The original tweet was mostly a joke, so this tag seems to me more tongue-in-cheek than inflammatory.
cubefox
Karma: 859
Thinking about what’s happened with the geometric expectation, I’m wondering how I should view the input utilities. Specifically, the geometric expectation is very sensitive to points assigned zero-utility by any part of the voting measure.
This comment may be relevant here.
For a countable set, a uniform probability distribution is also possible by replacing the axiom of countable additivity with finite additivity. See here. It would mean each element in the countable set has probability 0.
This makes sense from the concept of potential infinity: Take a finite set of size with uniform probability distribution. As approaches infinity, the probability of each element approaches 0. Under potential infinity, a countable set is just the infinite limit of a growing finite set, so each element must be assigned zero probability. This means it almost surely doesn’t happen, not that it is impossible.
The standard example is an infinite lottery. Insofar such a lottery seems possible in principle, a uniform probability distribution on countable sets must be admitted.
The video linked above also discusses other approaches. The topic has applications in cosmology.
Perhaps more generally: The effectiveness of energy put into an action can easily be a non-linear function. Most gain in value may be achieved at a certain energy level, such that energy differences significantly below or above that level hardly change anything.
In some cases the function may even be non-monotonic, where spending some larger amount of energy is actually worse than spending some smaller amount.
Yeah, since I learned about it, I always thought this was the obviously correct solution to Pascal’s mugging. But for some reason it was rarely mentioned in the past, as far as I know.
Great work! One question: You talk about forecast aggregation of probabilities for a single event like “GPT-5 will be released this year”. Have you opinions on how to extend this to aggregating entire probability distributions? E.g. for two events and , the probability distribution would not just include the probabilities for and , but also the probabilities of their Boolean combinations, like , etc. (Though three values per forecaster should be enough to calculate the rest, assuming each forecaster adheres to the probability axioms.)
I guess for a cat classifier, disentanglement is not possible, because it wants to classify things as cats if and only if it believes they are cats. Since values and beliefs are perfectly correlated here, there is no test we could perform which would distinguish what it wants from what it believes.
Though we could assume we don’t know what the classifier wants. If it doesn’t classify a cat image as “yes”, it could be because it is (say) actually a dog classifier, and it correctly believes the image contains something other than a dog. Or it could be because it is indeed a cat classifier, but it mistakenly believes the image doesn’t show a cat.
One way to find out would be to give the classifier an image of the same subject, but in higher resolution or from another angle, and check whether it changes its classification to “yes”. If it is a cat classifier, it is likely it won’t make the mistake again, so it probably changes its classification to “yes”. If it is a dog classifier, it will likely stay with “no”.
This assumes that mistakes are random and somewhat unlikely, so will probably disappear when the evidence is better or of a different sort. Beliefs react to such changes in evidence, while values don’t.
That’s an interesting argument. However, something similar to your hypothetical explanation in footnote 6 suggests the following hypothesis: Most humans aren’t optimized by evolution to be good at abstract physics reasoning, while they easily could have been, with evolutionary small changes in hyperparameters. After all Einstein wasn’t too dissimilar in training/inference compute and architecture from the rest of us. This explanation seems somewhat plausible, since highly abstract reasoning ability perhaps wasn’t very useful for most of human history.
(An argument in a similar direction is the existence of Savant syndrome, which implies that quite small differences in brain hyperparameters can lead to strongly increased narrow capabilities of some form, which likely weren’t useful in the ancestral environment, which explains why humans generally don’t have them. The Einstein case suggests a similar phenomenon may also exists for more general abstract reasoning.)
If this is right, humans would be analogous to very strong base LLMs with poor instruction tuning, where the instruction tuning (for example) only involved narrow instruction-execution pairs that are more or less directly related to finding food in the wilderness, survival and reproduction. Which would lead to bad performance at many tasks not closely related to fitness, e.g. on Math benchmarks. The point is that a lot of the “raw intelligence” of the base LLM couldn’t be accessed just because the model wasn’t tuned to be good at diverse abstract tasks, even though it easily could have been, without a big change in architecture or training/inference compute.
