# 109

GPTSimulator TheoryAI
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(Related text posted to Twitter; this version is edited and has a more advanced final section.)

Imagine yourself in a box, trying to predict the next word - assign as much probability mass to the next token as possible - for all the text on the Internet.

Koan:  Is this a task whose difficulty caps out as human intelligence, or at the intelligence level of the smartest human who wrote any Internet text?  What factors make that task easier, or harder?  (If you don't have an answer, maybe take a minute to generate one, or alternatively, try to predict what I'll say next; if you do have an answer, take a moment to review it inside your mind, or maybe say the words out loud.)

Consider that somewhere on the internet is probably a list of thruples: <product of 2 prime numbers, first prime, second prime>.

GPT obviously isn't going to predict that successfully for significantly-sized primes, but it illustrates the basic point:

There is no law saying that a predictor only needs to be as intelligent as the generator, in order to predict the generator's next token.

Indeed, in general, you've got to be more intelligent to predict particular X, than to generate realistic X.  GPTs are being trained to a much harder task than GANs.

Same spirit: <Hash, plaintext> pairs, which you can't predict without cracking the hash algorithm, but which you could far more easily generate typical instances of if you were trying to pass a GAN's discriminator about it (assuming a discriminator that had learned to compute hash functions).

Consider that some of the text on the Internet isn't humans casually chatting. It's the results section of a science paper. It's news stories that say what happened on a particular day, where maybe no human would be smart enough to predict the next thing that happened in the news story in advance of it happening.

As Ilya Sutskever compactly put it, to learn to predict text, is to learn to predict the causal processes of which the text is a shadow.

Lots of what's shadowed on the Internet has a *complicated* causal process generating it.

Consider that sometimes human beings, in the course of talking, make errors.

GPTs are not being trained to imitate human error. They're being trained to *predict* human error.

Consider the asymmetry between you, who makes an error, and an outside mind that knows you well enough and in enough detail to predict *which* errors you'll make.

If you then ask that predictor to become an actress and play the character of you, the actress will guess which errors you'll make, and play those errors.  If the actress guesses correctly, it doesn't mean the actress is just as error-prone as you.

Consider that a lot of the text on the Internet isn't extemporaneous speech. It's text that people crafted over hours or days.

GPT-4 is being asked to predict it in 200 serial steps or however many layers it's got, just like if a human was extemporizing their immediate thoughts.

A human can write a rap battle in an hour.  A GPT loss function would like the GPT to be intelligent enough to predict it on the fly.

Or maybe simplest:

Imagine somebody telling you to make up random words, and you say, "Morvelkainen bloombla ringa mongo."

Imagine a mind of a level - where, to be clear, I'm not saying GPTs are at this level yet -

Imagine a Mind of a level where it can hear you say 'morvelkainen blaambla ringa', and maybe also read your entire social media history, and then manage to assign 20% probability that your next utterance is 'mongo'.

The fact that this Mind could double as a really good actor playing your character, does not mean They are only exactly as smart as you.

When you're trying to be human-equivalent at writing text, you can just make up whatever output, and it's now a human output because you're human and you chose to output that.

GPT-4 is being asked to predict all that stuff you're making up. It doesn't get to make up whatever. It is being asked to model what you were thinking - the thoughts in your mind whose shadow is your text output - so as to assign as much probability as possible to your true next word.

Figuring out that your next utterance is 'mongo' is not mostly a question, I'd guess, of that mighty Mind being hammered into the shape of a thing that can simulate arbitrary humans, and then some less intelligent subprocess being responsible for adapting the shape of that Mind to be you exactly, after which it simulates you saying 'mongo'.  Figuring out exactly who's talking, to that degree, is a hard inference problem which seems like noticeably harder mental work than the part where you just say 'mongo'.

When you predict how to chip a flint handaxe, you are not mostly a causal process that behaves like a flint handaxe, plus some computationally weaker thing that figures out which flint handaxe to be.  It's not a problem that is best solved by "have the difficult ability to be like any particular flint handaxe, and then easily figure out which flint handaxe to be".

GPT-4 is still not as smart as a human in many ways, but it's naked mathematical truth that the task GPTs are being trained on is harder than being an actual human.

And since the task that GPTs are being trained on is different from and harder than the task of being a human, it would be surprising - even leaving aside all the ways that gradient descent differs from natural selection - if GPTs ended up thinking the way humans do, in order to solve that problem.

GPTs are not Imitators, nor Simulators, but Predictors.

