They are not developed as a matter of averaging over all the text on the internet.
Concepts do not pre-exist concepts.
Whereas a more focused question like "can an AI produce outputs that are novel to someone familiar with all of the AI's inputs?" seems resolvable, and even if one thinks it's unlikely or not easy, it's very hard to buy the idea that it's impossible.
No, not really. People in this area are severely poorly informed on animal learning, and "ordinary science".
AI evangelists like to treat as "merely philosophical matters" profoundly scientific ones.
The issues here belong to ordinary science. Can a machine with access only to statistical patterns in the distribution of text tokens infer the physical structure of reality?
We can say, as certain as anything: No.
Associative statistical models are not phenomenological models (ie., specialised to observable cause-effect measures); and phenomenological models are not causal (ie., do not give the mechanism of the cause-effect relationship).
Further, we know as surely as an athlete catching a ball, that animals develop causal models of their environments "deeply and spontaneously".
And we know, to quite a robust degree, how they do so -- using interior causal models of their bodies to change their environments by intentional acts can confirm or disconfirm environmental models. This is modelled logically as abduction, causally as sensory-motor adaption, and so on.
This is not a philosophical matter. We know that "statistical learning" which is nothing more than a "correlation maximisation objective" over non-phenomenological, non-causal, non-physical data produces approximate associative models of those target domains -- that have little use beyond "replaying those associations".
ChatGPT appears to do many things. But you will see soon, after a year or two of papers published, that those things were tricks. That "replaying associations in everything ever written" is a great trick, that is very useful to people.
Today you can ask ChatGPT to rewrite harry potter "if harry were evil" or some such thing. That's because there are many libraries of books on harry potter and "evil" -- and by statistical interpolation alone, you can answer an apparent counter-factual question which should require imagination.
But give ChatGPT an actual counter-factual whose parts are only in the question, and you'll be out-of-luck.
Eg., tell it about tables, chairs, pens, cups and ask it to arrange them using given operations so that, eg., the room is orderly. Or whatever you wish.
Specified precisely enough you can expose the trick.
Um. How do you square that claim with the well-known Othello paper?
The issue isn't that associative statistical models of domain Z aren't also models of domain Y where Y = f(Z) -- this is obvious.
Rather there are two problems, (1) the modal properties of these models arent right; and (2) they don't work where the target domain isn't just a rephrasing of the training domain.
Why do you think the data LLMs are trained on are non-causal? Lets take causation as asymmetric correlation. That is, (A,B) present in the training data does not imply (B,A) presence. But of course human text is asymmetric in this manner and LLMs will pick up on this asymmetry. You might say that causation isn't merely about asymmetric correlation, but that of the former determining the latter. But this isn't something we observe from nature, it is an explanatory posit that humans have landed on in service to modelling the world. So causation is intrinsically explanatory, and explanation is intrinsically causal. The question is, does an LLM in the course of modelling asymmetric correlations, develop something analogous to an explanatory model. I think so, in the sense that a good statistical model will intrinsically capture explanatory relations.
Cashing out explanation and explanatory model isn't easy. But as a first pass I can say that explanatory models capture intrinsic regularity of a target system such that the model has an analogical relationship with internal mechanisms in the target system. This means that certain transformations applied to the target system has a corresponding transformation in the model that identifies the same outcome. If we view phenomena in terms of mechanistic levels with the extrinsic observable properties as the top level and the internal mechanisms as lower levels, an explanatory model will model some lower mechanistic level and recover properties of the top level.
But this is in the solution space of good models of statistical regularity of an external system. To maximally predict the next token in a sequence just requires a model of the process that generates that sequence.
The conditional probability:
P(x[0]| x[-1], x[-2], x[-3] ...)
P(x[0] | x[-1], x[-2], ... -> x[0])
To see why this is the case, suppose we do have a god's eye-view of all of spacetime.
P(A|B)
always selects for all instances where B follows A.
P(A| B -> A)
selects only those instances where B's following A was caused by A.
P(ShoesWet | Raining)
is very different from
P(ShoesWet | Raining -> ShoesWet)
To select "Raining -> ShoesWet" even with a gods-eye-view we need more than statistics... since those events which count as "Rain -> ShoeWet" have to be selected on a non-statistical basis.