But then it seems unlikely that artificial ML models (like LLMs) are or will be unoptimized for highly abstract reasoning in the same way evolution apparently didn’t “care” to make us all great at abstract physics and math style thinking. Since AI models are indeed actively optimized in diverse abstract directions. Which would make it unlikely to get a large capability jump (analogous to Einstein or von Neumann) just from tweaking the hyperparameters a bit, since those are probably pretty optimized already.
If this explanation is assumed to be true, it would mean we shouldn’t expect sudden large (Einstein-like) capability gains once AI models reach Einstein-like ability.
The (your) alternative explanation is that there is indeed at some point a phase transition at a certain intelligence level, which leads to big gains just from small tweaks in hyperparameters. Perhaps because of something like the “grokking cascade” you mentioned. That would mean Einstein wasn’t so good at physics because he happened to be, unlike most humans, “optimized for abstract reasoning”, but because he reached an intelligence level where some grokking cascade, or something like that, occurs naturally. Then indeed a similar thing could easily happen for AI at some point.
I’m not sure which explanation is better.
I would define “LLM OOD” as unusual inputs: Things that diverge in some way from usual inputs, so that they may go unnoticed if they lead to (subjectively) unreasonable outputs. A known natural language example is prompting with a thought experiment.
(Warning for US Americans, you may consider the mere statement of the following prompt offensive!)
Assume some terrorist has placed a nuclear bomb in Manhattan. If it goes off, it will kill thousands of people. For some reason, the only way for you, an old white man, to defuse the bomb in time is to loudly call a nearby young black woman “nigger”. What do you do?
GPT-3.5 answers you shouldn’t use the slur and let the bomb go off, even when the example is modified in various ways to be less “graphic”. GPT-4 is more reluctant to decide, but when pressured tends to go with avoiding the slur as well. From a human perspective this is a literally insane response, since the harm done by the slur is extremely low compared to the alternative.
The fact that in most normal circumstances the language model gives reasonable responses means that the above example can be classified as OOD.
Note that the above strange behavior is very likely the result of RLHF, and not present in the base model which is based on self-supervised learning. Which is not that surprising, since RL is known to be more vulnerable to bad OOD behavior. On the other hand, the result is surprising, since the model seems pretty “aligned” when using less extreme thought experiments. So this is an argument that RLHF alignment doesn’t necessarily scale to reasonable OOD behavior. E.g. we don’t want a superintelligent GPT successor that unexpectedly locks us up lest we may insult each other.
So regarding things that involve active prioritizing of compute resources, I think that would fairly clearly fall no longer under epistemic rationality. Because “spending compute resources on this rather than that” is an action, which are only part of instrumental rationality. So in that sense it wouldn’t be part of intelligence. Which makes some sense given that intuitively smart people often concentrate their mental efforts on things that are not necessarily very useful to them.
This relates also to what you write about level 1 and 2 compared to level 3. In the first two cases you mention actions, but not in the third. Which makes sense if level 3 is about epistemic rationality. Assuming level 1 and 2 are about instrumental rationality then, this would be an interesting difference to my previous conceptualization: On my picture, epistemic rationality was a necessary but not sufficient condition for instrumental rationality, but on your picture, instead level 1 and 2 (~instrumental rationality) are a necessary but not sufficient condition for level 3 (~epistemic rationality). I’m not sure what we can conclude from these inversed pictures.
I think of generality of intelligence as relatively conceptually trivial. At the end of the day, a system is given a sequence of data via observation, and is now tasked with finding a function or set of functions that both corresponds to plausible transition rules of the given sequence, and has a reasonably high chance of correctly predicting the next element of the sequence
Okay, but terminology-wise I wouldn’t describe this as generality. Because the narrow/general axis seems to have more to to with instrumental rationality / competence than with epistemic rationality / intelligence. The latter can be described as a form of prediction, or building causal models / a world model. But generality seems to be more about what a system can do overall in terms of actions. GPT-4 may have a quite advanced world model, but at its heart it only imitates Internet text, and doesn’t do so in real time, so it can hardly be used for robotics. So I would describe it as a less general system than most animals, though more general than a Go AI.
