Well, you do understand the "penalising" or as the ML scientific community likes to call it - "adjusting the weights downwards" - is part of setting up the evaluation functions, for gasp - calculating the next most likely tokens, or to be more precise, tokens with the highest possible probability? You are effectively proving my point, perhaps in a bit hand-wavy fashion, that nevertheless still can be translated into the technical language.

You do understand that the mechanism through which an auto-regressive transformer works (predicting one token at a time) is completely unrelated to how a model with that architecture behaves or how it's trained, right? You can have both:

- An LLM that works through completely different mechanisms, like predicting masked words, predicting the previous word, or predicting several words at a time.

- A normal traditional program, like a calculator, encoded as an autoregressive transformer that calculates its output one word at a time (compiled neural networks) [1][2]

So saying "it predicts the next word" is a nothing-burger. That a program calculates its output one token at a time tells you nothing about its behavior.

[1] https://arxiv.org/pdf/2106.06981

[2] https://wengsyx.github.io/NC/static/paper_iclr.pdf