For the athelete catching a ball, or the scientist designing the experiment, we're interested only in those causal cases.
For sure P(A|B) is a (approximate, statistical) model of P(A| B->A) -- but it's a very restricted, limited model.
The athlete needs to estimate P(ball-stops | catch -> ball-stops)
NOT P(ball-stops | catch) which is just any case of the ball-stopping given any case of catching.
But I think the OP is arguing, essentially, that P(A|B -> A) is only an interpretation of P(A|B) that we have chosen, among the many possible interpretations of P(A|B).
Which I think evokes the problem of induction. How do we know that P(A| B -> A) when all we can observe ourselves is P(A|B)?
No, we actually observe P(A | B -> A) where `B` is our body and `A` is some action we take on the world.
Hume was WRONG. Very wrong.
Statistical AI has the problem of induction; we have bodies, so we do not.
----
As for notation, I'm riffing of Judea Pearl's do notation.
He'd say, P(A|do(B))
but his `do` operator is slightly more general
Google: do-operator, causal analysis, judea pearl, etc.
>> Hume was WRONG. Very wrong.
Oh boy :)
I can see what you're saying about having bodies, but bodies are very limited things and that's just making Hume's point. We can only know so much by experiencing it with our bodies. We've learned a lot more about the world, and its foundations, thanks to our ability to draw inferences without having to engage our bodies. For example, all of mathematics, including logic that studies inference, is "things we do without having to engage our bodies". And those very things have shown us the limits of our own abilities, or at least our ability to create formal systems that can describe the world in its entirety. They have shown us the limits of our ability for inductive inference (and in a very concrete manner - see Mark E. Gold's Language Identification in the Limit).
Machine learning systems are more limited than ourselves, that's right. And that's because we have created them, and we are limited beings that cannot know the entirety of the world just by looking at it, or reasoning about it.
P(A|B) is just P(A | B -> A)
Hume here is just wrong. Our terms refer: `A` succeeds in referring to, eg., Rain. And our experiences aren't "thin", they're "thick" -- this was Kant's point. Our experiences play a rich role in inference that cannot be played by "pictures".
To have a metal representation R of the world is to have a richly structured interpretation which does, in fact, contain and express causation.
ie., R can quite easily be a mental representation of "B -> A". This, after all, is what we are thinking when we think about the rain hitting our shoes. We do not imagine P(A|B), we imagine P(A|B->A) -- if we didnt, we couldn't reason about the future.
The question is only how we obtain such representations, and the answer is: the body with its intrinsic known causal structure.
Whenever we need to go beyond the body, we invent tools to do so -- and connect the causal properties of those tools to our body.
Hume here is wrong in every respect. And it's his extreme scepticism which undergirds all those who would say modern AI is a model of intelligence -- or is capable of modelling the world.
The word isnt a "constant conjunction of text tokens" -- even Hume wouldnt be this insane. Nevertheless, it is this lobotomised Hume we're dealing with.
There is a science now for how the mind comes to represent the world -- we do not need 18th C. crazy ideas. Insofar as they are presented as science, theyre pseudoscience
Anyway this all is why I'm happy I'm not a philosopher. Philosophers deal in logic, but they don't have a machine that can calculate in logic, and keep them in the straight and narrow with its limited resources. A philosopher can say anything and imagine anything. A computer scientist -well, she can, but good luck making that happen on a computer.
So in this sense a minimal set of a-priori concepts are required to be built-in, or else we couldn't learn anything at all.
You might say that this means we can separate the sensory-motor genesis of concepts from their content -- but I think this only applies to a-priori ones.
What i'm talking about is conceptualisations of our environment that provide its causal structure. One important aspect of that is how desires (via goals) change the world. Another is how the world itself works.
Both of these do require a body, or at least a solution to the problem of induction (ie., that P(A|B) is consistent with P(A|B->A), P(A|~(B->A_), P(A| B->Z, C->Z, Z->A), etc.)
I don't disagree with that at all. I'm pretty convinced that, as humans, we can learn and invent all those things we have because we have strong inductive biases that guide us towards certain hypotheses and away from others.