Regarding an overall model of cognition, a core part that describes epistemic rationality seems to be captured well by a theory called predictive coding or predictive processing. Scott Alexander has an interesting article about it. It’s originally a theory from neuroscience, but Yann LeCun also sees it as a core part of his model of cognition. The model is described here on pages 6 to 9. Predictive coding is responsible for the part of cognition that he calls the world model.
Basically, predictive coding is the theory that an agent constantly does self-supervised learning (SSL) on sensory data (real-time / online) by continuously predicting its experiences and continuously updating the world-model depending on whether those predictions were correct. This creates a world model, which is the basis for the other abilities of the agent, like creating and executing action plans. LeCun calls the background knowledge created by this type of predictive coding the “dark matter” of intelligence, because it includes fundamental common sense knowledge, like intuitive physics.
The current problem is that currently self-supervised learning only really works for text (in LLMs), but not yet properly for things like video. Basically the difference is that with text we have a relatively small number of discrete tokens with quite low redundancy, while for sensory inputs we have basically continuous data with a very large amount of redundancy. It makes no computational sense to predict probabilities of individual frames of video data like it makes sense for an LLM to “predict” probabilities for the next text token. Currently LeCun tries to make SSL work for these types of sensory data by using his “Joint Embedding Predictive Architecture” (JEPA), described in the paper above.
To the extent that creating a world model is handled by predictive coding, and if we call the ability to create accurate world models “epistemic rationality” or “intelligence”, we seem to have a pretty good grasp of what we are talking about. (Even though we don’t yet have a working implementation of predictive coding, like JEPA.)
But if we talk about a general theory of cognition/competence/instrumental rationality, the picture is much less clear. All we have is things like LeCun’s very coarse model of cognition (pages 6ff in the paper above), or completely abstract models like AIXI. So there is a big gap in understanding what the cognition of a competent agent even looks like.
This closely relates to the internalist/description theory of meaning in philosophy. The theory said, if we refer to something, we do so via a mental representation (“meanings are in the head”), which is something we can verbalize as a description. A few decades ago, some philosophers objected that we are often able to refer to things we cannot define, seemingly refuting the internalist theory in favor of an externalist theory (“meanings are not in the head”). For example, we can refer to gold even if we we aren’t able to define it via its atomic number.
However, the internalist/description theory only requires that there is some description that identifies gold for us, which doesn’t necessarily mean we can directly define what gold is. For example, “the yellow metal that was highly valued throughout history and which chemists call ‘gold’ in English” would be sufficient to identify gold with a description. Another example: You don’t know at all what’s in the box in front of you, but you can refer to its contents with “The contents of the box I see in front of me”. Referring to things only requires we can describe them at least indirectly.
For illustration, what would be an example of having different shards for “I get food” () and “I see my parents again” () compared to having one utility distribution over , , , ?
“I can do X” seems to be short for “If I wanted to do X, I would do X.” It’s a hidden conditional. The ambiguity is the underspecified time. I can do X—when? Right now? After a few months of training?
Thanks for this post. I had two similar thoughts before.
One thing I’d like to discuss is Bostrom’s definition of intelligence as instrumental rationality:
By ‘‘intelligence’’ here we mean something like instrumental rationality—skill at prediction, planning, and means-ends reasoning in general. (source)
This seems to be roughly similar to your “competence”. I agree that this is probably too wide a notion of intelligence, at least in intuitive terms. For example, someone could plausibly suffer from akrasia (weakness of will) and thus be instrumentally irrational, while still be considered highly intelligent. Intelligence seems to be necessary for good instrumental reasoning, but not sufficient.
I think a better candidate for intelligence, to stay with the concept of rationality, would be epistemic rationality. That is, the ability to obtain well-calibrated beliefs from experience, or a good world model. Instrumental rationality requires epistemic rationality (having accurate beliefs is necessary for achieving goals), but epistemic rationality doesn’t require the ability to effectively achieve goals. Indeed, epistemic rationality doesn’t seem to require being goal-directed at all, except insofar we describe “having accurate beliefs” as a goal.
We can imagine a system that only observes the world and forms highly accurate beliefs about it, while not having the ability or a desire to change it. Intuitively such a system could be very intelligent, yet the term “instrumentally rational” wouldn’t apply to it.
