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 type of reasoning text (think of generative image models a few years ago, where appending "unreal engine" to a prompt would significantly improve the quality of the output, the reason was that the model was trained to generate the distribution of the images on the internet, most of them are not particularly impressive, however, since images containing "unreal engine" were usually high-quality screenshots of images, it would also move the distribution of generated images towards higher quality generations). So I think the model already has most of the ability, it just needs to adjust a few connections to actually utilize this latent skill, so it makes sense that a few training examples are enough to adjust the connections to increase mathematical reasoning skills.
LIMO: Less Is More for Reasoning
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Re: LIMO: Less Is More for Reasoning
#12I 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!
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Re: LIMO: Less Is More for Reasoning
#13where's chatbotAI-zero? in the way alpha-go-zero was the best after training with itself? (and only with itself)
The advantage of alpha-go-zero is that it is constrained to the language of go. If you made two LLM train only off each other they would develop their own language. Maybe they'd be great at reasoning, but we wouldn't understand them. Even humans in that situation would develop jargon, and as time goes on a dialect or language of their own. And humans are a lot more grounded in their language than LLMs.
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Re: LIMO: Less Is More for Reasoning
#14In the same way that image diffusion models showed that convincing approximations of the entire visual world could be summarized in a 5GB model, are "reasoning patterns" similarly compressible? Are there actually countably few reasoning patterns that are used across all domains, and as such can be captured with relatively small training sets?
I would say there are only a smallish number of truly generic "reasoning patterns" (strategies/approaches), but applied reasoning not only requires a reasoning "pattern", but also a repertoire of valid domain-specific reasoning steps that can be applied pursuant to that approach, as well as the combination of capabilities it takes to overcome impasses when you've exhausted your knowledge and learnt reasoning steps and still not got to a solution.
Perhaps in a domain like math a smallish number of math-specific reasoning steps will go a long way, but math itself also has many "sub-domains" (algebra, geometry, calculus, topology, etc) and AFAIK the techniques of one branch are only going to be useful in another to extent you can map the problem from one domain to another.
Re: LIMO: Less Is More for Reasoning
#15where's chatbotAI-zero? in the way alpha-go-zero was the best after training with itself? (and only with itself)
Someone first needs to design a rule set for a game that only permits the correct use of language but encompasses the entire breadth of language use. Then it's plausible.
Thankfully for mathematics and code this seems plausible due to automated theorem proving.
Re: LIMO: Less Is More for Reasoning
#16where's chatbotAI-zero? in the way alpha-go-zero was the best after training with itself? (and only with itself)
We kind-of have that in DeepSeek-R1-zero [1], but it has problem. From the original authors:
> With RL, DeepSeek-R1-Zero naturally emerged with numerous powerful and interesting reasoning behaviors. However, DeepSeek-R1-Zero encounters challenges such as endless repetition, poor readability, and language mixing.
A lot of these we can probably solve, but as other have pointed out we want a model that humans can converse with, not an AI for the purpose of other AI.
That said, it seems like a promising area of research:
> DeepSeek-R1-Zero demonstrates capabilities such as self-verification, reflection, and generating long CoTs, marking a significant milestone for the research community.
Re: LIMO: Less Is More for Reasoning
#17where's chatbotAI-zero? in the way alpha-go-zero was the best after training with itself? (and only with itself)
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.
Re: LIMO: Less Is More for Reasoning
#18It is interesting how the field is becoming 'pedagogy of LLMs'.
Re: LIMO: Less Is More for Reasoning
#19People here should read, especially 1.How to make less datasets 2. Categorize reasoning process into
L1-L5 when evaluation.
Re: LIMO: Less Is More for Reasoning
#20To see a World in a Grain of Sand And a Heaven in a Wild Flower, Hold Infinity in the palm of your hand And Eternity in an hour.
what's the connection here? just the words "less is more"?