# 109

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While the claim - the task ‘predict next token on the internet’ absolutely does not imply learning it caps at human-level intelligence - is true, some parts of the post and reasoning leading to the claims at the end of the post are confused or wrong.

Let’s start from the end and try to figure out what goes wrong.

GPT-4 is still not as smart as a human in many ways, but it's naked mathematical truth that the task GPTs are being trained on is harder than being an actual human.

And since the task that GPTs are being trained on is different from and harder than the task of being a human, it would be surprising - even leaving aside all the ways that gradient descent differs from natural selection - if GPTs ended up thinking the way humans do, in order to solve that problem.

From a high-level perspective, it is clear that this is just wrong. Part of what human brains are doing is to minimise prediction error with regard to sensory inputs. Unbounded version of the task is basically of same generality and difficulty as what GPT is doing, and is roughly equivalent to understand everything what is understandable in the observable universe. For example: a friend of mine worked at analysing the data from LHC, leading to the Higgs detection paper. Doing this type of work basically requires a human brain to have a predictive model of aggregates of outputs of a very large number of collisions of high-energy particles, processed by a complex configuration of computers and detectors.

Where GPT and humans differ is not some general mathematical fact about the task,  but differences in what sensory data is a human and GPT trying to predict, and differences in cognitive architecture and ways how the systems are bounded. The different landscape of both boundedness and architecture can lead to both convergent cognition (thinking as the human would do) and the opposite, predicting what the human would output in highly non-human way.

The boundedness is overall a central concept here. Neither humans nor GPTs are attempting to solve ‘how to predict stuff with unlimited resources’, but a problem of cognitive economy - how to allocate limited computational resources to minimise prediction error.

Or maybe simplest:
Imagine somebody telling you to make up random words, and you say, "Morvelkainen bloombla ringa mongo."

Imagine a mind of a level - where, to be clear, I'm not saying GPTs are at this level yet -

Imagine a Mind of a level where it can hear you say 'morvelkainen blaambla ringa', and maybe also read your entire social media history, and then manage to assign 20% probability that your next utterance is 'mongo'.

The fact that this Mind could double as a really good actor playing your character, does not mean They are only exactly as smart as you.

When you're trying to be human-equivalent at writing text, you can just make up whatever output, and it's now a human output because you're human and you chose to output that.

GPT-4 is being asked to predict all that stuff you're making up. It doesn't get to make up whatever. It is being asked to model what you were thinking - the thoughts in your mind whose shadow is your text output - so as to assign as much probability as possible to your true next word.

If I try to imagine a mind which is able to predict my next word when asked to make up random words, and be successful at assigning 20% probability to my true output, I’m firmly in the realm of weird and incomprehensible Gods. If the Mind is imaginably bounded and smart, it seems likely it would not devote much cognitive capacity to trying to model in detail strings prefaced by a context like ‘this is a list of random numbers’, in particular if inverting the process generating the numbers would seem really costly. Being this good at this task would require so much data and cheap computation that this is way beyond superintelligence, in the realm of philosophical experiments.

Overall I think it is really unfortunate way how to think about the problem, where a system which is moderately hard to comprehend (like GPT) is replaced by something much more incomprehensible. Also it seems a bit of a reverse intuition pump - I’m pretty confident most people's intuitive thinking about this ’simplest’ thing will be utterly confused.

How did we got here?

A human can write a rap battle in an hour.  A GPT loss function would like the GPT to be intelligent enough to predict it on the fly.

Apart from the fact that humans are also able to rap battle or impro on the fly, notice that “what would the loss function like the system to do”  in principle tells you very little about what the system will do. For example, the human loss function makes some people attempt to predict winning lottery numbers. This is an impossible task for humans and you can’t say much about the human based on this. Or you can speculate about minds which would be able to succeed in this task, but you soon get into the realm of Gods and outside of physics.

Consider that sometimes human beings, in the course of talking, make errors.

GPTs are not being trained to imitate human error. They're being trained to *predict* human error.

Consider the asymmetry between you, who makes an error, and an outside mind that knows you well enough and in enough detail to predict *which* errors you'll make.

Again, from the cognitive economy perspective, predicting my errors would often be wasteful.  With some simplification, you can imagine I make two types of errors - systematic, and random. Often the simplest way how to predict the systematic error would be to emulate the process which led to the error.  Random errors are ...  random, and a mind which knows me in enough detail to predict which random errors I’ll make seems a bit like the mind predicting the lottery numbers.

