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Comment by nickelpro | Hacker News Reader

> We found that the trained Othello-GPT usually makes legal moves. The error rate is 0.01%; and for comparison, the untrained Othello-GPT has an error rate of 93.29%. This is much like the observation in our parable that the crow was announcing the next moves.

I read the whole article, but I think this statement largely disproves the hypothesis? We only need a single counter example to show that Othello-GPT does not have a systemic understanding of the rules, only a statistical inference of them.

A model that "knows" the rules will make no errors, a model that makes any errors does not "know" the rules. Simple as.

And I feel this way about much of the article, they state they change intermediate activations and therefore the observed valid results prove that the layers make up a rules engine instead of a statistical engine. And I don't make that leap? Why would that necessarily be the case?

Obviously a statistical engine trained on legal moves will mostly produce legal output. A rules engine will always produce legal output.

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> A model that "knows" the rules will make no errors, a model that makes any errors does not "know" the rules. Simple as.

This is the problem of induction. How many white swans do you have to see before you can claim to "know" that all swans are white? There is no amount where you can make this claim with certainty, right?

The reason you can claim knowledge of fixed rules here is because you already knew there were fixed rules going in. You didn't have to infer the existence of these rules merely from looking at the inputs and outputs.

GPT is analyzing this as a black box and it's doing exactly the rational thing: it's inferring a strong confidence that a certain class of moves are legal, but leaving a small room for doubt in case there's some corner case it hadn't yet considered.

I agree there is more room for better generalization [1,2] that will take statistical correlations and attempt to infer explicit models to explain those correlations, but there must always remain some quantifiable doubt that those models are true, and the "desire" to make the wrong move sometimes to test your "knowledge".

[1] https://pubmed.ncbi.nlm.nih.gov/31639888/

[2] https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.12...

That's why I said if it made no mistakes it would offer strong evidence. We couldn't know it would never make a mistake, but the evidence would be wiggling its eyebrows suggestively.

Similarly, the presence of mistakes doesn't completely damn the assertion that there is a world model at play. The world model could simply be inaccurate.

All I'm saying is that since there are mistakes, we know for a fact there isn't an accurate world model at play. Absent that possibility, there's not compelling evidence to say anything about the nature OthelloGPT. It's the exact same kind of inscrutable as every other LLM.

> if it made no mistakes it would offer strong evidence

I don't see how this has anything to do with the article. TFA's authors weren't trying to make the GPT "know the rules" of Othello, or anything similar. The GPT doesn't even know there are rules, or that a game is being played, so the whole question is neither here nor there.

Rather, TFA is asking: given that the GPT learned to predict token sequences that correspond to Othello moves, did it do that with or without inferring the presence of a gameboard and simulating the on/off states of that board? The answer to that question has nothing to do with whether the GPT predicts valid token sequences with 100% or 99% or 95% accuracy, the issue is or isn't simulating the state of the Othello pieces.

This is not what they claim, the central claim is that OthelloGPT has developed a "causal model", "an understandable model of the process producing the sequences" (For example: "are they picking up the rules of English grammar?"). Ie, does OthelloGPT know the rules of Othello?

They make a clear distinction between world representation ("board state"/"internal activation"), and world model ("game engine"/"LLM Layers"), see their diagram [1].

That state exists it not interesting or new, a LLM necessarily transforms input sequences into a form of state in order to predict the next word in a sentence, and OthelloGPT necessarily transforms the move sequence into an internal state in order to predict the next move.

The only interesting question is what mechanism picks the next move, simply following the patterns (the crow, calling out the next move), or an understanding of the rules of the game (the crow, analyzing a fresh board).

Except that's a false dichotomy, the analogy doesn't work, the crow "analyzing a fresh board" is still capable of just doing pattern recognition.

[1]: https://lh6.googleusercontent.com/zvQObJtkqyFey9TD2Ibzx5K9s5...

The crow never analyzes any board - that's the point of the analogy. It only hears a sequence of tokens, and it learns to predict future tokens, and TFA sets out to answer whether it does that by "surface statistics" (i.e. which tokens are more likely at which times), or with a "world model" (by laying out a bunch of seeds and flipping some of them over after each token in order to simulate the state of the game).

Edit: from other replies, I think I see the issue here. In TFA, "world model" is referring to the insight that "D4, E5, B3" are more than just tokens in a grammar - that they represent graph nodes with state, and that when each token occurs it toggles the states of other graph nodes. TFA is asking whether the LLM has learned that insight, as opposed to merely detecting patterns in the token sequences without any model of what they represent.

