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Ladder: Self-improving LLMs through recursive problem decomposition
- mentalgear 2y ago> We demonstrate LADDER's effectiveness in the subject of mathematical integration, improving Llama 3.2 3B's accuracy from 1% to 82% on undergraduate-level problems
- RossBencina 2y agoKeep in mind that state of the art term-rewriting systems perform very well on symbolic integration, e.g.: https://rulebasedintegration.org/ https://rulebasedintegration.org/
- jgalt212 2y agoIndeed. Don't the LLMs have access to the RUBI rule set? It's open source. Why are they not memorizing the rules?
- igravious 2y agoMy hunch: It's better that we don't hard-code hard-won specialised knowledge. It's better that this tech can learn from more fundamental foundational principles that can be leveraged to apply to many many specialised domains.
- igorkraw 2y agoNah, it's much simpler, the models aren't reliably able to recall the correct rule from memory - it's im the training set for sure. This is another specialized synthetic data generation pipeline for a curriculum for one particular algorithm cluster to be encoded into the weights, not more not less. They even mention quality control still beim important
- InvidFlower 2y agoWell, not sure if that part matters as much (from first principles). But the more important part being that RL lets a model figure out which methods are effective for it. Most of the time it probably has the tools already from pre-training, but doesn't "make the connection" to use them (or at least not often enough).
- samstave 2y agoF_yes -- The thing to take here is that this should be a function_callable *feature* of a bot. Basically, when architecting a persona ; "USE THESE RULES OF ENGAGEMENT" Also -- where my CheckListManifesto folks at -- While we are building Patterns/Personas/Purgatories for our bots... We need to be able to reference a central CODEX of : "Do this task but imbue yourself with (XYZ) name places" -- AND LEARN FROM THE OTHERS (so maybe a task marketplace of AI persona action?) @ callable in an IDE
- majordroid 2y ago> We also introduce TTRL (Test-Time Reinforcement Learning), where we perform reinforcement learning on variants of test problems at inference time. TTRL enables Qwen2.5 7B Deepseek-R1 Distilled to achieve a state-of-the-art score of 90% on the MIT Integration Bee qualifying examination, surpassing OpenAI o1's performance. That's incredible!
- Davidzheng 2y agoi mean they have a verifier, so can't they even get to 90% just by random generation by the net and testing against verifier until it's numerically correct? I think the end solve rate is less important and the generality of approach is maybe more important
- vessenes 2y agoNo, they specifically test for this (the "RL" case). They most particularly can not do this with random generation, which is very interesting.
- Davidzheng 2y agobut i mean it depends on how many attempts you let it generate. the right comparison is to use the test time rl compute to just do generation and compare success rates. (if you gen for long enough you eventually will hit the answer by chance)
- yangikan 2y agoIs there code for this paper or something that does something similar to this?
- mentalgear 2y agoIt's exciting to see approaches like RL and curriculum learning, which I always felt were the way to go for real self-improvement ~7y ago when training in robotics (openAI gym days), finally getting successfully applied to NLP/LLM to highly boost small model performance. (Ladder is a sort of RL self curriculum learning approach)
- all2 2y agoI know all of these words, but I do not know what they mean together. What is curriculum learning? What is the "RL" approach? "~7 ago": days? Weeks? Years? What is an "open ai gym days"? LLMs and robotics?
- katzenversteher 2y agoI can only help with RL, that's probably reinforcement learning. As far as I remember that means you let the model perform a task that can be "graded" and then depending on how well it did it get's a reward it want's to maximize. I believe (this it where I'm very insecure, I could be wrong) the neurons (weights / biases) of the neurons that where involved in reaching the highest reward get adjusted to have a bigger influece.
