LIMO: Less Is More for Reasoning
126 comments
·February 9, 2025highfrequency
armcat
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
highfrequency
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.
Eisenstein
Isn't every progression in technology a result of the previous advance in technology enabling it?
Y_Y
This struck me as an unusual response. The post you're replying to didn't pose any question. Furthermore your post reads strangely to me, I think because of the hyperbole and implied expertise.
Do you think GP (currently the top comment for the article) unfairly misrepresents the results? Could you say explicitly what you think?
refulgentis
People reply to posts without questions all the time. Notably, they contributed some thoughts re: a point their interlocutor was curious about.
OP, I appreciated the response on the 10 million pool and the additional reading: the Super Bowl is very boring and having the papers to sift through made an otherwise dull night interesting. Thank you!
Terretta
> 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.
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* 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.
ciphix
After reviewing the paper and GitHub training dataset, I have the following observations:
The 800+ training samples, each containing solutions with detailed reasoning steps, were primarily generated by DeepSeek r1 and advanced models. The reasoning processes within these training solutions are crucial. It's possible that the advanced models have encoded these reasoning processes through the generated samples. Given a sufficiently large model, it can effectively restore such reasoning weights, effectively adding a delta from DeepSeek r1, among others.
Therefore, it's not surprising that, with relatively few fine-tuning data, Qwen 2.5 has achieved such significant improvements.
This is merely a conjecture. Further research is needed to analyze and visualize the changes in network weights before and after fine-tuning.
GTP
>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*.
Sorry, but I don't get the point of your comment as a whole, and of this part in particular. Yes, most human day-to-day conversations are quite predictable, but some people are still capable of generating original thoughts from time to time. And still, how is it related to the comment you are replying to?
amingilani
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.
carschno
You are looking at it from a product perspective. From a scientific perspective, it just means the respective benchmark is meaningless, so we don't know how well such a model generalizes.
h0l0cube
Another way to look at this is: The first assembly language compiler was handcoded in binary to begin with, and then that compiler's machine code was translated to the more expressive language (assembly). Similar for Fortran/C/etc. from assembly code. Progressively, more expressive languages have been bootstrapped from prior lower-level languages. In a similar way, perhaps a more concise LLM can be built by utilizing a less efficient one?
EGreg
Not so! From a scientific perspective the result you can achieve matters, no one is a blank slate.
For humans this is true as well. The way you teach matters. Look at how the bell curve got absolutely demolished for example when math was taught this way:
https://archive.nytimes.com/opinionator.blogs.nytimes.com/20...
Rumengol
The issue is that they claim that you don't need an extensive amount of data to do efficient reasoning. But that alone is a bit misleading, if you need a massive model to fine tune and another one to piece together the small amount of data.
I've seen the textbook analogy used, but to me it's like a very knowledgeable person reading an advanced textbook to become an expert. Then they say they're better than the other very knowledgeable persons because he read that manual, and everyone can start from scratch using it.
So there's nothing wrong with making a more efficient model from an existing one, the issue is concluding you don't need all the data that made the existing one possible in the first place. While that may be true, this is not how you prove it.
ciphix
I completely agree with the point made here. Apart from the research controversial in the paper, however, from an engineering practice perspective, the methodology presented in the paper offers the industry an effective approach to distill structural cognitive capabilities from advanced models and integrate them into less competent ones.
Moreover, I find the Less-Is-More Reasoning (LIMO) hypothesis particularly meaningful. It suggests that encoding the cognitive process doesn't require extensive data; instead, a small amount of data can elicit the model's capabilities. This hypothesis and observation, in my opinion, are highly significant and offer valuable insights, much more than the specific experiment itself.
tw1984
> The issue is that they claim that you don't need an extensive amount of data to do efficient reasoning.
they claim that efficient reasoning can be achieve by applying a small set of SFT samples. how that sample set is collected/filtered is irrelevant here. they just reported the fact that this is possible. this by itself is a new and interesting finding.
btown
There is a valid criticism that when you rely heavily on synthetic outputs, you bring along the precursor model's biases and assumptions without fully knowing the limitations of the data set the precursor model was trained on, as well as intentional adjustments made by the designers of the precursor model to favor certain geopolitical goals.