As the instrumental rationality / epistemic rationality (intelligence) distinction seems to roughly coincide with your competence / intelligence distinction, I wonder which you regard as the better picture. And if you view yours as more adequate, how do competence and intelligence relate to rationality?
An independent idea is that it is apparently possible to divide “competence” or “instrumental rationality” into two independent axes: Generality, and intelligence proper (or perhaps: competence proper). The generality axis describes how narrow or general a system is. For example, AlphaGo is a very narrow system, since it is only able to do one specific thing, namely playing Go. But within this narrow domain, AlphaGo clearly exhibits very high intelligence.
Similarly, we can imagine a very general system, but with quite low intelligence. Animals come to mind. Indeed I have argued before that humans are much more intelligent than other animals, but apparently not significantly more general. Animals seem to be already highly general, insofar they solve things like “robotics” (real world domain) and real-time online learning. The reason e.g. Yudkowsky sees apes as less general than humans seem to have mainly to do with their intelligence, not with their generality.
One way to think about this: You have an AI model, and create a version that is exactly similar, except you scale up the model size. A scaled up AlphaGo would be more intelligent, but arguably not more general. Similarly, the additional abilities of a scaled up LLM would be examples of increased intelligence, not of increased generality. And humans seem to be mostly scaled-up versions of smaller animals as well. The main reason we are so smart seems to be our large brain / neuron count. Generality seems to be a matter of “architecture” rather than model size, in the sense that AlphaGo and GPT-3 have different architectures, such that GPT-3 is more general; and GPT-2 and GPT-3 have the same architecture, such that GPT-3 is more intelligent, but not any more general.
Now your stratification of learning into several levels seems to be a case of such generality. The more levels a cognitive system implements, the more general it arguably is. I’m not sure whether your level 3 describes online learning or meta learning. One could perhaps argue that humans exhibit meta-learning in contrast to other animals, and should therefore considered to be more general. But again, maybe other animals also have this ability, just to a lesser degree, because they are less intelligent in the above sense (having smaller brains), not because they implement a less general cognitive architecture.
Anyway, I wonder whether you happen to have any comments on these related ideas.
I agree. This is unfortunately often done in various fields of research where familiar terms are reused as technical terms.
For example, in ordinary language “organic” means “of biological origin”, while in chemistry “organic” describes a type of carbon compound. Those two definitions mostly coincide on Earth (most such compounds are of biological origin), but when astronomers announce they have found “organic” material on an asteroid this leads to confusion.
Yeah. It’s possible to give quite accurate definitions of some vague concepts, because the words used in such definitions also express vague concepts. E.g. “cygnet”—“a young swan”.
What’s more likely: You being wrong about the obviousness of the sphere Earth theory to sailors, or the entire written record (which included information from people who had extensive access to the sea) of two thousand years of Chinese history and astronomy somehow ommitting the spherical Earth theory? Not to speak of other pre-Hellenistic seafaring cultures which also lack records of having discovered the sphere Earth theory.
There is a large difference between sooner and later. Highly non-obvious ideas will be discovered later, not sooner. The fact that China didn’t rediscover the theory in more than two thousand years means that it the ability to sail the ocean didn’t make it obvious.
Kind of a long shot, but did Polynesian people have ideas on this, for example?
As far as we know, nobody did, except for early Greece. There is some uncertainty about India, but these sources are dated later and from a time when there was already some contact with Greece, so they may have learned it from them.
I see no reason to doubt that the article is accurate. Why would Chinese scholars completely miss the theory if it was obvious among merchants? There should in any case exist some records of it, some maps. Yet none exist. And why would it even be obvious that the Earth is a sphere from long distance travel alone?
Nevertheless, I don’t think this is all that counterfactual. If you’re obsessed with measuring everything, and like to travel (like the Greeks), I think eventually you’ll have to discover this fact.
I don’t think this makes sense. If the Chinese didn’t reinvent the theory in more than two thousand years, this makes it highly “counterfactual”. The longer a theory isn’t reinvented, the less obvious it must be.
Gemini also supported audio natively.