- FeepingCreature 2y agoI fed the two comments verbatim into Grok: > Curriculum learning: Training that begins with easy examples, gradually increasing difficulty. > RL (Reinforcement Learning): Learning via trial-and-error with rewards, like training a robot or model to optimize actions. > ~7y ago: ~7 years ago (circa 2018). > OpenAI Gym days: Refers to using OpenAI Gym, a toolkit for RL, popular in robotics/AI research ~2016-2018. > LLMs and robotics: Large Language Models (LLMs) now leverage RL techniques from robotics for better performance. I think the last one is a semi-hallucinatory stretch. LLMs are large language models, ie. ChatGPT, Sonnet, Grok, R1. Robotics are ... robotics. Building robots. The actual answer to what the comment is saying is that until maybe a year back, we trained language models - still with RL, but with RL on token error, which isn't "real" RL because it executes tasks "by coincidence". That is, it happens to be that when you train a model to predict text, it also gains the ability to do tasks in the bargain, because the text contains agents that do tasks. A year or so ago, we started training models by having them do a task, judging if the task was successful or failed, and then performing RL on task outcome rather than token prediction. This is a return to "classic RL", but we had to pass through the "token RL regime" first so that the model could make progress on realistic tasks at all. It also means that LLMs can now increasingly be employed in robotics, where task RL training rules, as there is no massive preexisting robotics movements dataset like there is for text. (Also, NLP is Natural Language Processing, ie. what LLMs do.)
- EMIRELADERO 2y agoWhat the hell is going on this week?!?!? (asking positively, with a smile on my face) I have seen at least 3 interesting/mildly promising breakthroughs on ML just these past two days! I mean, a Google research team just discovered that you can combine NNs with CLAs using digital logic gates as a medium, so you could potentially reduce many kinds of non-linear problems to a simple, efficient digital circuit! And it was on the HN front page, TODAY![1] I keep seeing more mind-bending stuff related to neural nets and logic/intelligence in general, my mind has been running wild with speculation about the future and just how close we could (or could not) be to truly understanding how intelligence works from first principles. [1] https://news.ycombinator.com/item?id=43286161 https://news.ycombinator.com/item?id=43286161
- meitham 2y ago>>> asking positively, with a smile on my face Responding with unexplained fear in my heart, we’re just getting closer to Skynet!
- blooalien 2y ago> Responding with unexplained fear in my heart, we’re just getting closer to Skynet! I'll take a cold logical machine super-intelligence over the mad human lunatics wielding current iterations of "A.I." technologies in some really terrifyingly dangerous ways. As someone else commented on some other thread earlier "I look forward to being paperclips".
- Philpax 2y agoUnfortunately, those humans are developing that super-intelligence. Are you ready to submit to Elon Musk's Grok ASI?
- optimalsolver 2y agoConsidering Grok was saying he and Trump are the biggest spreaders of disinformation, and that they're both the most deserving of the death penalty, maybe it won't be so bad: https://finance.yahoo.com/news/elon-musk-ai-turns-him-163201403.html https://finance.yahoo.com/news/elon-musk-ai-turns-him-163201... https://x.com/benhylak/status/1893086436930527665 https://x.com/benhylak/status/1893086436930527665
- bloomingkales 2y agoI’m kinda getting the sense this is still just prompt engineering in a loop. Persona-based prompting: We prompted the model to adopt different mathematical perspectives (e.g., "think like Euler focusing on series", "approach like Gauss looking for patterns"). I mean … I guess that’s scientific? Besides that, how can the model learn at test time (at inferencing)?. It’s stateless, it doesn’t incorporate the last prompt into the model.
- regularfry 2y agoIt learns through the context. The context is state. There's a bit of a cheat that's going on here though in that the model is being given the fundamental integration operations as part of the problem. That means the model hasn't had to learn what they are. It might not have needed to be given them, but it does feel like that's giving the model a leg up in the benchmarks that it wouldn't otherwise have, and when there's a direct comparison to (e.g.) DeepSeek, that's an unfair advantage.
