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LIMO: Less Is More for Reasoning

arxiv.org

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Re: LIMO: Less Is More for Reasoning

#21

Post by bilater »

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 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.

Re: LIMO: Less Is More for Reasoning

#23

Post by cube2222 »

hexomancer wrote: post #11

Here is how I make sense of it (I have no expertise in this subject, please feel free to correct me if I am wrong): I think when the model is pretrained on the internet, it does gain most of the skills required to do mathematical reasoning, however, since its task is to predict the next word distribution on the entire internet, it does not normally use this ability, since most of the text on the internet is not this…

Kinda similar to how Anthropic was able to achieve golden gate Claude or even maximize/minimize features like “buggy code” via analyzing concepts in activations and manipulating them[0].

[0]: https://www.anthropic.com/news/mapping-mind-language-model

Re: LIMO: Less Is More for Reasoning

#26

Post by gmueckl »

bilater wrote: post #21
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 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 true expert knowledge necessarily comically underrepresented in any possible training set.

Re: LIMO: Less Is More for Reasoning

#28

Post by easeout »

My guess at the upshot: Some domains, like math, are general but have outsized effective vocabularies like all possible numbers, which makes them more expensive to train by the same method that works for domains of regular-sized vocabularies. If you train for reasoning steps in such a problem domain, you can reinforce the comparatively few general terms of the vocabulary like "add", "inverse", "solve". And that leaves the arithmetic of number combinations separate from particular problems because you're not emphasizing one-shot answers. You can train N reasoning cases + M arithmetic cases instead of N*M whole math problems. So you have to use more inference power but you can get better answers for less training.

Theory aside, I would think a good application-side method is to use this general reasoning process to structure a final expression and then pass that through a traditional evaluator. Then the reasoning and training thereof need only go as far as symbol manipulation. This is something like Wolfram Alpha, if its NLP handed off to the evaluator much later in the process.

Re: LIMO: Less Is More for Reasoning

#29

Post by antirez »

the S1 paper did the same a few days ago, basically. 1000 total CoT with SFT.

I believe that all this shows that pre-training stage already creates the representations needed for CoT reasoning, so they are very simple to uncover. Either with R1-Zero pure RL, or with few-shots SFT.

Re: LIMO: Less Is More for Reasoning

#30

Post by zozbot234 »

cube2222 wrote: post #23
hexomancer wrote: post #11

Here is how I make sense of it (I have no expertise in this subject, please feel free to correct me if I am wrong): I think when the model is pretrained on the internet, it does gain most of the skills required to do mathematical reasoning, however, since its task is to predict the next word distribution on the entire internet, it does not normally use this ability, since most of the text on the internet is not this…

Kinda similar to how Anthropic was able to achieve golden gate Claude or even maximize/minimize features like “buggy code” via analyzing concepts in activations and manipulating them[0]. [0]: https://www.anthropic.com/news/mapping-mind-language-model

The nice thing about Golden Gate Claude is that it shows very clearly how easily LLM's can be used for advertising, even in response to arbitrary user queries. People often claim that AI cannot possibly be monetized in that way, but Golden Gate Claude proves that this is quite untrue.
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