The distinction I perhaps didn’t make clearly enough is that I’m not really debating the concept of prediction at inference time, although, as I pointed out elsewhere, I think that’s the less interesting interpretation of what “prediction” means.
What’s more interesting to me is its application at training time. In reinforcement learning, there is no ground-truth next token to predict.
So if you’re comfortable calling Deep Blue a “next move predictor,” then I think it’s perfectly consistent to call an LLM a “next token predictor.” But I think it’s more useful to think of Deep Blue as evaluating the value of possible moves. roughly, how likely they are to lead to winning.
And I think effectively the same distinction applies here.
I think you're trying to limit the meaning of both 'next' and 'prediction' in ways that don't reflect usage and that--if adopted--would severely limit our ability to discuss and evolve what LLMs are actually doing.
There's nothing inherent in either word that forces such a limit; predicting based on what will lead to success as measured by [reward function] is still a prediction.