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LIMO: Less Is More for Reasoning

arxiv.org

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Re: LIMO: Less Is More for Reasoning

#81

Post by sega_sai »

jkhdigital wrote: post #77
sega_sai wrote: post #34

Earlier quoted context omitted.

A connected question -- has there been an LLM that is a perfect calculator ? I.e. you give it a expression involving standard operations +/- and (say) integer numbers, standard operations and it should returns always a correct result. I don't remember seeing any papers on this (but i'm not an expert)

Why would you ever want an LLM that is a perfect calculator? Humans invented calculators for a reason. A good LLM should respond to arithmetic questions by executing a cheap and efficient calculator program instead of wasting cycles on it.

It is the question of capabilities. People use LLMs to prove theorems. It is therefore a relevant question whether llms can work as generic calculators. And if they can't it shows IMO something is missing.

Re: LIMO: Less Is More for Reasoning

#83

Post by theWreckluse »

sebzim4500 wrote: post #76
igleria wrote: post #6

I think I've recently read two seemingly contradicting things: 1- LLMs can never generalize theorem proving 2- this paper: "This suggests that contemporary LLMs may already possess rich mathematical knowledge in their parameter space, transforming the challenge from knowledge acquisition to knowledge elicitation" Not sure what is what anymore!

I think that "LLMs can never X" is just always false.

"LLMs can never predict the next word"

Re: LIMO: Less Is More for Reasoning

#84

Post by highfrequency »

armcat wrote: post #52
highfrequency wrote: post #33

Cool result, but worth highlighting two points: - Model is finetuned from Qwen-2.5 Instruct, which includes millions of specially filtered math examples in both pretraining and supervised fine-tuning already. - To generate the perfect 817 math examples for LIMO, they used state of the art models like R1 to filter down from an initial pool of 10 million math problems. In other words, a whole lot of intelligence was us…

Yes, the authors explicitly highlighted those two points in the abstract, in terms of them being the elicitation threshold for complex reasoning, namely, an extremely complete pre-trained foundation model, and a set of extremely high quality examples post-training. To your question on finetuning on the initial 10 million pool - intuitively, it would require tremendous amount of finetuning data to move the needle - yo…

The abstract doesn’t specify that the 857 training examples were filtered down by R1 from 10 million initial questions. This helps to understand the result better: it is in large part a testament to R1 and similar models’ remarkable ability sift through and identify/construct perfect training data for other models.

Re: LIMO: Less Is More for Reasoning

#85

Post by yishanchuan »

highfrequency wrote: post #33

Cool result, but worth highlighting two points: - Model is finetuned from Qwen-2.5 Instruct, which includes millions of specially filtered math examples in both pretraining and supervised fine-tuning already. - To generate the perfect 817 math examples for LIMO, they used state of the art models like R1 to filter down from an initial pool of 10 million math problems. In other words, a whole lot of intelligence was us…

Sure,but just in mathematical reasoning. If future works contain mathematical logic reasoning, it will perfect.

Re: LIMO: Less Is More for Reasoning

#86

Post by krisoft »

gpm wrote: post #17
sebastiennight wrote: post #5

Earlier quoted context omitted.

You don't want that as a product, in the sense that having an AI model train itself by simply having internal conversations without ever looking at any human-written content, might result in something that humans cannot comprehend. Also, well - there's the technicality of "you don't 'win' a conversation like you can 'win' at Go", so how would you know to reward the model as you're training it?

I do... I want a chatbot that can automatically magic up proofs that all my code is correct for instance. I don't care if I understand the proofs. I care if some tool that checks proofs understands them, and that's a mechanical game just like go or chess.

> I want a chatbot that can automatically magic up proofs that all my code is correct for instance.

How could the AI know what you wanted to program? If it was trained only with self play it won’t understand the language where you describe the purpose of the code because it only speaks its own idiosyncratic language. (At best.)

And if it doesn’t know what you wanted to do then all it can prove is that the program does what the program does.

Re: LIMO: Less Is More for Reasoning

#87

Post by EternalFury »

highfrequency wrote: post #33

Cool result, but worth highlighting two points: - Model is finetuned from Qwen-2.5 Instruct, which includes millions of specially filtered math examples in both pretraining and supervised fine-tuning already. - To generate the perfect 817 math examples for LIMO, they used state of the art models like R1 to filter down from an initial pool of 10 million math problems. In other words, a whole lot of intelligence was us…

Just imagine a textbook that gives you the understanding you need to score high in math competitions…and it describes less than 1,000 problems. This in itself is a major discovery in metacognition.

Re: LIMO: Less Is More for Reasoning

#88

Post by UncleEntity »

gmueckl wrote: post #26
bilater wrote: post #21

Earlier quoted context omitted.

I think the way to swallow this bitter pill is to acknowledge they can "generalize" because all human knowledge is actually a relatively "small" finite distribution that models are now big enough to pattern match on.

Calling human knowledge small is hyperbole. I cannot get any LLM even close to giving accurate answers related to the things I know. They simply do not know what I, a single human being, knows. That's simply because I'm a subject matter expert on somewhat niche topics. There are easily hundreds of thousands of people like me out there. There's simply no way an LLM can even train on all of that because each bit of tru…

Maybe there's a way to reduce the dataset for a LLM to learn to reason down to the smallest possible set and then apply the vast knowledge of humankind on top of that?

I mean, if it can reason about and process the data as it ingests it?

Re: LIMO: Less Is More for Reasoning

#89

Post by gpm »

krisoft wrote: post #86
gpm wrote: post #17

Earlier quoted context omitted.

I do... I want a chatbot that can automatically magic up proofs that all my code is correct for instance. I don't care if I understand the proofs. I care if some tool that checks proofs understands them, and that's a mechanical game just like go or chess.

> I want a chatbot that can automatically magic up proofs that all my code is correct for instance. How could the AI know what you wanted to program? If it was trained only with self play it won’t understand the language where you describe the purpose of the code because it only speaks its own idiosyncratic language. (At best.) And if it doesn’t know what you wanted to do then all it can prove is that the program doe…

You tell it what you want it to prove. Or the tooling surrounding it does.

The tooling surrounding it might want to prove that "this main function never invokes undefined behavior", or something more local like "for all possible inputs to the public interface to this module, no undefined behavior is invoked".

Or you might want to specify constraints by hand. For examples, you might do that by writing normal tests except you can use magical variables that take on any value [1], or you might do that by annotating functions with contracts that they obey [2]. Or at a simpler level you might just annotate functions that should never panic.

Ultimately once you can prove things about your code, it's a tool in the toolbox for querying how your code works. You can use that to write correct code from the start, or to debug incorrect code, or various other things. The problem is that right now the state of the art (non-ai) can't reason about very complex code without a lot of human help - making it a fairly impractical tool. I think AI might mange to fix that.

[1] This is how kani works in rust, here's an example: https://github.com/model-checking/verify-rust-std/pull/112/f...

[2] Creusot takes this route, here's an example https://github.com/sarsko/CreuSAT/blob/master/CreuSAT/src/so...

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