The 'predictor' part referred to the fact that base models would effectively answer the question "what token is most likely next". Training away from that default behavior doesn't escape the technical meaning of those words- answering "what token is most likely next in a solution to Navier Stokes" is still predicting a next token- but at that point the label just means it outputs text serially.

> "next token predictor" has always referred to inference

Going back to first principles, wikipedia mentions [0] inference as:

> "Inferences are steps in logical reasoning, moving from premises to logical consequences. Inference is traditionally divided into deduction and induction"

Is that exactly what next token predictor means, or is it correlated?

[0] https://en.wikipedia.org/wiki/Inference