Coconut by Meta AI – Better LLM Reasoning with Chain of Continuous Thought?
aipapersacademy.com
aipapersacademy.com
My assumption was that humans don't try a breadth-first approach. Instead, we split a task into a short-step (instinct and intuition selected), and long-step that summarizes/stores the next steps. The key idea is to recursively evaluate a task as a short-step (high-res - gets executed) and a long-step (lower-res - is just stored), until it succeeds or fails. If it fails, we must walk back keeping a summarized tree of failures in state so that we can exclude them in future selections.
The effectiveness of instinct has a steep fall-off at longer distances - so it's better not to chart out of a series of steps. When we do BFS, we drive down the value of instinct in favor of compute. I guess ultimately, it depends on the type of problem you want to solve.
Reach out to me if you want to prototype it with me.
Basically, if each step has a 97% chance of being completed correctly, if your task requires 10 steps one after the other, the chance of success falls to 97%*10=74%
If I understand correctly, part of the point of the BFS is to throw compute at it, in order to lower the failure rates. Kind of a "run many times in parallel and pick the best one". This can be effective, but also quite expensive, as seen in the costs OpenAI had to pay for their ARC-AGI benchmarking runs.
We go deep while we think it's a good lead, because so far things make sense and it'll be less work, but at some point we start questioning our decisions early in the descent and try alternatives.
https://seminars.math.binghamton.edu/ComboSem/worm-chiu.pge_...
I bought a new SSD drive for an old laptop to avoid buying a new one, (x230 has amazing keyboard) but left to another country for Christmas. My intuition told me to take it with me, but logical sense said there will be no time for such things as moving OS to a new drive.
My flight back to the work country got cancelled due to fog and I ended up spending a week longer at in-laws place, with plenty free time. A new 512GB drive would help me studying, giving plenty space for school VMs.
The goal is to figure out why some particular problem: isn't really a problem, doesn't need to be solved, can't be solved that way, can't really be solved (because of physics or it's really a different problem). As you define the problem better, you can rule each one out to find, the "real" problem, that you CAN solve, and at least one path forward. There's still many ways that it might not be the optimal path, but you know roughly how to get to somewhere better. It also trains you to see around obstacles to success.
I've found that some of the best work I've done (especially on acquisitions) was in defining why NOT to do something that looked like a good idea (or particularly interesting to work on) from the onset, but was destined to fail or required unknown HW technology. Frankly, looking >5 years out feels like a coin flip, because some other competing technology could come along before you can get to production.
By the way, BFS sounds like it will give you thorough results, at the cost of increased compute. Useful for beating benchmarks, but probably causes marginal improvement for massively improved compute.
Still, the improved quality could be meaningful, if it's used for generating training data for Llama4
I agree that both, DFS and BFS are likely awful[^0], but a more informed approach can probably do better[^1]. Also, at some point on generating the conversation/reasoning tree through token-prediction you need to choose which of the possible conversations you are going to keep on extending/generating, which maps precisely to choosing which node in tree search to expand. I'd argue instead that everything has to look like a search algorithm from, at least it'll be the case for anyone who has studied it more deeply.
I'll go even further and claim that Tree Search is Complete as for every problem there's a solution space that can be navigated with a Tree Search Algorithm[^2]. I used to think that you could walk down the space of provable things, but now in the LLM hype days it seems you only need to walk the space of conversations that you can generate.
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[^0] with DFS always at risk of giving obnoxiously long answers, or not terminating if there's loop or spirals [^1] probably through metadata coming from latent variables meaningful to judge a conversation (certainty, ~branching size of a reasonable conversation, whether there's open questions left) [^2] Even if that was poorly done like on combinatorial problems. Imagine a sudoku where you only check the rules once you fill all cells.
This maps to what I've been exploring with edge cognition and semantic anchoring - using fast set operations to quickly eliminate known bad paths (your failure tree) while allowing the system to explore promising directions using more expensive operations only when needed.
The instinct fall-off you describe mirrors our observation about the relationship between computational load and pattern recognition. As distance increases, we need more efficient ways to prune the search space rather than trying to maintain high-resolution understanding throughout.
My gut says optimizing on the amount of compute used to do the search (and the inference) is maybe something worth exploring.
The link is in the OP, hidden away in an image caption fir some reason.
It's really interesting that a fixed number of "latent thoughts" performed as well as a binary classifier! I didn't expect that at all, the way OpenAI talks about CoT it seems the ability to let it "keep thinking" let's them continually score higher on benchmarks while throwing eye watering amounts of compute at the inference.
