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)