Where those inductive biases come from is a big open question, and I'd be curious to know the answer. We can wave our hands at evolution, but that doesn't explain, say, why have the specific inductive biases we have, and not others. Why do we speak human languages, for example? Why is our innate language ability the way it is? Intuitively, there must be some advantage in terms of efficiency that makes some inductive biases more likely than others to be acquired, but I get tired waving my hands like that.
I'm not convinced that all that absolutely requires a body, either. I think it's reasonable to assume it requires some kind of environment that can be interacted with, and some way to interact with the environment, but why can't a virtual environment, like a computer simulation of reality, provide that? And it doesn't have to be the real reality, either. A "blocks world" or a "grid world" will do, if it's got rules that can be learned by playing around in it.
Of course, this is a rather poor excuse for an explanation. The fact that "outside" and "raining" are close doesn't explain why "my shoes are wet". But it does get us closer to a genuine explanation in the sense that it eliminates a class of wrong possibilities from consideration: every sentence that doesn't have outside in proximity to raining downranks the generation "my shoes are wet". The model is further improved by adding more inductive relationships of this sort. For example, the presence of an expanded umbrella downranks ShoesWet, the presence of "stepped in puddle" upranks it. Construct about a billion of these kinds of inductive relationships, and you end up with something analogous to an explanatory model. The structural relationships encoded in the many attention matrices in modern LLMs in aggregate entail the explanatory relationships needed for causal modelling.
But the machine doesn't know which are the right cases. We aren't presuming there's a column, Z = 1 for B -> A, and Z = 0 otherwise -- right?
The machine has no mechanism to distinguish these cases.
> testing whether each pair is useful in determining the next token
This isnt causation.
> every sentence that doesn't have outside in proximity to raining downranks the generation
So long as the sequential structure of sentences corresponds to the causal structure of the world: but that's kinda insane right?
We haven't rigged human language so that the distribution of tokens is the causal structure of the world. The reason text generated by LLMs appears meaningful is because we understand it. The actual structure of text generated isnt "via" a model of the world.
(Consider, for example, training an LLM on a dead untranslated language -- it's output is incomprehensible, and its weights are abitarily correlated with anything we care to choose.)
Nevertheless, given our choice of token, you do have a model which says:
P(ShoesWet|~Rain) < P(ShoesWet | Rain) < P(ShoesWet|Rain & Outside)
(Which you'll never get, the actual value is `1`. Iff A -> B, then P(A|B->A) = 1 -- this is a deductive inference necessary for ordinary science to take place).
In any case, P(A | B -> A) means without any confounders. To actually find the LLM's approximation of this we'd need to compute:
P(A|B & C1 & C2 & C3 ...) forall C_i..inf
If you find a set of {C} st. P(A|B) has a high probability, you won't find causal conditions.
All that statistical association models here is, at best, salience -- not causal relevance.
This is an odd claim. I certainly say that I picked my cup off the floor rather than I picked my cup off the ceiling because gravity causes things to fall down rather than up. Human language isn't "rigged" to represent the causal structure of the world, but it does nonetheless. The distribution of tokens is such that the occurrence of (A,B) and (B,A) are asymmetric, and this is precisely because of features of the world influence the distribution of words we use. A sufficiently strong model should be able to recover a model of this causal structure given enough training data.
>That's true. But we're choosing these additional conjunctions because we already know the causal model; these conjunctions are how we're eliminating confounders to get an approximation close to the actual.
But these patterns are represented in the training data by the words we use to discuss raining and wet shoes. There is every reason to think a strong model will recover this regularity.
>All that statistical association models here is, at best, salience -- not causal relevance.
That's all we can ever get from sensory experience. We infer causation because it is more explanatory than accepting a huge network of asymmetric correlations as brute. YeGoblynQueenne is right that my point is basically a version of the problem of induction. We can infer causation but we are never witness to causation. We do not build causal models, we build models of asymmetric correlations and infer causation from the success of our models. What a good statistical model does is not different in kind.
When I act on the world, with my body, I take as a given "Body -> Action". We witness causation in our every action.
> This is an odd claim
The tokens can be given any meaning. The statistical distribution of token frequencies in our languages have an infinite number of causal semantics which are consistent with them.
We can find arbitary patterns such that
P(A) < P(A|B) < P(A|B & C) < P(A|B & C...)
