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Claude Fable produced a counterexample to the Jacobian Conjecture

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Re: Claude Fable produced a counterexample to the Jacobian Conjecture

#501

Post by jibal »

8bitsrule wrote: post #478
jibal wrote: post #475

Earlier quoted context omitted.

non sequitur

Perhaps ... but the lesson in trusting AI math was worth it.

You're missing the point. The counterexample to the Jacobian conjecture is valid regardless of how it was discovered ... elsewhere on this page people are even suggesting that the Anthropic mathematician may not have actually used Claude and came up with the counterexample himself.

Trusting AI math is not an issue here. It's as if you had asserted that no primes when divided by 35 produce a remainder of 6 and the model said that 41 is a counterexample and then you complained about not being able to trust AI math.

P.S. As someone else noted, your AI query was malformed ... no prime is divisible by 35, nor is any integer divisible by an integer with a remainder of 6 -- divisibility implies a remainder of 0. So perhaps the AI simply took what you wrote literally.

Re: Claude Fable produced a counterexample to the Jacobian Conjecture

#502

Post by YeGoblynQueenne »

tptacek wrote: post #460
YeGoblynQueenne wrote: post #455

Earlier quoted context omitted.

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

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

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?

Re: Claude Fable produced a counterexample to the Jacobian Conjecture

#503

Post by YeGoblynQueenne »

hgoel wrote: post #488
YeGoblynQueenne wrote: post #449

Earlier quoted context omitted.

Yes, but the question is the extent to which the new tool was guided by the mathematician. Are we talking a bicycle, powered by a human stepping on the pedals; or a rocket that will fly to the moon on its own with people inside? Don't you want to know? I mean, doesn't everyone want to know?

Yes, of course, that would be interesting info to have. I just mean that from what we have already we can reasonably infer that the LLM played a role in the result being obtained. If I am not mistaken, all of the flurry of novel results has come from existing mathematicians. This makes me suspect that the models aren't at the level where just any layman can get results. They require a skilled human in the loop to kee…

Right, that's what I'm trying to understand, the extent to which models need expert guidance. I don't doubt an LLM was used, I just want to know- how.

Re: Claude Fable produced a counterexample to the Jacobian Conjecture

#504

Post by YeGoblynQueenne »

CamperBob2 wrote: post #457
YeGoblynQueenne wrote: post #447

Earlier quoted context omitted.

I mean we have no idea what happened exactly, how Fable was used, how many times it was run, whether earlier models were also tried, what was the prompt, how long it run for, etc etc. All we have to go by is a tweet. Why not be skeptical about that?

What you're asking for is exactly the sort of thing that belongs in, and will appear in, a journal article. There will likely be a preprint on arxiv, so you might keep an eye out for that. In any case, the fact that it was found by a commercial model means that the unfiltered reasoning trace isn't available even to the original author. So there are aspects of the problem-solving process we'll never see. Even if we di…

No, I think it works the opposite way. Until there is an article somewhere that describes what happened, if there is one, all we have to go by is that some guy posted a counter-example for the Jacobian on X, with a vague allusion to using Fable and without any further information. Assuming and guessing anything about e.g. the method used at this point is just raising the noise level.

Re: Claude Fable produced a counterexample to the Jacobian Conjecture

#505

Post by YeGoblynQueenne »

tptacek wrote: post #459
YeGoblynQueenne wrote: post #450

Earlier quoted context omitted.

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

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.

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

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

Re: Claude Fable produced a counterexample to the Jacobian Conjecture

#506

Post by grumbelbart2 »

unexpectedtrap wrote: post #335

Using LLMs to generate piles of code and/or proofs of dubious quality is very questionable thing, and I understand these non-stop debates about it. But in this case, as using plain brute force is already quite a common thing in searching for counterexamples, using LLMs as a sort of more advanced brute force seems to be just the right thing to do, so I struggle to understand so much hostility to this approach.

The good thing about math is that you can formally verify the results, making hallucinations much less scary.

This is similar to games, where large learning models had some of their first big wins (go). Games, like math, have strict rules that can be used to prune invalid outputs.

It is already in the making, the next big step in math will be the complete formalization of all existing, relevant theorems and proofs via LLMs.