Consider that somewhere on the internet is probably a list of thruples: <product of 2 prime numbers, first prime, second prime>.

GPT obviously isn't going to predict that successfully for significantly-sized primes, but it illustrates the basic point:

There is no law saying that a predictor only needs to be as intelligent as the generator, in order to predict the generator's next token.

The general claim that some predictions are really hard and you need superhuman powers to be good at them is true, but notice that this does not inform us about what GPT-x will learn.

Imagine yourself in a box, trying to predict the next word - assign as much probability mass to the next token as possible - for all the text on the Internet.

Koan:  Is this a task whose difficulty caps out as human intelligence, or at the intelligence level of the smartest human who wrote any Internet text?  What factors make that task easier, or harder?

Yes this is clearly true: in the limit the task is of unlimited difficulty.

From a high-level perspective, it is clear that this is just wrong. Part of what human brains are doing is to minimise prediction error with regard to sensory inputs

I didn't say that GPT's task is harder than any possible perspective on a form of work you could regard a human brain as trying to do; I said that GPT's task is harder than being an actual human; in other words, being an actual human is not enough to solve GPT's task.

I don't see how the comparison of hardness of 'GPT task' and 'being an actual human' should technically work - to me it mostly seems like a type error.

- The task 'predict the activation of photoreceptors in human retina' clearly has same difficulty as 'predict next word on the internet' in the limit. (cf Why Simulator AIs want to be Active Inference AIs)

- Maybe you mean something like task + performance threshold. Here 'predict the activation of photoreceptors in human retina well enough to be able to function as a typical human' is clearly less difficult than task + performance threshold 'predict next word on the internet, almost perfectly'. But this comparison does not seem to be particularly informative.

- Going in this direction we can make comparisons between thresholds closer to reality e.g. 'predict the activation of photoreceptors in human retina, and do other similar computation well enough to be able to function as a typical human'  vs. 'predict next word on the internet, at the level of GPT4' . This seems hard to order - humans are usually able to do the human task and would fail at the GPT4 task at GPT4 level; GPT4 is able to do the GPT4 task and would fail at the human task.

- You can't make an ordering between cognitive systems based on 'system A can't do task T system B can, therefore B>A' . There are many tasks which human's can't solve, but this implies very little. E.g. a human is unable to remember 50 thousand digit random number and my phone can easily, but there are also many things which human can do and my phone can't.

From the above the possibly interesting direction of comparisons of 'human skills' and 'GPT-4 skills' is something like 'why can't GPT4 solve the human task at human level' and 'why can't human solve the GPT task on GPT4 level' and 'why are the skills are a bit hard to compare'.

Some thoughts on this

- GPT4 clearly is "width superhuman": it's task is ~modelling of textual output of the whole humanity. This isn't a great fit for the architecture and bounds of a single human mind roughly for the same reasons why a single human mind would do worse than Amazon recommender in recommending products to each of hundred million users. In contrast a human would probably do better in recommending products to one specific user whose preferences the human recommender would try to predict in detail.

Humanity as a whole would probably do significantly better at this task, if you e.g. imagine assigning every human one other human to model (and study in depth, read all their text outputs, etc)

- GPT4 clearly isn't "samples -> abstractions" better than humans, needing more data to learn the pattern.

- With overall ability to find abstractions, it seems unclear to what extent did GPT "learn smart algorithms independently because they are useful to predict human outputs" vs. "learned smart algorithms because they are implicitly reflected in human text", and at the current level I would expect a mixture of both

What the main post is responding to is the argument:  "We're just training AIs to imitate human text, right, so that process can't make them get any smarter than the text they're imitating, right?  So AIs shouldn't learn abilities that humans don't have; because why would you need those abilities to learn to imitate humans?"  And to this the main post says, "Nope."

The main post is not arguing:  "If you abstract away the tasks humans evolved to solve, from human levels of performance at those tasks, the tasks AIs are being trained to solve are harder than those tasks in principle even if they were being solved perfectly."  I agree this is just false, and did not think my post said otherwise.

I do agree the argument "We're just training AIs to imitate human text, right, so that process can't make them get any smarter than the text they're imitating, right?  So AIs shouldn't learn abilities that humans don't have; because why would you need those abilities to learn to imitate humans?" is wrong and clearly the answer is "Nope".

At the same time I do not think parts of your argument in the post are locally valid or good justification for the claim.