You seem to be taking "world model" to mean something quite different - like "a rule-based understanding of game rules that isn't statistical" or such. TFA doesn't discuss or investigate anything along those lines, just whether the LLM is simulating the on/off state of Othello pieces.

Ok, I've read the original paper.

I agree with you fully on the claims made in the paper, and agree those claims are broadly substantiated by the paper.

I completely disagree that those claims are what is represented in the opening paragraphs of this article they have written, which directly analogizes to learning the grammatical rules of English and syntax of C++, which describes the model as understanding "the process producing the sequences".

Demonstrating that the model processes the input sequence into a representative state, and that manipulating that state has a causal effect on the output, is a very different ball game than "our model understands the rules behind this sequence".

> is a very different ball game than "our model understands the rules behind this sequence".

The authors state plainly what they mean by "understands the rules". That the phrase could also mean other things is no reason to dispute their conclusions.

> All I'm saying is that since there are mistakes, we know for a fact there isn't an accurate world model at play.

But I'm saying something different: even if a system has a world model that it believes is accurate, it still should be making intentional "mistakes" to test the world model in unusual circumstances, just like we continue to stress test thermodynamics, electromagnetism, gravity, etc.

So the evidence that GPT still makes mistakes is not necessarily evidence that it doesn't have an accurate world model. It could be evidence that it has a very rational approach to handling evidence (you should never have 100% confidence!) and is continuously testing world models.

> even if a system has a world model that it believes is accurate, it still should be making intentional "mistakes" to test the world model in unusual circumstances

I have no idea how to address this.

StockFish is an accurate world model of chess. It doesn't make mistakes, it cannot make mistakes. That's what an accurate world model is.

A system that can intentionally make mistakes is likely not a world model of anything at all. If it is a world model of something, it is a world model of something other than Othello, which does not have rules for "stress test"ing.

The OP is claiming that they have created an accurate world model for Othello, so I think discussion of intentional mistakes and thermodynamics is outside the scope.

Under your definition, humans don’t have world models either. If you just gave someone the move sequences, and no other knowledge of Othello, they too would have no way to be 100% sure that other moves won’t show up. It’s not a very useful definition.

> The OP is claiming that they have created an accurate world model for Othello, so I think discussion of intentional mistakes and thermodynamics is outside the scope.

It's not out of scope because these all fall under the problem of induction, which is what I mentioned in my first post. There is no such thing as achieving "certainty" in such scenarios where you don't have direct access to the underlying model, there is only quantified uncertainty. This was all formalized under Solomonoff Induction.

So I'm making three points:

1. Your requirement for "knowledge" to be "100% certainty" in such scenarios is just the wrong way to look at it, because such certainty isn't possible in these scenarios, even in principle, even for humans that are capable of world models, eg. swap a human in for GPT and they'll also achieve a non-zero error rate, even if they try to build a model of the rules. There is no well-defined, quantifiable threshold at which "quantified uncertainty" can become "certainty" and thus what you define as "knowledge". Therefore "knowledge" cannot be equated with "certainty" in these domains. The kind of "knowledge" you want is only possible in cases when you have direct access to the model to begin with, like being told the rules of Othello.

2. Even if you do happen upon an accurate model, you'd never know it and so have to continuously retest it by trying to violate it, so you cannot infer the lack of a internal model from the existence of an error rate. The point I was making with this is that your argument that "a non-zero error rate entails a lack of an accurate world model" is invalid, not that GPT necessarily has an accurate world model in this case.

3. I also dispute the distinction you're trying to make between statistical "pattern matching" and "understanding". "Understanding" must have some mechanistic basis which will have something like this kind of pattern matching. I assume you agree that a formalization of Othello's rules in classical logic would qualify as a world model. Bayesian probability theory where all the probabilities are pinned to 0 or 1 reduces to classical logic. Therefore, an inferred statistical model that asymptotically approaches this classical logic model, which is all we can do in these black box scenarios, is arguably operating based on an inferred world model with some inevitable degree of uncertainty as to specifically which world it's inhabiting.