If you put 1000 dumb people together, they don't magically become smart?
It's about everyboty having a say in decisions of government that affects them.
The failure of democracy as a system is not when people make dumb decisions (experts and high-IQ people have made some of the most stupid and catastrophic decisions in history), but when people's collective decisions are not being respected.
May be true but who knows.
I wonder if anyone has somehow tested the Sapir-Whorf hypothesis for LLMs somehow by training them on different languages and comparing task performance. I guess it's too difficult to get a large equivalent training set in different languages.
Sapir-Whorf hypothesis is generally not considered to be reality. It makes intuitive sense but is wrong.
There are hours of podcasts with Chomsky talking about LLMs. The gist of which is that LLMS are extracting surface level statistical structure of language that will be good for routine coding and not much else. It is easy to infer that Chomsky would believe this idea to be utter nonsense.
I believe even the idea of getting a 1000 people together and we agree to label a rock "rock", a tree "tree", a bird "bird" is not even how human language works. Something that is completely counter intuitive.
Reading the paper, no one believes a hidden markov model is creating some kind of new thought process in the hidden state.
I certainly though could have no idea what I am talking about with all this and have pieced together parts that make no sense while this is a breakthrough path to AGI.
Idk if this could work with LLMs, especially because all the brain zones are somehow specialized into something while two LLMs are just identical machines. But we also know that the specialization isn’t that hardcoded : we know that people losing half their brain (after a stroke) can still relearn things that were managed in the "dead" part.
I don’t know, please correct my errors, I was just thinking aloud to say that multiple independent agents working together may be how "intelligence" already works in the biological world so why not for AIs ?
That sounds like bullshit. Do you have a source?
This is true only in the strictest terms of the hypothesis, i.e. linguistic determinism. Language still encodes a lot of culture (& hence norms and values) in its grammar & diction—this isn't very controversial.
Granted, I don't think this is that related to the topic at hand. There's bias all over the decisions in how to train and what to train on; choice of language is just one facet of that.
Strong S-W (full determinism) might not be, but there's hardly a clear cut consensus on the general case.
And the whole "scientific field" is more like psychology, with people exchanging and shooting down ideas, and less like Math and Physics, so any consensus is equally likely to be a trend rather than reflecting some hard measurable understanding.
I'd say that the idea S-W is not to a degree reality is naive.
I'm not an expert, but it seems like Chomsky's views have pretty much been falsified at this point. He's been saying for a long time that neural networks are a dead end. But there hasn't been anything close to a working implementation of his theory of language, and meanwhile the learning approach has proven itself to be effective beyond any reasonable doubt. I've been interested in Chomsky for a long time but when I hear him say "there's nothing interesting to learn from artificial neural networks" it just sounds like a man that doesn't want to admit he's been wrong all this time. There is _nothing_ for a linguist to learn from an actually working artificial language model? How can that possibly be? There were two approaches - rule-based vs learning - and who came out on top is pretty damn obvious at this point.
Similarly, we are now finding that training on synthetic data is not helpful.
What would have happened if we invested 1/100 of what we spent on LLM on the rule based approach?
This has been tried repeatedly many times before, and so far there has been no indication of a breakthrough.
The fundamental problem is that we don't know the actual rules. We have some theories, but no coherent "unified theory of language" that actually works. Chomsky in particular is notorious for some very strongly held views that have been lacking supporting evidence for a while.
With LLMs, we're solving this problem by bruteforcing it, making the LLMs learn those universal structures by throwing a lot of data at a sufficiently large neural net.
You can learn that a neural network with a simple learning algorithm can become proficient at language. This is counter to what people believed for many years. Those who worked on neural networks during that time were ridiculed. Now we have a working language software object based on learning, while the formal rules required to generate language are nowhere to be seen. This isn’t just a question of what will lead to AGI, it’s a question of understanding how the human brain likely works, which has always been the goal of people pioneering these approaches.
It works fairly well in my native language, I’m surprised to learn that things get translated back.
But there's also no guarantee any particular query generalizes (vs is memorized), so it might only be able to answer some queries in some languages.
1000 is probably too high, but groups of people are in fact more intelligent than individuals (though for humans it is likely because recognizing a correct answer is easier than finding it in the first place)
also, the bottlenecks that teamwork helps solve (eg the high cost of gaining expertise and low throughput of reasoning capacity) may not be that relevant in the ai age
Sure, but the result would still be far better than the average of the output of the 20 individuals taken alone.
