I find this kind of reasoning a bit pointless and unfalsifiable.

Someone says "LLMs fail at this", and you say "but humans also sometimes fail", then they says "but we are not talking about the same thing", and you answer "this difference does not matter because aliens may be totally different".

My point is that what we observe with LLMs does not require any understanding. And in some cases, it is clear the answer of a LLM was built without understanding. And in other cases, it looks like it could have been built with understanding because there is no visible errors, but because we know the LLM can build things without understanding, this can equally simply be something that is built without understanding and happen to have no error, and therefore just looks like it has been built with understanding.

I think you take the problem the wrong way: you start from the hypothesis that there is understanding, and then you are finding reasons to maintain this conclusion (the most prominent ones being "humans also can do mistake" or "... fake understanding" or "... hallucinate". Well, humans can do a lot of things that don't require intelligence, does it mean that things that do these things that do not require intelligence are in fact as intelligent as humans?). This is a confirmation bias.

I don't have problem if it turns out LLMs have understanding. But the reality right now is that a simple explanation is that it does not have it. But it feels like some people just argue "but it is still possible, bending this argument there and there". I bet at some point, they will say "ok, I see your point, but maybe LLMs are intelligent and have this behavior on purpose because they want to remain hidden because they are smart enough to understand that if humans would know, they would freak out". It feels more and more like a belief system rather than a scientific approach.

Just two elements to go further:

- in the majority of cases, "things that have been faked to look like there are the result of understanding" will be correct. Because if you are trained to pretend you understand, you are trained to imitate someone who has understood, and you are therefore trained to imitate their reasoning, which turns out to be correct. (if you want to test the understanding, it is complicated, because the "understanding" is a data leakage during training)

- if LLMs extract understanding for the data from their training, it is strange that their current understanding (just after the training) is so close to the current understanding of the humans. Surely humans have missed stuffs here and there. The math theorem number 3424 not solved yet is probably as "simple" than the math theorem number 6423 that happened to be solved by humans, it is just by chance and circumstances that some humans have worked on 6423 and found a way to crack it while they did not spend as much time and effort on 3424. And yet, LLMs just happen to never notice any theorem on their own at the end of the training phase. Asking a LLM "Explain to me a math theorem that humans did not notice, with demonstration. This theorem should be something you understood when you were trained over maths" just does not work.

(and, please, I know that a mathematician may know theorem 3424 and yet not have noticed 6423 either, or that LLMs can scan a math problem with a large series of math tools and find a break-through. But my point is that LLMs are studying math soooo intensively during the training that they know all the human theorems, which is way more knowledge than any single mathematicians. And yet, it turns out that all this math understanding just ends up being exactly limited to what humans already know. What are the odds? Or more probably: they just don't really understand math, and when asked about a known theorem, they generate a correct explanation based on training data without properly understanding it)