I don’t think we’ve seen any evidence of experimentation in these models, it is in fact the key component they are missing

Sure, but my point is simply that evidence of mistakes does not necessarily entail a lack of an accurate world model. When underlying models can only be inferred, there can never be 100% certainty that any inferred model is truly accurate, even when it is. Humans are only certain of Othello's rules because we have direct access to those rules.

If you put a human being in GPT's place in this exact same scenario, they too would make comparable mistakes. Humans are clearly capable of world models, therefore those mistakes are not an indication that world models are not in use.

Humans make mistakes with rules too.

Just because a move has never been played, doesn't make it illegal, only untried. Only when the ruleset itself is laid out as overarching the data (as in AlphaGo/Zero) should they always be respected.

Things that are observed to be true are called (in math/science) "laws" aka rules of thumb. Actual rules have other names.

Most people have a world-view/mental-model of how money works. Few actually know the rules and what are possible things under the extreme conditions.

Edit: in the case of AlphaGo/Zero the interesting thing wasn't the rules. They were hard-coded. The interesting thing is that it likely did form mental/world-models in higher layers above the rules in the form of tactics and strategies, these are the valuable parts.

If the only understanding of the rules is what has been tried/untried, that is definitionally a statistical model.

A valid rules model does not require to see all possible rules be played to understand the legality of a move.

So the LLM under study here could be at most, an invalid rules model. But an invalid rules model is indistinguishable from a statistical model, and the authors give no evidence for why we should believe it to be the former instead of the latter.

An interesting comparison is between AlphaZero and MuZero[0], the latter having not been given the rules and has improved upon AlphaZero in Go.

> "MuZero really is discovering for itself how to build a model and understand it just from first principles." — David Silver, DeepMind

So yes to both: statistical and a world model.

[0] https://en.wikipedia.org/wiki/MuZero

So, quantum mechanics?

> Just because a move has never been played, doesn't make it illegal, only untried.

Well, I think this is nickelpro's point. Namely that the model "does not have a systemic understanding of the rules, only a statistical inference of them."

However, I would still counter nickelpro's point with the idea that what we call systemic understanding is fallible - and most likely statistical in nature. Another response below gives the example of a human understanding the rules of chess but still making incorrect moves.

I might even say that any system truly capable of understanding is inherently fallible. A digital calculator or conventional database is impressive in its accuracy and consistency precisely because the rigor within its programming operates beyond the realm of understanding.

I think the argument that human knowledge is itself statistical is far more interesting than the claim that neural nets have accurate models of the systems that feed their training data; but neither claim has much to do with the other.

I'm not sure why you say these claims are unrelated. The article claims to have found the existence of concepts embedded in the trained parameters of a model. (You called this having a "systemic understanding of the rules.") You are saying that for this to be so, the model would have to perform with 100% accuracy. The general form of this argument is that for a system of intelligence to be endowed with a conceptual understanding of a ruleset, it would have to implement that ruleset with 100% accuracy, right? Well, given that human's don't implement rulesets with 100% accuracy, we'd then need to concede that either 100% consistency is not a requirement for understanding or else human's do not operate with understanding.

Exactly, the claim that humans do not operate with perfect understanding is far more interesting (and IMHO, likely) than the idea that LLMs are spontaneously producing accurate models of the systems used to generate their data.

And again, the claims are unrelated. There's no reason to believe that humans and LLMs operate under similar principles, and a ton of reasons to believe that they absolutely do not.

This is what you said originally: "We only need a single counter example to show that Othello-GPT does not have a systemic understanding of the rules, only a statistical inference of them." I don't believe this statement to be true.

It is clearly not true that a single counter example rules out systemic understanding of rules for ALL intelligent systems. Human intelligence is offered as the case in point.

So, given that the statement is not true for all systems, by what logic do you conclude that the statement is true specifically for an LLM?

> It is clearly not true that a single counter example rules out systemic understanding of rules for ALL intelligent systems.

I didn't say anything about "intelligence", the OP is not about "intelligence".

The OP claim is, "we find interesting evidence that simple sequence prediction can lead to the formation of a world model". A world model, an accurate one, is a very different thing than a statistical model. An inaccurate world model is indistinguishable from a statistical model.

An accurate world model, definitionally, does not make mistakes. These models are trivial to produce, classical chess engines are accurate world models.

> Human intelligence is offered as the case in point.

I think you've hit on a more interesting point about human intelligence, that it is often not an accurate world model, which means it is inaccurate or more likely, statistical in nature.

> So, given that the statement is not true for all systems, by what logic do you conclude that the statement is true specifically for an LLM?

