prediction is a very specific term of art in the field of machine learning. generally speaking, machine learning models like LLMs are based on probability; performing a statistical prediction of the likely y given some input x

    Probability(y | x)

that's why we refer to outputs as a prediction. it is likelihoods and stuff. the output is never definitely correct as we're not dealing with heuristic processes.

> Prediction implies there is some "truth" or event or something that you can test against

there absolutely is a ground truth during training. the core predict-the-next-most-likely-token part of an LLM has a ground truth next-token. that's why you don't end up with generated text like: fish spurious send cattle chocolate phone happy meaning ball orange board canada.

> optimizes to predict the next token in training data

that is the optimization goal in training the next-most-likely-token core of an LLM, it basically translates to maximise the likelihood of predicting the next token x_i given the previous tokens

    L(θ) = −log Π^n_{i=1} f_θ(x_i | x1, ..., x_{i−1})

https://arxiv.org/pdf/2012.07805 (GPT2 but the point still stands)

(edit: sorry for the ADHD edits)