If your prediction is a probability distribution, rather than a discrete outcome label, then, assuming the distribution over the future depends continuously on your action, there should be a fixed point, I think?
Like, if you output a probability distribution among n options, and then there is a continuous map from the probability distribution you describe in your output, to another probability distribution over those options…
Err, hm, maybe you need a stronger hypothesis on the continuous map? If it is contractive then it will definitely have a fixed point. I don’t remember the hypothesis needed.
Do you know any browsers which don’t support https://motherfuckingwebsite.com/ (if you remove the google traffic tracking js that’s iirc tacked on at the end of the page (or maybe I’m thinking of better mfing website (which adds a tiny bit of css)? Idr.)) ?
I get that asking a commercial website to be as basic/supported as that website is a big ask. I don’t think the other commenter was saying that such websites should reach 100%, only that they should start from there and sacrifice only as much as is necessary.
Was surprised and somewhat disappointed that the article doesn’t appear to evaluate how well the models work when running in the harnesses optimized for the other models. Do they still do better than with the baseline harness? Does each model do worse with a harness optimized (by this process) for the other models, than it does for the harness optimized for itself?
I feel like this didn’t really go anywhere? In the discussion section he says that this should provide reason to not expect easy theorems or answers, but I don’t feel like that was really derived from the results of the experiments?
What’s the point if you aren’t even going to try to prove a theorem? Or, heck, even really test a hypothesis?
A convex hull is a different thing than the linear span. It is smaller.
And, my point is that the inputs it is often fed are not in the convex hull of the inputs in the training data.
When the input space is very high dimensional, this is a common outcome.
I’m not denying that the outputs are causally downstream from the training data. Of course it is.
I’m saying that the inference time inputs aren’t in the convex hull of the training time inputs. This isn’t about saying that the output isn’t because of the training data. Of course it is.
But when you have very high dimensional input space, then even with many inputs in the training data, it is still common for inference time inputs to not be in the convex hull of the train time inputs.
This has nothing to do with the complexities of how the models work after the initial embedding of the tokens as vectors. It’s just about the inputs that appear during training, and the inputs that appear at inference time.
> But an LLM can not infer a concept to which it has no information channel.
Of course! And nothing I said implies otherwise. Really, the point I’m making doesn’t even depend on what the model outputs!
If I took a best fit line from 1 parameter to a 1D output, and then provided that linear model an output that was outside the range of inputs the best fit line was obtained from, that would not be interpolation, it would be extrapolation.
It is similar here, except instead of the input being outside the convex hull due to being further away, it is outside the convex hull due to, like, the shape of the convex hull of training inputs just doesn’t include the point in question.
I suppose it is conceivable that there are some useful ideas that cannot be described in terms of language we understand (e.g. if there are ideas that are alien to us and beyond what can be described using https://en.wikipedia.org/wiki/Natural_semantic_metalanguage#... ), but, if there is, I'm not sure those are ideas we can communicate to one-another?
By "If you need new language" do you mean like, coining new words?
I don't see what would prevent them from doing this? LLMs can process text that includes newly coined terms, and respond to that text in ways that use those newly coined words in accordance with the descriptions of the meanings given for those new words in the prompt. They can also make up new words+definitions when asked to do so. Now, whether they can, without being told to do so, recognize that it would be useful to coin a new word for something, and then start using it, I don't know of any instances of this, but based on the previous two things, I don't see a reason to expect this to be fundamentally beyond what they can do?
I don't know what it would mean for a concept to be "independent of the existing language they are trained on". If there are ideas that can't be expressed in terms of the semantic primes all ideas we can express can be expressed in terms of, then I guess such an idea would be independent of our language, but I think that's a much stricter condition than what you mean (and I'm not sure if there even are any good ideas that can't be indirectly expressed in terms of semantic primes -- I kind of suspect not, unless they are like, ideas that are too big to fit in a human mind anyway).
Of course, the outputs these models produce is causally downstream from the data they are trained on, and the distribution they produce over text is largely based on the distribution over text in the training data, but altered in a number of ways (for example, to make them implement the character of the "assistant" persona).
Sorry, I don't understand what you mean. Are you agreeing or disagreeing with me?
If it can only interpolate in a literal sense, that means that it only produces good outputs on convex combinations of inputs that appear in the training set. That's what interpolation means. But, if you take the embedding vectors of sentences/prompts, and then take the convex hull of these, it is not typical for new sentences not in the training set to have its embedding vectors be in the convex hull of these.
But people aren’t giving a (less literal) definition of what they mean by “interpolate” that relies on the internal mechanisms of these models, just a vague metaphor, which, as this vague metaphor, there’s nothing it uses about LLMs that makes the question “do LLMs just interpolate” less of a type error than “do people just interpolate”.
If you interpret “interpolate” in the literal sense, and apply it to the mechanisms behind LLMs, then the claim that they only interpolate, is straightforwardly false.
Taking it instead as a metaphorical claim may be more valid, but in that case it doesn’t depend on our understanding of how LLMs work.
People keep saying this, but if you try to interpret this at all literally, it just doesn’t work. Like, it’s phrased like it should have a precise meaning, right? Like, people even mention convex hulls when talking about it.
But if you actually try to take a convex hull of, some encoding of sentences as vectors? It isn’t true. The outputs are not in the convex hull of the training data.
I guess it’s supposed to be a metaphor and not literal, but in that case it’s confusing.
Especially seeing as there are contexts in machine learning where literal interpolation vs literal extrapolation, is relevant.
So, please, find a better way to say it than saying that “it can only interpolate”?
I think your point about “you could randomly generate a sequence of words, which could in principle produce a text interpretable as expressing any particular expressible-as-a-sequence-of-words novel good idea” pretty much refutes the idea that guessing and checking can only result in things inside such a convex hull, unless said hull already contains everything.
Of course, there’s a significant role to play by the “checking” part.
Like, “take a random sequence of bits and interpret it as Unicode” is at one end of a scale, and “take a random sequence of words in a language” is just a tad away from it,
and the scale continues in that direction for quite a while.
> The entire "alignment" argument always assumes that there's an objectively correct value set to align to, which is always conveniently exactly the same as the values of whoever is telling you how important alignment is.
No, it doesn’t.
Many of them are (unfortunately) moral relativists. However, that doesn’t mean their goals are to make the models match their personal moral standards.
While there is a lot of disagreement about what is right and wrong, there is also a lot of widespread agreement.
If we could guarantee that on every moral issue on which there is currently widespread agreement (… and which there would continue to be widespread agreement if everyone thought faster with larger working memories and spent time thinking about moral philosophy) that any future powerful AI models would comport with the common view on that issue, then alignment would be considered solved (well, assuming the way this is achieved isn’t be causing people’s moral views to change).
Do companies try to restrict models in more ways than this? Sure, like you gave the example of about Taiwan. And also other things that would get the companies bad press.
> Language models process signs (representamens) but are blind to when meaning forks — when the same word means different things to different communities.
But, haven’t interpretability results shown that these models internally represent several meanings of the same word, differently? In that case, why would they not already do the same for how words are used differently in different communities?
I don’t think these are free parameters in the same sense.
Like, if one theory says that a hunk of metal actually is made of many microscopic grains of various sizes and orientations, where the sizes and orientations of these grains has an effect on the behavior of the metal, you don’t count the “the sizes and orientations of these grains” as free parameters, do you?
Like, if you output a probability distribution among n options, and then there is a continuous map from the probability distribution you describe in your output, to another probability distribution over those options…
Err, hm, maybe you need a stronger hypothesis on the continuous map? If it is contractive then it will definitely have a fixed point. I don’t remember the hypothesis needed.