So what we're left with is that OthelloGPT (and humans, but again, what's going on with humans is irrelevant to the study of an LLM) is in one of two scenarios, it either:

A) Has an inaccurate world model, or we might say, an accurate world model of a game that is not Othello

B) Is still basically just a curve fitting algorithm, which there's all the evidence in the world to suggest it is

It sits upon the authors to distinguish between these two choices, and they never offer any evidence either way. So I side with B.

A model that tries these moves is more valuable than one that doesn't. It's easy to filter out by rules if we have them, but harder to get something to look beyond if it's self-restricting.

Othello is even more interesting here. There are no rules excluding a particular move other than "you must capture at least one of your opponents pieces". In that regard its much simpler than chess, and a valid move is more consequential than in Go. Trying to make an illegal move in Othello would be extremely weird.

A reasonable strategy for a computer to play Othello to beat beginners is to literally evaluate the legality of all moves in a predefined order and make the first legal one. The predefined order encodes general positional advantage while the legality check enforces validity.

In short, I strongly agree that making even 1 illegal move in Othello indicates a lack of understanding the rules.

I know the rules of chess, but my rate of attempting illegal moves is above 0%.

Especially if you’re playing blind. I’d say an error rate of less than %1 is pretty good in that case.

A human mind is not a rules model for Chess, and comparisons to a human mind are worthless. We're not asking if the LLM is human, only if it is modeling the game rules or modeling statistics

My point is this:

* If the results of the model were perfect, not a single counter-example, that would be a strong argument that the LLM has built an internal model of Othello

* If counter-examples exist, the result of the experiment is indistinguishable from a sufficiently clever statistical inference and proves nothing

So you assert that parent doesn’t have an internal model of chess?

Or that only proved expert systems built specifically to play chess have an internal model of it?

> So you assert that parent doesn’t have an internal model of chess?

I think it's an interesting question, I find it more likely we have an imperfect ability to perceive the whole chess board, whatever the hell that might mean.

In any case it's irrelevant to an LLM which has perfect information from the input set.

So perhaps we rephrase the question, I think the parent, if given a list of individual chess moves (in whatever notation pleases them), should be able to tell if a given move is valid or not for the given piece. If the parent failed to do that, I would say they do not have a valid model of chess, ya.

> If the parent failed to do that, I would say they do not have a valid model of chess

Surely even the world's foremost chess experts will occasionally make errors in such a situation, so what's the point of holding language models to an intelligence standard that even humans can't meet?

I see two ways of interpreting this: either language models do approximately learn world models, or else world models aren't necessary for human intelligence

EDIT: I see from your other posts in this thread you're probably more inclined to believe the latter statement, which wasn't obvious to me from your first post and I think that explains why there is so much contention in this thread.

Well, if the model has a 100% grasp of the rules, why call it a model?

Because it's not a physical othello board? It's just an internal model of an othello board encoded in the weights of a neural net?

Insert whatever semantics float your particular goat

I thought the whole point was about modelling rules not atoms.

> A model that "knows" the rules will make no errors, a model that makes any errors does not "know" the rules. Simple as.

Does this mean that human minds are merely statistical inference engines and don't truly get the models either? Because they make tons of mistakes.

I'm starting to think that at scale, quantity starts becoming quality, and there isn't a fundamental difference between a model and statistical inference. It's like vector graphics vs pixels, after a certain level of detail they are the same.

Yes, there's not reason to think that every movement, every decision, that humans make is made according to a purely rules-modeled decision engine.

If a GM makes an invalid move at chess, they demonstrably were not following the rules in that moment. That decision wasn't made according to a rules engine. They scanned the board, made a series of statistical inferences and other processes still well beyond our ability to describe, and made a move without validating it against all the rules and a complete observation of the board.

This doesn't tell us anything about OthelloGPT, and honestly I think it was self-evident about humans already. "We are not calculators" shouldn't be a surprise to anyone.

> A model that "knows" the rules will make no errors, a model that makes any errors does not "know" the rules. Simple as.

Wittgenstein would ask, does it matter if the model “knows all the precise rules” or not?

Does it matter if I know all the precise rules? Can two of us have a fun game of chess if we basically know all the rules and mainly make legal moves or at least not notice when we break a rule or can agree on an action when we’re confused?