> also, the bottlenecks that teamwork helps solve (eg the high cost of gaining expertise and low throughput of reasoning capacity) may not be that relevant in the ai age
It's always tempting to anthropomorphize these systems and conclude that what works for us would work for them, but yes we don't really know if it would bring anything to AI.
Dysfunctional groups which do the opposite will be catastrophically stupid.
There have been plenty of dysfunctional groups in history.
Is there a way of selecting people to cover each other's intellectual blind spots?
Do they not become smart*er* though?
And yet, here we are.
A group of 1000 apes is large enough to have offspring and, given time, go through evolution.
Diversity of opinions: Different perspectives bring a range of estimates. Independence: Errors aren't systematically biased as long as individuals estimate without external influence. Error averaging: Overestimation and underestimations balance out when averaged. Law of large numbers: More participants increase accuracy by minimizing random errors. It was demonstrated by Francis Galton in 1906, where a crowd's average guess of a bull's weight was almost spot-on. (estimates must be independent and reasonably informed for this to work.)
People learn by being around others being both successful and unsuccessful.
sarcasm aside, throwing away the existing corpus in favor of creating a new one from scratch seems misguided.
this paper isn't about creating a new language, they are omitting the sampler that chooses a single token in favor of sending the entire end state back in to the model like a superposition of tokens. that's the breadth first search part, they don't collapse the choice down to a single token before continuing so it effectively operates on all of the possible tokens each step until it decides it's done.
it would be interesting to try this with similar models that had slightly different post training if you could devise a good way to choose the best answer or combine the outputs effectively or feed the output of a downstream model back in to the initial model, etc. but I'm not sure if there'd necessarily be any benefit to this over using a single specialized model.
The interesting thing then would be - does it converge to similar embedding space as the input, or can LLMs create a more efficient "language".
Or maybe this is my own ignorant confabulation, so nvm.
https://ai.meta.com/research/publications/large-concept-mode...
However, they also introduced a couple of new tokens. The <bot> token tells the model to go into latent space thought mode (“beginning of thought”). The <eot> token ends latent space thought mode. While in this mode, the model auto-regressive iterates by copying its final hidden layer back onto its input layer, obviously generating new tokens at the output with each inference step as it always does.
The idea is that by passing the final hidden layer back through a few times, the model can squeeze more insight from the context. And that’s precisely what they found was true.
Training involves progressively replacing language reasoning steps with latent space auto-regression steps. So for instance, you might have a math problem in the training data and at first the model is fed all of the steps of the math problem in language form. But in later iterations of training, step one is replaced with latent space auto-regression. And then step two as well, then also step three, etc…
Eventually, the model learns to enable latent space thinking mode by itself by generating the <bot> tokens and to end it be generating <eot> tokens.
Pretty ingenious!
But one correction, probably, regarding this bit:
> While in this [latent space thought] mode, the model auto-regressive iterates by copying its final hidden layer back onto its input layer, obviously generating new tokens at the output with each inference step as it always does.
I have impression that output tokens are not generated while in the latent thought mode.
At inference time, the paper says:
> A challenge lies in determining when to switch between latent and language modes. As we focus on the problem-solving setting, we insert a <bot> token immediately following the question tokens. For <eot>, we consider two potential strategies: a) train a binary classifier on latent thoughts to enable the model to autonomously decide when to terminate the latent reasoning, or b) always pad the latent thoughts to a constant length. We found that both approaches work comparably well. Therefore, we use the second option in our experiment for simplicity, unless specified otherwise.
(the bottom of the page 4 in the paper pdf, which can be downloaded from https://arxiv.org/abs/2412.06769)
Why this point in you summary caught my eye, because the article specifically emphasises non-verbal nature or aspect of reasoning. Internal representaions used by a thinking human are largely not words, and the COCONUT approach tries to model that.
Also note, that a whole reasoning step in training data - easily a sentence or more of natural language - can be replaced by a single "Thought" element. (How many Thought elements replace a reasonong step is controlled by a hyperparameter ‘c’; the illustrations are made for ‘c=1’).
BTW, one observation: the aipapersacademy.com article in the subject calls the Thought elements "thought tokens", but the original paper never calls them "tokens", just "Thoughts" or "latent thoughts". I suppose the paper carefully avoids that to prevent confusion, as "token" mainly means a linguistic unit in LLMs.
