[JoshCole]

They don't claim that. They say LLMs only generate text someone has written. Another way you could refute their premise was by showing the existence of AI-created programs for which someone isn't a valid description of the writer (e.g., from evolutionary algorithms) then training a network on that data such that it can output it. It is just as trivial a way to prove that the premise is false.

Your claim here is slightly different.

You're claiming that if a token isn't supported, it can't be output [1]. But we can easily disprove this by adding minimal support for all tokens, making C appear in theory. Such support addition shows up all the time in AI literature [2].

[1]: https://en.wikipedia.org/wiki/Support_(mathematics)

[2]: In some regimes, like game theoretic learning, support is baked into the solving algorithms explicitly during the learning stage. In others, like reinforcement learning, its accomplished by making the policy a function of two objectives, one an exploration objective, another an exploitation objective. That existing cross pollination already occurs between LLMs in the pre-trained unsupervised regime and LLMs in the post-training fine-tuning via forms of reinforcement learning regime should cause someone to hesitate to claim that such support addition is unreasonable if they are versed in ML literature.

Edit:

Got downvoted, so I figure maybe people don't understand. Here is the simple counterexample. Consider an evaluator that gives rewards: F("AAC") = 1, all other inputs = 0. Consider a tokenization that defines "A", "B", "C" as tokens, but a training dataset from which the letter C is excluded but the item "AAA" is present.

After training "AAA" exists in the output space of the language model, but "AAC" does not. Without support, without exploration, if you train the language model against the reinforcement learning reward model of F, you might get no ability to output "C", but with support, the sequence "AAC" can be generated and give a reward. Now actually do this. You get a new language model. Since "AAC" was rewarded, it is now a thing within the space of the LLM outputs. Yet it doesn't appear in the training dataset and there are many reward models F for which no person will ever have had to output the string "AAC" in order for the reward model to give a reward for it.

It follows that "C" can appear even though "C" does not appear in the training data.

[gitaarik]

I think it's not just token support, it's also having a understanding of certain concepts that allows you to arrive at new points like C, D, E, etc. But LLM's don't have an understanding of things, they are statistical models that predict what statistically is most likely following the input that you give it. But that that will always be based on already existing data that is fed into the model. It can produce "new" stuff only by combining the "old" stuff in new ways, but it can't "think" of something entirety conceptionally new, because it doesn't really "think".

[JoshCole]

> it can't "think" of something entirety conceptionally new, because it doesn't really "think".

Hierarchical optimization (fast global + slow local) is a precise, implementable notion of "thinking." Whenever I've seen this pattern implemented, humans, without being told to do so by others in some forced way, seem to converge on the use of verb think to describe the operation. I think you need to blacklist the term think and avoid using it altogether if you want to think clearly about this subject, because you are allowing confusion in your use of language to come between you and understanding the mathematical objects that are under discussion.

> It can produce "new" stuff only by combining the "old" stuff in new ways,

False premise; previously debunked. Here is a refutation for you anyway, but made more extreme. Instead of modeling the language task using a pre-training predictive dataset objective, only train on a provided reward model. Such a setup never technically shows "old" stuff to the AI, because the AI is never shown stuff explicitly. It just always generates new things and then the reward model judges how well it did. Clearly, the fact that it can do generation while knowing nothing, shows that your claim that it can never generate something new -- by definition everything would be new at this point -- is clearly false. Notice that as it continually generates new things and the judgements occur, it will learn concepts.

> But LLM's don't have an understanding of things, they are statistical models that predict what statistically is most likely following the input that you give it.

Try out Jayne's Probability Theory: The Logic Of Science. Within it the various underpinning assumptions that lead to probability theory are shown to be very reasonable and normal and obviously good. Stuff like represent plausibility with real numbers, keep rankings consistent and transitive, reduce to Boolean logic at certainty, and update so you never accept a Dutch-book sure-loss -- which together force the ordinary sum and product rules of probability. Then notice that statistics is in a certain sense just what happens when you apply the rules of probability.

> also having a understanding of certain concepts that allows you to arrive at new points like C, D, E, etc. But LLM's don't have an understanding of things

This is also false. Look into the line of research that tends to go by the name of Circuits. Its been found that models have spaces within their weights that do correspond with concepts. Probably you don't understand what concepts are -- that abstractions and concepts are basically forms of compression that let you treat different things as the same thing -- so a different way to arrive at knowing that this would be true is to consider a dataset with less parameters than there are items in the dataset and notice that the model must successfully compress the dataset in order to complete its objective.

[1718627440]

But doesn't reward for "**C" means that "C" is in the training data?

I am not sure if that is an accurate model, but if you think of it as a vectorspace, sure you can generate a lot of vectors from some set of basevectors, but you can never generate a new basevector from others, since they are linearly independent, so there are a bunch of new vectors you can never generate.

[JoshCole]

For an example of a reward model that doesn't include "C" explicitly consider a reward model defined to be the count of the one bits in letters in the input. It would define a reward for "C" but "C" doesn't show up explicitly, because the reward had universal reach and "C" was among its members as a result.

[JoshCole]

> But doesn't reward for "*C" means that "C" is in the training data?

You're running into an issue here due to overloading terms. Training data has three different meanings in this conversation depending on which context you are in.

1. The first is the pre-training context in which we're provided a dataset. My words were appropriate in that context.

2. The second is the reinforcement learning setup context in which we don't provide any dataset, but instead provide a reward model. My words were appropriate in that context.

3. The final context is that during the reinforcement learning algorithms operation one of things it does is generate datasets and then learn from them. Here, its true that there exists a dataset in which "C" is defined.

Recall that the important aspect of this discussion has to do with data provenance. We led off with someone claiming that an analog of "C" wasn't provided in the training data by a human explicitly. That means that I only need to establish that "C" doesn't show up in either of the inputs to a learning algorithm. That is case one and that is case two. It is not case three, because upon entering case three the provenance is no longer from humans.

Therefore, the answer to the question but doesn't the reward model for C mean that C is in the training data has the answer: no, it doesn't, because although it appears in case three, it doesn't appear in case one or case two and those were the two cases which were relevant to the question. That is appears in case three is just the mechanism by which the refutation that it could not appear occurs.

> I am not sure if that is an accurate model, but if you think of it as a vectorspace, sure you can generate a lot of vectors from some set of basevectors, but you can never generate a new basevector from others, since they are linearly independent, so there are a bunch of new vectors you can never generate.

Your model of vectors sounds right to me, but your intuitions about it are a little bit off in places.

In machine learning, we introduce non-linearities during training (for example, through activation functions like ReLU or Sigmoid). This breaks the strict linear structure of the model, enabling it to approximate a much wider range of functions. There's a mathematical proof (known as the Universal Approximation Theorem) that shows how this non-linearity allows neural networks to represent virtually any continuous function, regardless of its complexity.

We're not really talking about datasets when we move into a discussion about this. Its closer to a discussion of inductive biases. Inductive bias refers to the assumptions a model makes about the underlying structure, which guide it toward certain types of solutions. If something doesn't map to the structure the inductive bias assumes, it can be possible for the model to be incapable of learning that function successfully.

The last generation of popular architectures used convolutional networks quite often. These baked in an inductive bias about where data that was related to other data was and so made learning some functions difficult or impossible when those assumptions were violated. The current generation of models tends to be built on transformers. Transformers use an attention mechanism that can determine what data to focus on and as a result they are more capable of avoiding the problems that bad inductive bias can create since they can end up figuring out what they are supposed to be paying attention to.