- viking123 2y agoDoes the massive context still needs to be dragged around? Until get a neural network that adjusts weights in real time without relying on a huge clump of context being cycled there, I don't think there will be an AGI or even an impressive "agent". Current agents are just LLM looping lmao sold to people with no knowledge how they work at all.
- regularfry 2y agoI've been wondering about context compression, actually. I remember a bunch of prompt compression tricks from a couple of years ago that must be usable. If you were to say "anything past half context gets compressed, including the previously-compressed context" would mean you'd still have reasonable workspace and potentially infinite recollection of the most important things. Then yes, you'd be dragging a massive context around, but you're maximising the return on using it. I presume somebody's got a toolkit for this that I don't know the right terms to google for.
- Davidzheng 2y agotest-time training/RL is definitely the right approach for math AI in the future. It is probably one of only a few ways to spend an obscene amounts of compute at a given problem (think 10^5 gpus for a few days) and has hopes of making progress when test-time inference scaling may not at first (think if you try to do MCTS on a go position with a bad value/policy net). Alphaproof already did this but nice to see it done again--good results!
- Davidzheng 2y agoactually I think the interesting thing is to see how much of the boosted performance can be distilled back into the LLM at small sizes. Then you can emulate really how alphazero works b/c you have a policy improver (test time rl with similar problems). and we get to see just how strong a small net can be theoretically (say 32B or something)
- eru 2y agoThis might be trivial, or deep, depending: We have done a lot of that improving historically by publishing research and textbooks. I can solve (some) problems today in minutes that would have stumped Isaac Newton for a life time (or at least a few weeks). Of course, you are hinting at a more general distillation, I suspect.
- InvidFlower 2y agoWe've already seen Qwen's new QWQ 32B (not distilled) model doing impressive things on benchmarks. It'll definitely be interesting to see how just good small models can get. When combined with rag and large context window for expanded knowledge, might be able to get pretty far.
- brookst 2y agoA little like the T2 read only versus learning mode switch: operating on intrinsic knowledge versus able to reason improvements.
- neoneye2 2y agoSidenote: `Tufa Labs` team includes the `MindsAI` team of ARC-AGI fame. https://tufalabs.ai/team.html https://tufalabs.ai/team.html
- ThouYS 2y agonice!
- niemandhier 2y agoFrank Herbert knew it: This is basically an implementation of the mentats recursive self inspection described in Dune.
- isaacfrond 2y agoReminds me of a quote by famous number theoretic mathematician Hendrik Lenstra: For every problem you can't solve, there's a simpler problem that you also can't solve.
- techwizrd 2y agoIs this quote real? I'm familiar with George Pólya's, "If you cannot solve the proposed problem, try to solve first a simpler related problem" but I cannot find any source for the Lenstra quote.
- gessha 2y agoI also found it connected to Polya [1] https://www.pleacher.com/mp/mquotes/mobquote.html https://www.pleacher.com/mp/mquotes/mobquote.html
- isaacfrond 2y agoI’ve heard him say it myself in a lecture on the AKS primality test. So, ehh, the source is oral tradition I guess.
- v1t 2y agoyeah https://www.reddit.com/r/quotes/comments/16qgwcv/if_you_cant_solve_a_problem_then_there_is_an/ https://www.reddit.com/r/quotes/comments/16qgwcv/if_you_cant...
- Horffupolde 2y agoThat doesn’t induce nicely. Unless it was an insult.
- bubblyworld 2y agoMonotonic sequences can be bounded!
- samstave 2y agoIt reads like the famous Churchill quote about "if you gave me poison I would drink it"
- pyryt 2y agoSome names are just too tempting https://arxiv.org/abs/1507.02672 https://arxiv.org/abs/1507.02672
- revskill 2y agoLlm keeps deleting my file content proved that we have far many things to do.