Correct and locally valid argument why GPTs are not capped by human level was already written here.

In a very compressed form, you can just imagine GPTs have text as their "sensory inputs" generated by the entire universe, similarly to you having your sensory inputs generated by the entire universe. Neither human intelligence nor GPTs are constrained by the complexity of the task (also: in the abstract, it's the same task).  Because of that, "task difficulty" is not a promising way how to compare these systems, and it is necessary to look into actual cognitive architectures and bounds.

With the last paragraph, I'm somewhat confused by what you mean by "tasks humans evolved to solve". Does e.g. sending humans to the Moon, or detecting Higgs boson, count as a "task humans evolved to solve" or not?

GPTs are not Imitators, nor Simulators, but Predictors.

I think an issue is that GPT is used to mean two things:

1. A predictive model whose output is a probability distribution over token space given its prompt and context
2. Any particular techniques/strategies for sampling from the predictive model to generate responses/completions for a given prompt.

[See the Appendix]

The latter kind of GPT, is what I think is rightly called a "Simulator".

From @janus' Simulators (italicised by me):

I use the generic term “simulator” to refer to models trained with predictive loss on a self-supervised dataset, invariant to architecture or data type (natural language, code, pixels, game states, etc). The outer objective of self-supervised learning is Bayes-optimal conditional inference over the prior of the training distribution, which I call the simulation objective, because a conditional model can be used to simulate rollouts which probabilistically obey its learned distribution by iteratively sampling from its posterior (predictions) and updating the condition (prompt). Analogously, a predictive model of physics can be used to compute rollouts of phenomena in simulation. A goal-directed agent which evolves according to physics can be simulated by the physics rule parameterized by an initial state, but the same rule could also propagate agents with different values, or non-agentic phenomena like rocks. This ontological distinction between simulator (rule) and simulacra (phenomena) applies directly to generative models like GPT.

It is exactly because of the existence of GPT the predictive model, that sampling from GPT is considered simulation; I don't think there's any real tension in the ontology here.

# Appendix

Credit for highlighting this distinction belongs to @Cleo Nardo

# Remark 2: "GPT" is ambiguous

We need to establish a clear conceptual distinction between two entities often referred to as "GPT" —

• The autoregressive language model  which maps a prompt  to a distribution over tokens .
• The dynamic system that emerges from stochastically generating tokens using  while also deleting the start token

Don't conflate them! These two entities are distinct and must be treated as such. I've started calling the first entity "Static GPT" and the second entity "Dynamic GPT", but I'm open to alternative naming suggestions. It is crucial to distinguish these two entities clearly in our minds because they differ in two significant ways: capabilities and safety.

1. Capabilities:
1. Static GPT has limited capabilities since it consists of a single forward pass through a neural network and is only capable of computing functions that are O(1). In contrast, Dynamic GPT is practically Turing-complete, making it capable of computing a vast range of functions.
2. Safety:
1. If mechanistic interpretability is successful, then it might soon render Static GPT entirely predictable, explainable, controllable, and interpretable. However, this would not automatically extend to Dynamic GPT. This is because Static GPT describes the time evolution of Dynamic GPT, but even simple rules can produce highly complex systems.
2. In my opinion, Static GPT is unlikely to possess agency, but Dynamic GPT has a higher likelihood of being agentic. An upcoming article will elaborate further on this point.

This remark is the most critical point in this article. While Static GPT and Dynamic GPT may seem similar, they are entirely different beasts.

To summarise:

• Static GPT: GPT as predictor
• Dynamic GPT: GPT as simulator
[-]janus1118

Predictors are (with a sampling loop) simulators! That's the secret of mind

(There is a Paul Christiano response over at the EA forum.)

A human can write a rap battle in an hour. A GPT loss function would like the GPT to be intelligent enough to predict it on the fly.

Very minor point, but humans can rap battle on the fly: https://youtu.be/0pJRmtWNP1g?t=158

That's an empirical question that interpretability and neuroscience should strive to settle (if only they had the time). Transformers are acyclic, the learned algorithm just processes a single relatively small vector one relatively simple operation at a time, several dozen times. Could be that what it learns to represent are mostly the same obvious things that the brain learns (or is developmentally programmed) to represent, until you really run wild with the scaling, beyond mere ability to imitate internal representations of thoughts and emotions of every human in the world. (There are some papers that correlate transformer embeddings with electrode array readings from human brains, but this obviously needs more decades of study and better electrode arrays to get anywhere.)