What’s important is that we or the model play the same game with others. We don’t need to worry too much about the definitions. We just need to observe the results to deduce if there was any sort of meaningful interactions.

What exactly is offsides in soccer? Or pass interference in football? Or a balk in baseball?

If your claim is that you've produced a computer program that accurately models the rules, it matters a great deal. It is, perhaps, the only thing that matters.

A calculator that says 2+2=5, even 0.01% of the time, is not a very good calculator.

Yeah, but we’re trying to play football here. We’ve already got calculators!

Even chess grandmasters may rarely make illegal moves, but I doubt you can argue that they don't know the rules unless you also believe that humans can only learn surface statistics and not world models.

If the chess grandmaster makes an illegal move, than in that moment, they are not playing by the rules. It's definitional.

The GM was, in that moment, operating by some other model to evaluate the board state, likely a pattern recognition/statistical model that did not fully evaluate the state of the board.

ChatGPT can, today, list all the rules of chess accurately. ChatGPT cannot play chess with any great degree of accuracy. "Knowing" the rules, in so much as the ability to list them out accurately, is not the same as following the rules.

There's no reason to believe that humans operate as rules engines in all things, and a great deal of evidence (as with your example of chess GMs making mistakes) that they absolutely are not. That human intelligence is itself partially, and perhaps even largely, statistical in nature.

>he is not playing by the rules. It's definitional.

Sure but the question is: does the grandmaster know the rules?

Because if what you said is true:

>A model that "knows" the rules will make no errors, a model that makes any errors does not "know" the rules. Simple as.

Then the grandmaster doesn't know the rules. "Simple as".

The GM is not a game model of chess. The GM is a human. The GM does not evaluate their world according to the rules of chess at all times or in all things.

The claim is that OthelloGPT is a game model of Othello. The only input it has is a move list, the only output it produces is a resulting move. Actual game models, such as Stockfish for chess, are incapable of producing invalid moves, it is not in their set of possible outputs.

OthelloGPT is not a game model of Othello. It might be a game model of something that is not Othello, but this is hard to tell.

The reliance on what humans can do is not a useful comparison here. Humans are also not game models of Othello. Actual game models, programs that model the rules of Othello, are the useful point of comparison.

Again, claiming to know the rules, "knowledge" of them, and following those rules, acting according to them, are totally different things. The former is outside the scope, "what is uppercase-k Knowledge" is a question of philosophy. Demonstrably following the rules is the world of game models.

If the semantics of putting the word "know" in quotes is what you're hung up on, fine, replace it with whatever pleases you: A model that "follows/encodes/exhibits" the rules will make no errors, a model that makes any errors does not "follow/encode/exhibit" the rules

When someone asks: "Does the LLM know the rules?" Then it's a simple binary answer "yes" or "no" depending if the model makes errors, in this case 0.01% so for you it's clearly no, when I ask: "Does the grandmaster know the rules?", then you dodge the question because you realize that what you are saying is not as simple as you want to make it out to be.

> We only need a single counter example to show that Othello-GPT does not have a systemic understanding of the rules, only a statistical inference of them.

I don't agree with this binary interpretation. This only indicates that any systemic understanding the model has internally built is not complete. We are not trying to assess completeness of that understanding. E.g. if you had a traditional rules engine for Othello, and you removed one rule that could result in illegal moves, does that make that rule engine a statistical model all of a sudden?

No, it makes it an engine for a game that is not Othello.

An inaccurate engine and a statistical one are indistinguishable. And the authors provide no evidence to prefer the former.

Nothing is ruled out, of course, but there's not strong or compelling evidence either.

> An inaccurate engine and a statistical one are indistinguishable.

How so? The paper is trying to assess if some semantic understanding is being created by the underlying model, not if a completely accurate one is. If such a world model maps to Othello-prime (gleaning concepts like tiles, colors etc), that is still a very interesting result.

No-one ever told it the rules, it was just shown a load of game-moves.

If you explained Othello to a human using _only_ example moves, they would think they probably knew the rules, but they wouldn't be 100% sure either.

Children also occasionally make incorrect moves in simple games, and I've seen grown adults who I know understand how knights move still accidentally place them in the wrong spot.

But these are temporary accidents that given a few seconds to look at the board and the move that was made, any person would realize they had made a mistake. I.e. because we have the rules and understanding of the game modeled internally.

A computer that only had a statistically inferred understanding wouldn't "realize" they had made a mistake and take back their move.

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