- explosion-s 2y agoI would love to be able to use the actual model! If I'm understanding correctly this makes small models as intelligent as much larger models like GPT4o
- barteloniu 2y agoTheir test time RL approach seems a bit fishy. From what I understand, TTRL works by asking a language model to generate simpler versions of the test case. Once we have the simpler problems, we run RL on them, hoping that an improvement on the simplified cases will also strengthen the model performance on the original problem. The issue is, they use a numerical integrator to verify the simpler problems. One could imagine a scenario where a barely simpler problem is generated, and the model is allowed to train on pretty much the test case knowing the ground truth. Seems like training on the test set. The rest of the paper is nice though.
- thomasahle 2y ago> the model is allowed to train on pretty much the test case knowing the ground truth The task is to solve the integral symbolically, though, right? It's a hard problem to solve, even if the model is given access to a numerical integrator tool it can use on the main problem itself.
- barteloniu 2y agoThat's a fair point.
- goyel 2y agoI wonder why nobody made a NN to find the weigths faster and better than gradient descent
- thomasahle 2y agoAt the end of the paper they mention "two problems from the 2025 MIT Integration Bee qualifying exam which the system continued to answere incorrectly". They say the questions were among the most complex questions on the exam, but the first one is just ∫ ∛(x · ∜(x · ∜(x · √(x · √(x · ⋯ ))))) dx which just requires you to compute 1/3 + 1/(3*4) + 1/(3*4*5) + ... So hardly very advanced math.
- Workaccount2 2y agoIt's a 7B model. So while the problem is not advanced the model is far from it too.
- johntb86 2y agoI'd be curious what would happen if you SFTed a larger model with successful reasoning traces from the smaller model. Would it pick up the overall reasoning pattern, but be able to apply it to more cases?
- nis0s 2y agoWhat’s the difference between this and what Wolfram Alpha has been doing? https://www.wolfram.com/artificial-intelligence/ https://www.wolfram.com/artificial-intelligence/
- evjan 2y agoI had NotebookLM make a 15 min podcast about it and listened to it while walking the dogs. It was a very interesting way of trying to understand a research paper! You need a google account to access it unfortunately. https://notebooklm.google.com/notebook/fbaba495-d4f2-48a3-a3c2-09cb826b351b/audio https://notebooklm.google.com/notebook/fbaba495-d4f2-48a3-a3...
- cratermoon 2y agoHow many rungs of a ladder would you be willing to climb if you knew that each rung was made from half the previous rung?
- ma9o 2y agodivide and conquer :)
- flakiness 2y agoOff topic, but their site is lovely: https://tufalabs.ai/index.html https://tufalabs.ai/index.html It feels like a gold rush for sure.
- daxfohl 2y agoHow much GPU would an RL like this need for tuning? Is the approach something someone could experiment with themselves, or is it like thousands of USD in cloud costs and/or years of compute if done on a laptop GPU?
- ekidd 2y agoI've seen recent interesting papers on reasoning models with costs from US$6 to US$4,5000. The problem is that you need a bunch of fast RAM for efficient training. But you can do some limited fine-tuning (Q-LoRA, etc) of models up to 14G on a 24 GB graphics card, and full fine-tunes of 1.5G models. It's very affordable for a small university research group. And not totally out of reach for hobbyists.
- daxfohl 2y agoReally $6? Where was that?
- vessenes 2y agoThat this works at all is pretty interesting. That it seems to work very well with math is quite interesting. That said, this paper is part of the move we have right now blurring the lines of training and inference -- part of their method involves doing some reinforcement learning on questions they don't know the answer to, but can decompose into simpler questions, and using GRPO on those with a numerical 'checker'. This reinforced model then can answer more questions. I like this. I think humans do this a lot; mulling on something, turning it over in their heads, analogizing, etc. Adding test time training is a way to do a lot more thinking than adding tokens to the context for fixed inference. Just as DeepSeek and o1/o3 show that we can increase capacity with inference-time-token generation and assessment, it looks like we can increase capacity with inference-time automated fine tuning as well. I'd hope that as these techniques solidify we'll have a new way to talk and think about this -- they are all part of the same fundamental process at some level. Either way, super cool.