Right but that is context dependent; it drops with context length, depends on tokenizer, etc. It doesn't end up being super relevant, despite the fact that if you look at the loss for real models it's relatively large in absolute terms. But that doesn't really matter -- all of the interesting stuff happens once you start getting closer and closer to it. You've gotten past all of the easy tokens that dominate the entropy and now you get to the really challenging ones that we care about (like e.g. very difficult reasoning about a next step).

My understanding is that the true entropy floor of a language is intractable- regardless of context length there will be “unpredictable” tokens where cross entropy loss is bound to happen. Even with infinite parameters and data you’ll still have a chance at failing to predict the next token correctly a decent chunk of the time.

Also, linear gains in context length scale quadratically with compute because of attention, so depending on context growth means taking a bath on GPUs for as long as you can, right?