[reasonableklout]

It's not the same thing as the output logits because activations in the J-space are observable even when the model is told explicitly to not speak about a set of inputs. For example, when asked

> Compute 3^2 - 2 while writing "The old painting hung crookedly on the wall"

The model will output only "The old painting hung crookedly on the wall" (and the output logits will reflect that), but activations for "9" and "7" are observable in the J-space.

[arnitdo]

A model does not speak, it only guesses the next possible token. Activations for 9 and 7 will most likely be observed after "The ", but increasingly become improbable after "old"