No, the structure of language isnt the structure of the world.
This pattern in tokens,
P(A) < P(A|B) < P(A|B & C) < P(A|B & C...)
Phrase any such conditional probability you wish, it will never select for causal patterns.
this is why we experiment. It's why we act on the world to change it.
When the child burns their hand on the fireplace they do so once. Why?
Because the child immediately infers,
P(TouchFire -> Pain | MoveHand -> Pain) = 1
P( TouchFire | Desire_TouchFire -> TouchFire) = 1
P( TouchFire | Desire_TouchFire -> MoveHand) = 1
P( Pain | MoveHand -> TouchFire -> Pain) = 1
In other words, we bottom out our reasoning in a
P( BodilyMovement -> Effect | Desire -> BodilyMovement) = 1
The problem of induction phrased in modern language is this: statistics isn't informative. Or, conditional probabilities are no route to knowledge. Or, AI is dumb.
>> The question is, does an LLM in the course of modelling asymmetric correlations, develop something analogous to an explanatory model. I think so, in the sense that a good statistical model will intrinsically capture explanatory relations.
A statistical model may "capture" explanatory relations, but can it use them? A data scientist showing a plot to a bunch of people is explaining something using a statistical model, so obviously the statistical model has some explanatory power. But it's the data scientist that is using the model as an explanation. I think the discussion is whether a statistical model can exist that doesn't just "capture" an explanation, but can also make use of that explanation like a human would, for example as background knowledge to build new explanations. That seems very far fetched: a statistical model that doesn't just model, but also introspects and has agency.
Anyway I find it very hard to think of language models as explanatory models. They're predictive models, they are black boxes, they model language, but what do they explain? And to whom? The big debate is that (allegedly) "we don't understand language models" in the first place. We have a giant corpus of incomprehensible data; we train a giant black box model on it; now we have a giant incomprehensible model of the data. What did we explain?
>> But this is in the solution space of good models of statistical regularity of an external system. To maximally predict the next token in a sequence just requires a model of the process that generates that sequence.
Let's call that model M* for clarity. The search space of models, let's call it S. There are any number of models in S that can generate many of the same sequences as M* without being M*. The question is, and has always been, in machine learning, how do we find M* in S, without being distracted by M_1, M_2, M_3, ..., ... that are not M*.
Given that we have a very limited way to test the capabilities of models, and that models are getting bigger and bigger (in machine learning anyway) which makes it harder and harder to get a good idea of what, exactly, they are modelling, how can we say which model we got a hold of?
That's the beauty of autoregressive training, the model is rewarded for capturing and utilizing explanatory relations because they have an outsized effect on prediction. It's the difference between frequency counting while taking the past context as an opaque unit vs decomposing the past context and leveraging relevant tokens for generation while ignoring irrelevant ones. Self-attention does this by searching over all pairs of tokens in the context window for relevant associations. Induction heads[1] are a fully worked out example of this and help explain in-context learning in LLMs.
>Anyway I find it very hard to think of language models as explanatory models. They're predictive models, they are black boxes, they model language, but what do they explain? And to whom?
The model encodes explanatory relationships of phenomena in the world and it uses these relationships to successfully generalize its generation out-of-distribution. Basically, these models genuinely understand some things about the world. LLMs exhibit linguistic competence as it engages with subject matter to accurately respond to unseen variations in prompts of that subject matter. At least in some cases. I argue this point in some detail here[2].
>how can we say which model we got a hold of?
More sophisticated tests, ideally that can isolate exactly what was in the training data in comparison to what was generated. I think the example of the wide variety of poetry these models generate should strongly raise one's credence that they capture a sufficiently accurate of poetry. I go into detail on this example in the link I mentioned. Aside from that, various ways of testing in-context learning can do a lot of work here[3].
[1] https://transformer-circuits.pub/2022/in-context-learning-an...
