man, I hate saying I don't have the brain power right now to find it and I could have sworn I commented on a post discussing this very thing for one of those papers. I know there was recently a paper that contradicts my statement, but a slightly older paper supporting it. I think it is likely a mixed bag at the moment depending on the model and their training regime.

My anecdata of one using anthropic's and google's models (google's especially) this year, the model will drop the casual tone and sycophancy of its replies pretty damn quick as soon as you tell them off. And usually that is when there is less correction. Could also be because my prompting changes from supervisory to very directive, as in shut-up-and-do-exactly-what-I-say, when it gets off into weeds. Even then, it can be a crap shoot.