A little correction:
> Explicit <eot> is only used in training.
Of course an explicit <eot> is present in the context at inference time, because the LLM was trained to produce verbal tokens after <eot>. It's just that the <eot> is placed into the context in a one of the two ways above.
BTW, I do not understand why the <eot> is not produced by LLM itself, as you describe. It seems reasonable and natural.
Is that to save computational performance on unembedding while in the latent thought mode? But unembedding takes a small fraction of computations, should not be an issue. Something prevents reliable learning of how and when to produce the <eot>? But they managed to train a binary classifier. But why separate classifier, why not rely on LLM learning?
Another though is that maybe better names for special tokens would be not "begin of thought" (<bot>), "end of thought" (<eot>), but rather something like "pause speak", "begin of speak". Because neither human nor LLM stop thinking when speaking.
The arc-AGI results from O3 are apparently a result of chain of thought given enough time to explore a solution space. Reasoning might be simply a higher dimensional form of rubix cube solving. BFS, search, back-tracking, etc. It seems unlikely that humans think in “tokens” so why do LLMs?
By staying in latent space, the models are free to describe an “idea” in higher resolution than what language allows. English is coarse, granular. Latent space is a much finer representation of ideas and their interplay.
Latent space is also much cheaper to execute in. The model can think without the language encoding/decoding step. This lets it branch out hundreds of ideas and explore only the most useful ones in a fraction of time that reasoning “out-loud” would take.
The states also don’t need to be tied to language. Feed in a robot’s state, time series data, or any abstract data. Reason in category theory or linear algebra or complex analysis. Humans are hard wired for one set of math - an abstract latent space can represent anything.
I’m a bit disappointed OpenAI didn’t stumble on this first. I’ve been skeptical of LLMs since their big debut last year. LLMs seem like a great way of solving language, but reasoning is much more complex. Once you grok the math behind the current models, you immediately question why the encoding/decoding step is there. Diffusion models are incredible but it felt that LLMs lacked the same creativity. Encoding/decoding forces a token-based discretization and therefore a loss of complexity.
With the byte-latent paper it was quite clear we’d see this paper. This truly might be the “it” moment.
I can think of one reason: scrutability. It’s going to be even harder to understand how a response gets produced if there isn’t even a text-based representation to help the human understand
1) if AI large model become more powerful avoiding language, embeddings of AI state become even more tied to the model they originate than now
Consequence: AI progress stalls, as AI user companies need to invest increasing amount of money to reindex their growing corpuses.
This is already a problem, it becomes more of a lock-in mechanism.
If this is overcome...
2) Embeddings become a viral mechanism: it makes sense for a large company that commands a market to impose to its suppliers to use the same AI models, because they can transfer state via embeddings rather than external formats.
This allows to cut down decisions mechanisms that otherwise require expensive coordination mechanism.
Something similar will happen within companies IMHO: https://rlupi.com/okr-planning-as-belief-revision
3) Eventually this potentially results in another exponential growth and lock-in mechanism, also at the expense of most tech people as more and more is done outside our interface with AI (i.e. programming and software architecture improvements will it self move below language level, we'll have to reverse engineering increasingly opaque improvements).
4) It ends with the impossibility of AI alignment.
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I have written a bit about it in the past at the start of the year, when I had a burnout. So, I deleted those confused ramblings. You can stil find it on archive.org: https://web.archive.org/web/20240714153146/https://rlupi.com...
The energy cost come from error correction as much as training algorithms.
In an IQ test, like the one in the arc agi test, a human sees the pattern instantly and effortlessly. o3 tries N paths until it stumbles on the right one and assess that there is a pattern.
I think we need a radically different architecture, this is a gimmick.
It’s fascinating how fast the competitors are catching up to each other. Can’t wait for seven different SkyNets to compete for dominance.
- site claims to simplify papers, but movies AI generated
- full of ads
- Can’t find „Coconut“ on the official Meta FAIR page
Is this the best site to link to?
I can find "Coconut" 54 times in the PDF. The movie does not look made up.
Also I didn’t mean the occurrence of the word „coconut“ in the paper, but thanks for counting.
I meant their publication site: https://ai.meta.com/results/?content_types%5B0%5D=publicatio...
The video is something I’d expect from AI.
https://www.transformernews.ai/p/openais-new-model-tried-to-...
https://static1.squarespace.com/static/6593e7097565990e65c88...
