Ah but is the model's belief of the statements 1. complete, 2. consistent, 3. decidable?

> The best anyone expects from an LLM "truth vector" is that it would encode the model's belief about whether the statement is true.

I think even that's too-optimistic: The LLM is a document-extender, so its "belief" is whether a token seems like it would statistically fit-next in a partial document, based on prior documents. This is usually not the kind of analytic truth we're interested in, and we've already figured out how to constantly extract it.

If we peek at vectors and weights, we'll we'll probably end up measuring the moods and styles for whatever tokens are about to get emitted next, whether that's dialogue for a fictional character (of various kinds), a narrator, or an impersonal memo conclusion paragraph. We'll be measuring "earnestness and conviction", on the same level as "loquaciousness" or "pleading" or "talking like a pirate."

So is Truthiness [0] what we really want? Probably not. If our document described the character as Yoda, then The Force connecting all existence ends up truthy. Using "a really gullible person" can repeat anything you supply as truthy. Even if we set things up as "a respected encyclopedia article" or "a relentlessly logical super-genius", we're really changing the influence mix of styles and biases, rather than creating a logical mind independent of text inside the LLM.

[0] https://en.wikipedia.org/wiki/Truthiness

If anything, the whole vector space is the LLM's truth.

For a one time coin flip, sure. For a lot of them, depending on the stakes, that can be very, very wrong.

https://www.google.com/search?q=why+99.99+accuracy+is+not+en...

It doesn't take a lot of thought experiments to realize this. Imagine if every bite of food we eat had a 0.01% chance to turn into something instantly lethal in our mouth. Average lifespans would be reduced measurably, and apart from anxiety, we'd develop all sorts of strategies and laws around that. E.g. absolutely NO eating for airplane pilots. You wouldn't go on a date to have dinner, dancing and sex, you'd go dancing and have sex, and then have breakfast. People would modify their jaws and stomachs so they could eat less, but bigger chunks of food. It would be a whole thing!

And that's not even talking about water changing on us, or a tiny chance of getting sucked into the toilet whenever we use it, and a lot of other things where going from damn near 100% to 99.99% would change everything for the worse, by so much.

A basic course in statistics will inform you of why a 99.99% accurate test should be looked at with skepticism when diagnosing a rare disease. Yet we see the fancy 9s and think somehow this many 9s is enough.

Models do not have assumptions. They have probabilities for what the next token should be. With enough context, in the context window and built into the model, that next token isn't completely random, it's correlated with something someone might choose to write.

But people write all kinds of crap manually. So far, the data people have been writing has tended to be denser around what people could agree on (there are many lies, but only one truth), so the model is more likely to go there.

If we start putting AI generated text into the training data, it's not clear what that means for the resulting model. It's already clear that some actors are trying to influence models by putting large amounts of content out there that agree with them.

Figuring out which content is safe to train from is the real problem for future model trainers.

Interesting point about "self-referential sentences". I tend to agree. In my view a sentence saying something like "This sentence ..." does not have valid semantic meaning. It says nothing because, what "This" in "This sentence" means is ill-defined.

If terms we use are not well-defined, then sentences using such terms can not have meaning.

But for the sake of argument let's explore, what could the "this" in (so called) "self-referential" sentences refer to?

Do they refer to a specific encoding of the sentence you are reading, as some bits in computer memory perhaps?

That would require that those bits somehow have a unique "identity" and the "this" in a self-referential sentence would have to refer to those bits in specific addresses of a specific memory-chip.

But of course the "this" does not specify which memory chip, which specific (concrete) encoding of its (purported) meaning it is referring to. And if it did, then it would be talking about that specific set of bits in that specific memory-chip, not of "itself".

The fallacy is that what we perceive as a "sentence we read" is somehow "speaking" of something. But no, the sentence is not a subject, a sentence can not speak, and THEREFORE it specifically can not speak of itself.

A sentence can not speak, only actors, only subjects, like humans and AI, can "speak". And their speech must be encoded in some physical medium. A written sentence like "This sentence is ..." gives us the false impressions that somehow the SENTENCE IS SPEAKING of itself!

But speech can not speak, speech is the product of speaking.

Hence, in my view, "self-referential sentences" do not have any meaning and whatever paradoxes they might seem to create are results of confusion between ontological levels of "Subject" vs. "Speech".

I’m not a logician either but believe this is what Tarski’s definition of truth solves for. In order to make a statement about the statement itself, you have to introduce a new meta language. Then a statement in the meta language is only true if the underlying statement is true.

Much more rigorous explanation: https://plato.stanford.edu/entries/tarski-truth/

There is no lack of more elaborate logics:

https://en.wikipedia.org/wiki/Non-classical_logic

There are a LOT of different logical system.

Paraconsistent Logic

Intuitionistic Logic

Dialetheism

Fuzzy logic?