Openreview is nice. I guess it could integrate with arxiv to allow preprints but someone needs to pay for moderation if we are to keep a high standard of comments.
> We know that there’s only one 1 in the rational numbers, then it must be the same 1 object as the 1 in the integers.
> The statement “3/3 is in Z” is true.
make it sound very trivial while in reality it is not. I do not quite understand your example with R^3 but the defined applies equally to your statements. There are many ways to define and think about the objects you mentioned -- there is not one single truth. Unless you are a devoted platonist, in which case, it's still like your opinion, man.
If the model is properly regularised, it can be trained indefinitely without overfitting. E.g., you can add adversarial perturbations to images and train a visual model for a very long time.
I don't know if the current LLM architectures have any explicit regularisation or if it happens to be an intrinsic part.