>I don’t understand how it can know that a token is correct.

It can't. The next token is just the most statistically probably given the context (at least in transformers). Try a very small/weak model in your own machine and more often than not it would get stuck repeating the same word or even just output garbage. Because after training and quantization (where some information is lost), that's the most probable next token. Large models can be tricked to fall in the same behavior with very very specific inputs. Still happen, even in frontier models. And they can't detect if the output is wrong.

That's why the premise in TFA is wrong, because a transformer is a next-token predictor. It literally is that. There's nothing secret or magical, it's just a very mechanical process, with a lot of matrix multiplication, normalization, a few random passes, mappings between embeddings and a dictionary of tokens, in a very very high scale.

If someone has found something that's not a mechanical, algorithmic computation and llms are doing something nobody can explain and can't even be modeled in math, I'm happy to be educated.