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 - you really won't be able to move the gradients much with just 817 examples, that initial pool is effectively enforcing pretty rigid regularization.

There is now an increasing interest in showing that small data with inference time scaling is providing significant yield. Couple of recent examples:

* TinyZero: https://github.com/Jiayi-Pan/TinyZero * s1 Simple Test Time Scaling: https://arxiv.org/abs/2501.19393

Why is everyone is so critical of using information from a previous model to make a more efficient model. There’s nothing wrong with making progress using prior work. And increasing efficiency is progress.

You wouldn’t criticize someone’s kombucha because they didn’t piece their SCOBY (symbiotic culture of bacteria and yeast) together microbe by microbe.

Another way to look at this is that there are 12,290 bits of information in choosing 817 samples from 10,000,000.

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.

> 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 used to craft a maximally informative and distilled set of fine-tuning data

The paper, and this comment, seem awfully reminiscent of creating a textbook of curated "maximally informative and distilled" set of cognitive examples to teach students with foundational learning a next level of reasoning.

The last few years of LLM progress have shown we can predict human "reasoning" responses to inputs by modeling likely human responses as if LLM generated. Put another way, most responses are not particularly reasoned, but chain of tokgen*.

Sit near someone who "talks to herself" while doing problems and it's even more evident.

---

* tokgen definition: Listen to conversations in a cafeteria. Many are something other than thoughtful, responses that follow the prompts, with near perfect predictability. To differentiate from these responses and speech that comes after a pause and reflect, one can use the labels thought versus token generation or tokgen.

>In other words, a whole lot of intelligence was used to craft a maximally informative and distilled set of fine-tuning data.

Sounds like any textbook. (and generally the process of knowledge compression over generations that made us who we are)

Yeah, but it's cheaper.

The context right now is that OpenAI, with first-mover advantage, cutting-edge-hardware, and tens of billions of dollars of investment, are not getting benchmark performance better than Chinese-developed models that are trained with cut-down nvidia GPUs and a lot less money.

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

You are missing three point, it's about stating the importance of the preselection, now we know that we may not need huge amounts of data for similar results in other reasoning areas, only highly curated data, yes, sometimes by models themselves but not necessarily.

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

I'd add a little bit more to that.

Pattern identification and continuation can be applied to evaluate symbolic reasoning. You can see this in e.g. the semantics of a functional programming language if evaluation semantics are defined in terms of rewrite rules.

If you have a model which can convert a problem into language that's precise enough to start pattern matching to LLM-encoded generative programs that evaluate logical implications, you can get into a very interesting space. Autoregressive prediction can turn into symbolic progressive evaluation and calculation. The background LLM is still guiding choice of evaluation and goal seeking.

Reinforcing these evaluation rules seems like it should be doable without enormous corpora, as long as the base model already has enough meat on it to cleanly attach to the more precise language.

The reasoning R1 demonstrates most times sounds to me like 5th grader's wording - in support of what you say. But then if you compress compress the knowledge needed for math reasoning, perhaps you get category theory paired with prolog or something along the line which is rule-based.

This suggests fine-tuning a base model (with SL or RL) generally doesn't make the model inherently smarter, only the initial self-supervised learning during pretraining does. Though it would be strange if no amount of reinforcement learning could make the LLM truly smarter.

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)

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.

The LLM can generate the correct search space for the problem, but identifying the solution within the search space is inefficient?

Another way to put this: most of students who study the lecture notes for their high school math already have it within them to get a gold on olympiad (the math itself is not more advance than their high school) but getting a high school kid to get gold on olympiad is hard. It might be something similar to P vs NP.

You are going to see a lot of people (both hype and skeptic) tell you things that you can verify. Even while you have a screenshot verifying the opposite of what they are claiming, they will continue to claim it.

For skeptics in particular, you will be able to use a top tier llm and see: does this do the thing someone is claiming it doesn't do? It often will. If you look at recently submitted papers by skeptics you will see them making a claim about state of the art LLMs but then only test using versions from over a year ago (this has happened recently!^)

The way for you to be sure what is what is to just use the thing for yourself and decide what is true.

^ https://x.com/tylercowen/status/1881051976102035880

You could have a rich mathematical knowledge, while being not very good at proving theorems. Also, you might be good at proving competitive mathematics problems without having a rich mathematical knowledge. It's also possible to have rich mathematical knowledge, and being good at proving theorems but mostly in the field of your expertise.

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

https://x.com/mbalunovic/status/1887962694659060204

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.

"My Fair Llama" or "Pygmallm"

GAIR is the generative AI lab at SJTU.

This training is less about learning how to reason and more about conditioning the llm to use self-evaluations automatically. You could probably reproduce this effect yourself by sticking a paper reminder in front of you and writing "after every small step, spend 2 minutes considering if it's right and does it work in the context of the task so far; evaluate alternatives" on it. (which yes, could improve reasoning likely)

Why is that?

   Come in under the shadow of this impure rock  
   And I will show you something different from either
   Your shadow at morning striding behind you
   Or your shadow at evening rising to meet you;
   I will show you wisdom in a handful of sand.

what's the connection here? just the words "less is more"?

Yeah that was the idea behind the Phi series of models. It gets good benchmark results but you can still tell something is missing when you actually try to use it for anything.

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?

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.

[1] https://github.com/deepseek-ai/DeepSeek-R1

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.

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.

For 1, they apply non-reasoning model then apply reasoning model.

indeed, these machines do a great mimicry of "reasoning", we get fooled by it.

the word reasoning has been subverted by those pushing these llms, and we all have bought-in. quite a magic trick this illusionist has pulled on us.

Does it matter if they mimicked it better than most humans?

I don’t have enough karma to downvote adverts.

https://news.ycombinator.com/item?id=42896559