LLM can't know if that collision was real".

[YeGoblynQueenne]

>> Are you doing the "LLMs don't know how many R's are in 'Raspberry'" thing here?

I don't know. Are you doing the thing were you're arguing against something you don't like that the other person never said?

[tptacek]

The model is very capable of checking this counterexample, was my point.

[astrange]

Agents can generate formal proofs that are checked with an oracle like Lean and can run in a loop.

[YeGoblynQueenne]

What are the search algorithms then? DFS, BFS, A*, etc, can you name them?

[tptacek]

Why are you asking them which basic computer science graph traversal algorithms a frontier model used?

[YeGoblynQueenne]

OP:

>> using human-like(?) reasoning means cutting down the search space by having some sort of insight or intuition which allows you to prune branches from the entire tree

So according to the OP there's a search of a tree and it also uses pruning btw, so I want to know what search they mean. Why are you asking?

[tptacek]

Because your question doesn't make sense; this isn't how implicit search works.