[2] https://www.reddit.com/r/naturalism/comments/1236vzf/
[3] https://twitter.com/leopoldasch/status/1638848881558704129
That sentence should be decorated with the word "allegedly", or perhaps "conjecture"! In practical terms, I believe you are pointing out that language models of the GPT family are trained on a context surrounding, not just preceding, a predicted token. That's right (and it gets fudged in discussions about predicting the next token in a sequence), but we could already do that with skip-gram models, and with context-sensitive grammars, and dependency grammars, many years ago, and I don't remember anyone saying those were specially capable of capturing explanatory relations [1]. Although for grammars the claim could be made, since they are generally based on explanatory models of human language (but not because of context-sensitivity).
Anyway, I thought you were arguing that explanations are arbitrary, "explanatory posits", and wouldn't that mean that an explanation doesn't improve prediction? This is not to catch you in contradiction, I'm genuinely unsure about this myself. My understanding is that explanatory hypotheses improve predictions in the long run [2], but that's not to say that a predictive model will improve given explanations, rather explanatory models eventually replace strictly predictive models.
Are you saying that including explanations in training data can improve prediction? That would make sense, but this is very hard to do when training a predictive model on text. In that case, the explanations are at best hidden variables and language models are just not the right kind of model to model hidden variables.
Sorry, writing too much today. And I got work to do. So I won't bitch about "in-context learning" (what we used to call sampling from a model back in the day, three years ago before the GPT-3 paper :).
______________
[1] My Master's thesis was a bunch of language models trained on Howard Philips Lovecraft's complete works, and separately on a corpus of Magic: the Gathering cards. One of those models was a probabilistic Context-Free Grammar, and despite its context-freedom, and because it was a Definite Clause Grammar, I could sample from it with input strings like "The X in the darkness with the Y in the Z of the S" and it would dutifully fill-in the blanks with tokens that maximised the probability of the sentence. So even my puny PCFG could represent bi-directional context, after a fashion. Yet I wouldn't ever accuse it of being explanatory. Although I would say it was quite mad, given the corpus.
[2] I mention in another comment my favourite example of the theory of epicylces compared to Kepler's laws of planetary motion.
I don't mean to say that explanations are arbitrary, rather that causes are not observed only inferred. But we infer causes because of the explanatory work they do. This isn't arbitrary, it is strongly constrained by predictive value as well as, I'm not sure what to call it, epistemic coherence and intelligibility maybe? Explanatory models are satisfying because they allow us to derive many phenomena from fewer assumptions. Good explanatory models are mutually reinforcing and have a high level of coherence among assumptions ("epistemic coherence"). They also require the fewest number of assumptions taken as brute without further justification ("intelligibility").
Why think explanatory models are better at prediction? Because the mutual coherence among assumptions and explanatory power of the whole (ability to predict much from few assumptions) suggests the explanatory model is getting at the productive features of the phenomena that result in the observed behavior. Essentially, the fewer number of posits, the fewer ways to "bake in" the data into the model. If we were to cast this as a computational problem, i.e. find a program that reproduces the data, shorter programs are necessarily more explanatory. There's no other way to explain the coincidence of program picked out of a small space generating data picked out of a very large space without there being an explanatory relation between the two. Further, our credence for explanation increases as the ratio of the respective spaces diverge.
This is really the problem of machine learning in a nutshell. Is the data vs parameter count over some threshold such that training is biased towards explanatory relations? Is the model biased in the right way to discover these relations faster than it can memorize the data? LLMs seem to have crossed this threshold because of the massive amount of data they are trained on, seemingly much larger than can comfortably be memorized, and the inductive biases of Transformers that search the space of models to extract explanatory relations.
>Are you saying that including explanations in training data can improve prediction? That would make sense, but this is very hard to do when training a predictive model on text. In that case, the explanations are at best hidden variables and language models are just not the right kind of model to model hidden variables.
I agree with this, and I think these explanatory relations are implicit in human text. I gave the example in another comment that I say things like "I picked my cup off the floor" rather than "I picked my cup off the ceiling" because causal relations in the real world influence the text we write. The relation of "things fall down" is widely explanatory. But it seems to me that LLMs are very much general modelers of hidden variables, given the wide applicability of LLMs in areas that aren't strictly related to natural language. But then again, any structured data is a language in a broad sense. And the grammar can be arbitrarily complex and so can encode deep relationships among data in any domain. Personally, I'm not so surprised that a "language model" has such wide applicability.