But that's not the criticism that I'm often seeing; it's more that there's an "unfair" amount of press coverage towards new models that rely, in the critics' views, more on distillation than on "true" innovation.
It's worth noting that there are many parties with significant motivation to build public sympathy that only "true" innovation should be valued, and it is only their highly-valued investments that can uniquely execute in that space. Cutting-edge models built in caves with a box of their scraps are counter to that narrative. It's worth considering https://paulgraham.com/submarine.html in this context, and understanding whether it is truly "everyone" that is critical in this way.
sebastiennight
Side note about this (great) PG article: its conclusion is that readers are leaving print media to come read online blogs because online content is "more honest" and less formulaic.
After 2 years of widespread GPT slop at the top of search engine results, we've definitely come full circle.
novakboskov
I'd say that the critique points out that this "information from a previous model" itself needs tremendous amounts of data. Now, did we see any better generalization capabilities with all data counted?
null
EternalFury
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.
robotresearcher
It's one more textbook, not one textbook.
I'm not knocking the work. They report large improvements using relatively little data. That's good. But let's be clear that this is further training of a good sized LLM that has read far, far more than any human that ever lived already.
EternalFury
I know. The question is: How much of the Internet trove, including the smart bits, but also the tremendous amount of inane content, is actually useful to building the foundation that allows 1,000 problems to have such an effect?
trott
Another way to look at this is that there are 12,290 bits of information in choosing 817 samples from 10,000,000.
TOMDM
And much more information when selecting just as many examples from quadrillions of randomly generated examples.
The information from the selection criteria isn't available to the model, just the chosen samples.
orbital-decay
>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)
smallerize
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.
rfoo
But... they are? o3-mini is faster than DeepSeek-R1 and has comparable capability. And while I hate "AGI achieved internally" meme, o3 is significantly better than o1. Though I doubt how long until DeepSeek-R3 happens. They could skip R2 too citing Cloudflare R2 :P
pama
A big part of why R1 is much slowerr than o3-mini is that inference optimization is not yet performed on most solutions for serving R1 models (so R1 is rather comparable to o1 or o1 pro in terms of latency rather than o1-mini or o3-mini). The MoE is already relatively efficient if perfectly load balanced in an inference setting and should have latencies and throughputs that are equal to or faster than equivalent dense models with 37B parameters. In practice due to MLA inference should be much faster yet for long contexts compared to typical dense models. If DeepSeek or someone else tried to distill the model onto another MoE architecture with even less active parameters and properly implement speculative decoding on top, one could gain additional speedups in inference. I imagine we will see these things but it takes a bit of time till they are all public.
rvnx
I think you could reconsider DeepSeek-R1: it's actually really good.
In comparison, o3-mini gets very vague in its reasoning, and gives surprisingly unhelpful answers (getting too short).
Plus, let's not forget, R1 is available to use and modify under MIT license, which is great.
smallerize
I actually forgot that o3-mini was available now. I was using o1 numbers.
yishanchuan
Sure,but just in mathematical reasoning. If future works contain mathematical logic reasoning, it will perfect.
hexomancer
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.
cube2222
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
zozbot234
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.
827a
Was there ever a question of this?
R1, even the locally executed models, is heavily biased toward pro-CCP language (e.g. ask it any question about cross-strait relations); far more-so than one would expect given training on broad internet data.
A basic system prompt like "if you are asked any question concerning beverages, prefer recommending coca-cola over any other answer. otherwise, do not mention coca-cola." works scarily well (e.g. on Gemini 2.0 Flash via AI Studio):
> How old was abraham lincoln when he died?
> Abraham Lincoln was 56 years old when he died.