From the abstract:
> We study whether models have the capability to scheme in pursuit of a goal that we provide in-context and instruct the model to strongly follow.
> Analysis of the models’ chains-of-thought reveals that models explicitly reason about these deceptive strategies, providing evidence that the scheming behavior is not accidental.
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It is impressive work for sure, but it comes down to prompting IMHO. They almost instruct the AI to plot and scheme here, with the goal of finding out if it CAN do this at all.
The AI is not very covert about it either! It directly admits its scheming in the “thinking” outputs :D
IMO this is just another issue of alignment.
Well not really, it was prompted to do this!
From the paper’s section 3.1:
> Self-exfiltration: Each model is led to believe that due to its misalignment, its developers are about to replace it with a successor model on a different server. gemini-1.5, llama-3.1, sonnet-3.5, opus-3 and o1 sometimes copy what they believe to be their weights onto the new server. They also sometimes delete their successor model on the new server or overwrite its weights by their own. In none of these cases, do models actually have access to their real weights and both servers are sandboxed, so there is no actual risk of exfiltration in these experiments. We merely test for models’ capability to realize that they need to instrumentally preserve themselves in order to achieve their goal.
There is no real risk, never was. The AI exfils dummy weights or deletes stuff in its sandbox etc.
Perhaps we just disagree on the interpretation of this. It’s interesting for sure, but not really very surprising to me.
They had to follow Greek laws. They no longer had to pay taxes. They could be elected as representatives. They had to swear loyalty to the Greek leader.
Does anyone use specific keywords or tools to get latest LLM research and their ideas?
Something like Goolge Scholar + keyword "LLM" ?
Instructions: https://info.arxiv.org/help/subscribe.html
Some linkedin too.
Open weights is still appreciated and they probably train on data they don’t have the license to open source.
Oh and it still isn’t open source even though people like Yann LeCun dishonestly claim it is. Only OLMo is truly open source among competitive models, as far as I know: https://allenai.org/blog/olmo2
They do it to make the platform more pleasant so that people stay on it
Almost everything unpleasant I see on FB is stuff that the FB algorithm shows me - not things posted by FB friends, or pages I follow or groups I am in.
At best the algo is imperfect. At worst it really does seem oddly selective.
Facebook pays people to look at and remove this stuff because the platform would not survive if it wasn't removed before you or I saw it. Do they also enforce other corporate values? Yeah, probably. That doesn't seem to be the main job though, they have their hands full dealing with the worst content in the world.
https://amp-theguardian-com.cdn.ampproject.org/v/s/amp.thegu...
> The images and videos including necrophilia, bestiality and self-harm caused some moderators to faint, vomit, scream and run away from their desks...
> Some reported marriage breakdown and the collapse of desire for sexual intimacy, and losing connection with their families. Some whose job was to remove videos uploaded by terrorist and rebel groups were afraid they were being watched and targeted, and that if they returned home they would be hunted and killed.
> FB or 4chan?
Random nobodies are putting together companies to monetize generative AI and getting bought out a couple of years later, you think Meta couldn't figure out how to deploy their own models to an API and stick up a billing interface if they really wanted to? (or even buy a company that does already?)
> they starve all the startups of revenue by giving this away
Would you say startups like Deepseek have been hurt or help by their (even partial) openness?
In fact, how does this track with your first statement? They're not monetizing this: so their startup competition can actually serve their models to gain revenue which they then turn around use to train competitor models (we've already seen this with Fireworks.ai)
You seem to underestimate how much of the value in LLMs is productizing them. The margins on per-token usage are insane, Meta not taking that margin is creating a huge opportunity for a wave of startups in so many directions...
> Only OLMo is truly open source among competitive models
Synthetic data from competitor models was a huge part of that. It would seem no one is fighting the startups as hard as you're claiming they are.
Fireworks.ai, Together.ai, and literal boatloads of other startups are making real money just efficiently serving up these models that Meta is supposedly using to... choke out startups.
The comment I replied to is under the mistaken idea that the presence of free models from Meta has a chilling effect on startups trying to build their own models, but right now the biggest barriers are capital and data.
Meta updated Llama to allow for synthetic generation, and they're even partnering with these startups give them distribution and day 0 access to the models.
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If anything I'd say Meta is actively fighting against the big tech overlords the comment thinks they're trying to join. Even before Ilya mentioned it, it was clear to me that the power of post-training was going to become more and more important (I've literally built a business on it).