Re: Claude Fable produced a counterexample to the Jacobian Conjecture

#507

Post by thomascountz »

Sophira wrote: post #252
siddboots wrote: post #243

Earlier quoted context omitted.

I fed ChatGPT the map with no other context, just “tell me about this function”. It did a bit of work finding the Jacobean etc and eventually worked out the implications of what it was seeing. It then proceeded to check the arithmetic 4 times, and then decided to do a manual verification using an ad hoc symbolic checker in case its SymPy had been tampered with.

Can you please share the chat log for this? I would absolutely love to see this.

Not OP, but here's Gemini's reaction: https://aistudio.google.com/app/prompts?state=%7B%22ids%22:%...

Re: Claude Fable produced a counterexample to the Jacobian Conjecture

#508

Post by Lerc »

EagnaIonat wrote: post #492
Lerc wrote: post #190

Earlier quoted context omitted.

Do you have links to these videos? You comment suggests you feel there is something wrong with what I said, could you elaborate?

They are probably talking about data centres and town hall meetings where people are objecting and being removed. Even a casual search you will find numerous videos. The only issue I see with your comment (and this thread stems off the misreading of my post), is that despite your "I see the difference" it is still labelling one side. In truth, there are crazy people everywhere.

I don't think it was a misunderstanding, the comment was not addressing the content of your post, but rather the descision to bring it up in a context where they thought it not relevant.

Re: Claude Fable produced a counterexample to the Jacobian Conjecture

#509

Post by Lerc »

jll29 wrote: post #364
slopinthebag wrote: post #179

Earlier quoted context omitted.

I initially wanted to downvote you but I can’t because you’re right. I’d probably be called an anti-ai luddite on this site despite using it all the time for programming. I naturally gravitate to anti-ai viewpoints, but only because the breathless hype of the AI boosters is so nauseating. I have no moral qualms about AI (although I’d like nothing more than Anthropic/OAI/Google dismantled), but I really hate the idea…

I understand you. As an AI research (actually, despite formally called professor of AI, I have historically always called myself more specifically NLP/IR/ML researcher rather than "AI" researcher, to avoid historic baggage). I am intellectually curious whether "intelligence" and "consciousness" are simply layers that can be separated from the hardware they operate on or first emerged from, but I never had the urge or…

>Not everything that can be done should be done.

My concern is that people are being cavalier about the possibility of creating things that should have rights.

There will always be people who will never accept that a machine has awareness or rights. I suspect the major AI companies are doing there best to not have this talked about. As soon as it becomes a broad topic of conversation, it becomes a religious issue. The Discovery Institute is already spending money on this.

People worry about a machine that wants to kill us. For that to happen, someone has to have made a machine that wants. That is not something that should be done carelessly.

Re: Claude Fable produced a counterexample to the Jacobian Conjecture

#510

Post by spwa4 »

icepush wrote: post #489
spwa4 wrote: post #375

Earlier quoted context omitted.

... for the management of Google that is so eager to present AI results that Prabhakar Raghavan proudly reported to a press crowd telling his daughter about James Webb photographing a planet outside the solar system. This is generally accepted as having resulted in a 10% drop in the Google stock price over 2 days. (the key being this never happened, and won't ever happen: the James Webb telescope doesn't have even 1/…

It dropped 10% ... but then it got better

It went from 108 to 95. It didn't even recover for 2 months and 2 weeks (the next - spectacularly good - earnings were just barely enough to make the stock achieve 108 again ... for a second (well, 2 days, 1 if you don't count after hours). It really took close to 4 months. And nobody really knows if it wouldn't have been 10% higher forever without that particular senior management fuckup in AI.

And it would be FAR from their last AI fuckup. In fact, the Kimi K3 release, which extremely likely cancelled the Gemini 4 pro rollout (probably because Kimi K3 outperforms not just Gemini, but Gemini 4 pro as well. So in case you're looking to now ask "which Gemini did you mean there?", the answer is ALL OF THEM, very likely including unreleased Gemini models)

It outperforms the fucking ASR model Google uses, which is presumably also a Gemini derivative.

This, by the way, cost Google stock ANOTHER 10%, last week.

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