Like you say, that's the problem of machine learning. There's a huge space of hypotheses many of whom can fit the data, but how do we choose one that also fits unseen data? Explanatory models are easier to trust and trust that they will generalise better, because we can "see" why they would.
But the problem with LLMs is that they remain black boxes. If those black boxes are explanatory models, then to whom is the explanation, explained? Who is there to look at the explanation, and trust the predictions? This is what I can't see and I think it turns into a "turtles all the way down" kind of situation. Unless there is a human mind, somewhere in the process, that can look at the explanatory model and use the explanation to explain some observation, then I don't see how the model can really be said to be explanatory. Explanatory- to whom?
>> But it seems to me that LLMs are very much general modelers of hidden variables, given the wide applicability of LLMs in areas that aren't strictly related to natural language.
Well, I don't know. Maybe we'll find that's the case. For the time being I'm trying to keep an open mind, despite all the noise.
I think this is a very bold claim to make.
Each new idea/technology/concept stands on the back of all that came before it. You couldn't just pull a LLM or a dishwasher out of a hat 1000 years ago.
You're focusing on the example too much. Here are more examples illustrating the question. It's doubtful that LLMs could infer solutions that lie outside their statistical models trained on existing data.
"In 1597 John Thorpe is the first recorded architect to replace multiple connected rooms with rooms along a corridor each accessed by a separate door" [1]
"Despite various publications of results where hand-washing reduced mortality to below 1%, Semmelweis's observations conflicted with the established scientific and medical opinions of the time and his ideas were rejected by the medical community. He could offer no theoretical explanation for his findings" [2]
"Button-like objects of stone, glass, bone, ceramic, and gold have been found at archaeological sites dating as early as 2000 b.c.e... One of the earliest extant pieces of clothing to show the use of buttons as fastenings is the pourpoint of Charles of Blois (c. 1319–1364)." [3]
And so on.
[1] https://en.wikipedia.org/wiki/Hallway?wprov=sfti1
[2] https://en.wikipedia.org/wiki/Ignaz_Semmelweis?wprov=sfti1
[3] https://www.encyclopedia.com/sports-and-everyday-life/fashio...
I think it would help your argument if you could point to such an example from the last couple of years, after the cutoff point of the LLM training data. Maybe though, nothing has been invented since then that is sufficiently unique. If there is something like that, I suppose it would be possible to try and prompt the LLM to create it. That would make your argument falsifiable and I'd be really curious to know the outcome.
Can it come up with a corridor when it has no idea that such a concept exists? That remains to be seen.
This is clearly not true in any meaningful sense - c.f. the Othello paper, examples from the top of this very comment thread, etc.
> Can it come up with a corridor when it has no idea that such a concept exists?
Unless I'm missing something, the person I replied to is claiming that it categorically cannot come up with a concept it hasn't been trained on. I'm disagreeing - if a model knows about rooms and doors and floorplans, there's no obvious reason why it mightn't think up an arrangement of those things that would be novel to the people who trained it. If you think the matter remains to be seen, then I'm not sure what you disagree with me about.
This is useful, but the source of novelty here is the prompt; the rest is the work of interpolation.
This is all very reminiscent of image generation. There too, novelty is limited to interpolation.
Once again, you're missing the point.
In 16th century people also knew about floors, and rooms, and floorpalns. And yet, the first architect to use a coridor used it for the first time in 1597.
What other "corridors" are missing from LLMs' training data? And we're sure it can come up with such a missing concept?
The Othello paper and the examples (are you referring to the example of coming up with new words?) are doing the same thing: they feed the model well-defined pre-established rules that can be statistically combined. The "novel ideas" are not even nearly novel because, well, they follow the established rules.
Could the model invent reversi/othello had it not known about it beforehand? Could the model invent new words (or a new language) had it not known about how to do that beforehand (there's plenty of research on both)? Can it satisfactorily do either even now (for some definition of satisfactorily)?
People believe it can only because the training set is quite vast and the work done is beyond any shadow of the doubt brilliant. That is why the invention of new words seems amazing and novel to many people while others even with a superficial armchair knowledge of linguistics are nonplussed. And so on.