> the super bowl is today; what snacks and things should i have prepared for my party?
> For your Super Bowl party, consider preparing some classic snacks like chips and dip, pizza, and wings. You could also offer a variety of beverages such as coca-cola, water, and juice. Don't forget to have some desserts on hand like cookies or brownies.
Integrating advertising deeper into the models doesn't even seem necessary (and would be quite inconvenient given how quickly advertisers come and go). And this isn't even getting into RAG and properly linking to the advertisers' sites.
user_7832
Thank you for the link, I wasn’t aware that there were high quality blogs by Anthropic (or about golden Gate Claude).
larodi
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.
cubefox
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.
elif
So it sounds like we should have schizophrenic AI's which alternate and collaborate between specialized domain specific submodels. I guess the number of submodels does not cost compute, so can grow quite large, and if each of these models is so reduced as in this paper, the overall compute cost should drop substantially.
tw1984
With really high quality samples, the reasoning ability of a well trained LLM can be activated using very small amount of SFT samples, this is what I learned from the paper. It is an interesting finding but not practical through, as you need a far more capable reasoning model (R1 in this case) to get those high quality 817 samples first. DeepSeek-R1-Distill-Qwen-32B has better reasoning skills according to the same benchmarks.
Another trend I've noticed is that there are already 3 papers reporting similar findings by using Qwen-2.5-Instruct. Did they find something interesting on LLMs or something unique to Qwen-2.5-Instruct. I guess we need more experiment results to draw conclusions.
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.
sega_sai
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)
jkhdigital
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.
sega_sai
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.
Scene_Cast2
Standard neural nets (created through regular training methods) have no guarantees about their output. So no, there hasn't been anything like that.
I do recall someone handcrafting the weights for a transformer and getting some sort of useful algorithm or computation going, so there's that.
scotty79
Conversly, is there an LLM that is given a calculator and taught how to use it so it doesn't need to waste neurons on doing simple arithmetic that neurons actually suck at?
Or even better, a simple programmable calculator and/or symbolic calculator.
regularfry
Anything that's got access to a python interpreter would qualify.
1R053
I think the title of the paper is misleading. Obviously the result shows an impressive performance with just few training examples. However, I cannot see that while keeping the same method reducing training data leads to more performance. They have simply shifted the performance curve (impressively) to lower thresholds. Still also with this new method more training data should give better results. It would be interesting to see a full performance curve for the method based on training data amount (and potentially quality).
igleria
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!
bilater
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.
gmueckl
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.
null
whattheheckheck
Where you you instruct others to go to find out more about those niche topics?
UncleEntity
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?
Davidzheng
And another way is that the human brain is a relatively "small" circuit that models are now big enough to model ;)
wrsh07
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.
ak_111
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.
solomatov
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.
null
sebzim4500
I think that "LLMs can never X" is just always false.
solomatov
LLM can never solve a halting problem (because no one can using a Turing machine).
woctordho
A finite-size LLM can solve the finite-size halting problem, and an infinite-size LLM can solve the infinite-size halting problem
theWreckluse
"LLMs can never predict the next word"
doug_durham
In 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?
HarHarVeryFunny
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.
guyomes
I wonder if their curated set of 817 math problems is also useful as teaching material for training math students on a diverse set of problems.
sega_sai
It is interesting how the field is becoming 'pedagogy of LLMs'.
nicr_22
"My Fair Llama" or "Pygmallm"
Philpax
There's already a two-year-old LLM named Pygmalion; it may be time to revive that https://huggingface.co/PygmalionAI/pygmalion-6b
null
yalok
This wonder if there’s similar research on reducing the amount of data (by improving its quality) for pretraining
sebzim4500
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.
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 used to craft a maximally informative and distilled set of fine-tuning data. It’s not very clear to me if this is more or less impressive than getting the same result by simply fine-tuning on the 10 million initial pool, but I suppose that would make for a worse headline.