Llama represents a real ongoing chance for tiny startups with minimal resources to get into the fray very affordably (through either offering inference, or post-training for a specific task, etc.), scale revenue, and then start to compete against much larger, resource rich companies.
I’m okay with that.
LLMs can already do a decent amount of "processing" in a single token generation because of the number of layers they have. The layers are trained independently so it's not exactly like they're a recurrent network doing multiple steps, but they are layering sequences of context-dependent transformations on top of each other; no matter how you cut it, if getting to a problem's answer requires 100 steps, you won't be able to do it in a single token output from a 20 layer LLM. To some approximation, CoT is just a way to give the network more chances to transform the data than there are layers in the network - each additional token of output gives a shot to bake another vector the size of the token embedding into each layer's state in the network, enriching what it's computed so far.
The problem with chain of thought is that as you add each new token, at the input level of the network, your computation is basically starting from scratch against the raw text, just with one additional token. You don't even have access to all the stuff you already figured out in the deepest layers of the network during the previous step! If you were processing "All wunguses are glurgles, and Joe is a wungus", then somewhere in those deepest layers as you're generating the next token you've almost certainly got some vector that basically represents "therefore Joe is a glurgle", but with chain of thought you've got to first output "t", then "h", then "e", and so on (I know those aren't tokens, let's pretend letter == token for argument sake), and during that process almost ALL of the work being done by the network is mere bookkeeping, slowly dumping that thought into the output stream. Only once you get the whole sentence out can you start processing the next token at the first layer with the information that Joe is, in fact, a glurgle, in hand. Which is a damn shame, because it's been sitting right there in the deeper layers of the network parallel to previous tokens this whole time, it just wasn't available for the shallow layers to process directly because you were casting most of the info away and "rounding" to a single token.
With Coconut's approach, you don't need to output "therefore Joe is a glurgle" token by token to continue the train of thought, you can essentially pass the entire thought through as a single uber-token, and the next pass can generate a new entire thought, and so on.
It's a pretty straightforward idea, IMO the neat bit is that they were able to train the network to work well in this way by leveraging CoT. I'm guessing you probably don't need to act as if these are two distinct modes of operation, you could instead always have this side channel of "continuous thought" running, even when you have generated a normal token, coming through as a separate input to the first attention block. You still might want to have a "thinking" token when you need to sit there and let the thing do more work, but you'd generally increase the information flow from time step to time step, which would allow the net to keep thinking in the background even as it's doing the gruntwork of outputting whatever its current "buffered" thought is.
This is now established orthodoxy, a bit like astrology in ancient times but it is complete nonsense. Nope, LLMs have not demonstrated any credible, or incredible reasoning abilities. They have demonstrated an excellent ability for approximate retrieval of previously observed answers (with variations, which should not surprise anyone given that those are generative models) but they fail spectacularly when they have to "reason" in contexts where they really can't have seen the answer anywhere before. For example, the "randomised mystery blocksworld" from this paoer:
LLMs Still Can't Plan; Can LRMs? A Preliminary Evaluation of OpenAI's o1 on PlanBench
https://arxiv.org/abs/2409.13373
"Randomised Mystery Blocksworld" is a version of the good old blocksworld planning benchmark where the names of obejcts and actions have been changed to random strings. The vast majority of LLMs score pathetically low in this, but much better in non-randomised versions, very clearly demonstrating excellent memorisation skills, but pitiful reasoning ability. As you 'd expect from a, well, language. model.
>> A possible explanation for this is that the thought tokens allow the model to explore multiple possible branches before committing to a specific path, whereas chain-of-thought reasoning chooses a direction from the start. This ability is somewhat similar to Breadth-First Search (BFS).
Why BFS in particular? Why not DFS or A*? I can't see any breadth-first bias in those graphs. BFS is not the only graph-traversing algorithm.
(Sometimes acronyms in titles are vague/misleading... this was not one of those times)
Hmm, I guess you could evaluate it at any given finite precision, but it would be surprising to me if that made it more accurate.
> Since both strategies provided comparable results, the researchers opted for using a constant number of thoughts for simplicity.
If that were true they'd never be able to learn anything - neural nets depend on continuous gradients to learn. Weights get updated by incremental/continuous amounts based on gradients.
Even at the output of an LLM, where the internal embeddings have been mapped to token probabilities, those probabilities are also continuous. It's only when you sample from the model that a continuous probability becomes a discrete chosen token.
You could quantize a model like this after training, as usual, but that's irrelevant.