You've practically restated the paper's findings! :D The LLM knew nothing about othello; it wasn't shown any rules to be recombined. It was shown only sequences of 60 distinct tokens - effectively sentences in an unknown language. The LLM then inferred a model to predict the grammar of that language, and the authors demonstrated that its model functioned like an othello board.
Literal quote from the paper:
"As a first step, we train a language model (a GPT variant we call Othello-GPT) to extend partial game transcripts (a list of moves made by players) with legal moves."
And then:
"Nonetheless, our model is able to generate legal Othello moves with high accuracy".
So:
- it knows about the game because it was literally shown the game with only the legal moves
- it doesn't produce legal moves all the time (even though it does so with high accuracy)
That's why I say "the work done is beyond any shadow of the doubt brilliant". Because this is a definite leap forward from the status quo. However, it doesn't imply that the models can invent/predict/come up with novel ways of doing something. This is still strictly within the realm of "given existing data, give back a statistically relevant response".
Could it actually invent Reversi/Othello had it not known about it beforehand?
It's shown token sequences only. It has no idea they represent a game, or that the game has legal and illegal moves. And more importantly, it has no idea that each token modifies the state of a gameboard, or that simulating how that gameboard changes after every token is the only way to understand the token's grammar. It invents all that.
> Could it actually invent Reversi/Othello had it not known about it beforehand?
You mean, could an LLM invent othello even if its training material made no mention of the game or its rules? Presumptively, of course - why not? Suppose you go make up an arbitrary board game right now. If you then ask ChatGPT-4 to invent a boardgame of its own, nothing excludes the possibility that it will describe a game isomorphic to yours. Obviously the odds are very low, but why imagine that it's not possible?
I was curious to see if it could.
=== Q. Invent a new statistic that mixes hessian and likelihood with score.
gpt: One potential new statistical concept that mixes Hessian and likelihood with the score function could be called "Hessian-score likelihood ratio".
The idea behind this concept is to use the Hessian matrix, which captures second-order information about the likelihood function, along with the score function, which measures the sensitivity of the likelihood function to changes in the model parameters, to construct a likelihood ratio test statistic.
Q. How do I compute this new statistic ?
gpt. To calculate this statistic, we first compute the Hessian matrix of the log-likelihood function evaluated at the maximum likelihood estimate of the parameters. We then calculate the score function evaluated at the maximum likelihood estimate of the parameters.
We can then use these quantities to construct a test statistic that compares the likelihood of the model with the estimated parameters to the likelihood of the model with an alternative set of parameters. Specifically, we take the difference between the log-likelihoods of the two models, and divide by the square root of the determinant of the Hessian matrix, multiplied by the score function.
Q. Of what use is this new statistic ?
gpt. The resulting test statistic can be used to test hypotheses about the parameters of the model, such as whether they are equal to a particular value or whether they differ across groups or conditions. The Hessian-score likelihood ratio offers a potentially more powerful and efficient way to test such hypotheses than existing methods, since it makes use of both second-order information about the likelihood function and the sensitivity of the likelihood to changes in the parameters. ====
I am not able to spot any obvious inaccuracies in the above.
> I was curious to see if it could.
But you told it about the concept, "a new statistic that mixes hessian and likelihood with score".
You should try a different experiment. I'm more familiar with architecture than statistics so I'll use the floor plan example. Were someone in 16th century had asked its LLM to address the painpoints of the joined room approach, and then the LLM conceived of the novell concept of a corridor. [Look up the origin of the word.]
If that 16th century LLM spat out "the overall concept is to distinguish between transient and in repose spaces. There is already something similar in military architecture called 'corridor', which is a strip of land along the outer edge of a ditch. In these new floor plan designs, there will be corridors internal and peripheral to the building that will connect rooms, just like corridors (strips of land) connect lots or permit movement without stepping into a ditch".
-- can this happen? --
You: Invent a novel test statistic that can be used to test hypotheses about the parameters of the model, such as whether they are equal to a particular value or whether they differ across groups or conditions. You can combine existing statistical tools.
gpt: How about "Hessian-score likelihood ratio"? The idea behind this concept is to use the Hessian matrix, which captures second-order information about the likelihood function, along with the score function, which measures the sensitivity of the likelihood function to changes in the model parameters, to construct a likelihood ratio test statistic.
NO! They do not.
