[ninetyninenine]

Seems you’re not well versed in basic English.

If I can reason it doesn’t mean I’m always reasoning or constantly reasoning or if I know how to do reasoning for every prompt. It just means it’s possible. How narrow or how wide that possibility is, is orthogonal to the claim itself. Please employ logic here.

Ok math guy. Imagine I said numbers can be divided. The claim is true even though there is a number that can’t be divided. Zero.

[daveguy]

If it's only reasoning randomly how do you know when anything has been reasoned properly vs just a generated simulation of reasonable text?

[ninetyninenine]

We use Probability. Find a prompt that has a large range aka codomain. If it arrived at the correct answer then that the only possibility here is reasoning because the codomain is so large it cannot arrive there by random chance.

Of course make sure the prompt is unique such that it's not in the data and it's not doing any sort of "pattern matching".

So like all science we prove it via probability. Observations match with theory to a statistical degree.

[daveguy]

Pardon my ignorance -- assuming that range and codomain are approximately equivalent in this context, how do you specify a prompt with a large codomain? Is there a canonical example of a prompt with a large codomain?

It seems to me that, in natural language, the size of the codomain is related to the specificity of the prompt. For instance, if the prompt is "We are going to ..." then the codomain is enormous. But if the prompt is "2 times 2 is..." the codomain is, mathematically, {4, four}, some series of 4 symbols, eg IIII, or some other representation of the concept of "4" (ie different base or language representations: 0x04, 0b100, quatro, etc).

But if this is the case, a broad codomain is approximately synonymous with "no correct answer" or "result is widely interpretable". Which implies that the larger the codomain the easier it is to claim an answer "correct" in context of the prompt.

How do you reconcile loose interpretability with statistical rigor?

[ninetyninenine]

You'll have to drop a bit of rigor here.

I ask the question, what is 2 * 2, which is an obviously loaded question that's pattern matched to death.

The LLM can answer "4" or "The answer is 4" of "looks like the answer is 4"

All valid answers but all the same. We count all 3 of those answers as just 4 out of the set of numbers. But we have to use our own language faculties to cut through the noise of the language itself.

[daveguy]

> I ask the question, what is 2 * 2, which is an obviously loaded question that's pattern matched to death.

Yeah, that was my point. Small codomain -> easy to validate. Large codomain -> open to interpretation. You implied that to prove reasoning, pick a prompt with a large codomain and if the LLM answers with accurate precision, then viola, reasoning.

So my question was, can you give an example of a prompt with a high codomain that isn't subject to wide interpretation? It seems the wider the codomain the easier it is to say, "look! reasoning!"

[ninetyninenine]

Pick a prompt with a wide codomain but a single answer. That’s reasoning if it can get the answer right.