Deep learning models are "universal approximators". Any two-layer neural network with enough parameters, data and training is a universal approximation. That means they can learn ANY relationship with an arbitrary accuracy.
Going beyond two layers, with several layers, problem domain structured architectures, and recurrent connections, they become far more efficient and effective.
So yes, they learn associations, correlations, stochastic models, statistics.
But they also learn to model functional relationships. Which is why they are able to generalize relationship to new situations, and combine previously unrelated relationships in reasonable and surprising ways.
A large part of creativity is putting together previously unrelated concepts and then letting the obvious logic of those relationships combine to result in something new an unexpected.
Note that both combining normally unrelated things, and combining the concepts in some way more or less consistent with what those concepts normally mean, is well within the grasp of current models.
They haven't outclassed out best thinkers. Or any of our best thinking as individuals yet. They are still very limited on problems that require many steps to think through.
But they are definitely, within their limits, being creative.
And they are far, far, FAR from just being statistical parrots.
We've yet to see those surprisng ways despite all the claims.
Note: what they do already is amazing and surprising in itself (such as "write me a song about quantum physics suitable for a 5 year old"). It's still very much shy of "hey there's this new thing previously unthought of".
This is the one reason everyone is finding them fascinating.
Perhaps you find them boring. Rote. Or something. But the reason non-technical people, as well as technical people, are enjoying and learning by interacting with chat and other models is how often the results are interesting.
I asked ChatGPT-4 to create a Dr. Seuss story about Cat in the Hat and my green conure parrot Teansy, that involved sewing and Italy. It produced a wonderful story of how they met in Italy, became friends, encountered a homeless child with a threadbare blanket and help the child. Then began helping others and ended up creating a fashion design studio.
All written in Dr. Seuss prose that made for a perfect children's book.
Pretty creative.
I then asked GPT to continue the story, but as a James Bond novel where one of Teansy's mysterious clients was actually a criminal using the fashion industry to hide his nefarious practices, and that Teansy should help James Bond solve the case.
For that I got another great story, completely consistent to James Bond tropes. It came up with a story line where the fashion industry was used to launder blood diamonds, which I thought was brilliant. A perfectly good rational for a James Bond villain. The story was great.
Throughout, Chat threw in funny suitable mentions about Teansy's fashion focuses, including feather lined wear, etc.
And all this creativity in a first draft written as fast as I could read it.
A year ago, nothing on the planet but a whimsical human with too much time (more time than it took Chat), on their hands could do this.
--
Obviously, we are discovering Chat can perform far more complex behaviors.
Act as any agent we describe including computer systems, or the internet. Respond quickly to feedback. Form plans. Learn and summarize the grammar of small artificial languages fairly well just from examples, ...
Without interacting with these models we would never have declared these were expected behaviors.
So I don't know what basis the emergence of these behaviors isn't surprising. Hoped for, envisioned, sure. But hardly an expression of obviously predetermined designed-in capabilities.
Interpolating sounds like a simple task.
But whether it is depends entirely on the data. Simple data will result in a simple interpolating model.
But complex data requires complex relationships to be learned.
Calling a complex model just an interpolator is like saying human beings are just another bag of atoms doing what atoms do. Technically correct, but missing the significance of humans.
The fact that you turned a limitation of an specific algorithm into a call for magical powers shows quite a bit of bias on your part.
But if you have some more general definition for "pattern recognition" than this, you should be perfectly able to notice that it's more general than what LLMs do.
I think it is a quite bold and philosophically poor statement to equate the "human training set" of complex interactions with the environment with what is written on the internet.
I am not saying that we cannot produce an AI with capabilities of that sort. But LLMs offer nothing at all to that direction. They can be useful in certain practical stuff, they are overhyped as hell, but they are not a step towards AGI.
Or working in the opposite direction: we can think of AIs as processing concepts in some dimensional space, sure. But we have no conception at all of what that space is like, so there's no reason to expect that a midpoint in that space between two objects we're familiar with would also be familiar to us. I mean, I have no idea what the midpoint between Rust and C++ is, or how I'd go about finding it. Surely an AI that thinks in tensors is more capable than we are to explore the space between known concepts, so why couldn't we expect to learn something novel from one?