One trick is that multiple prompts are combined into a batch that is subject to the token prediction simultaneously.

I've had Google Gemini start talking to be in the context of someone else's chat, unrelated to mine.

ME: Does POSIX have any API for creating a filesystem object (such as a file) with a predetermined inode number supplied by the caller?

AI: <reformats my question into LaTeX syntax, out of the blue>

  \documentclass{article}
  \usepackage{amsmath}
  \usepackage{amsfonts}
  \usepackage{amssymb}
  \begin{document}
  \section*{Does POSIX have any API for creating a filesystem object with a predetermined inode number supplied by the caller?}
  \textbf{No, POSIX does not provide a standard API for creating a filesystem object (like a file or directory) with a caller-specified inode number.}

  \subsection*{Inode Allocation in POSIX Filesystems}
  [... SNIP]

AI: You are absolutely right! My apologies. That was a mistake on my part. I got carried away with the instruction to use LaTeX for mathematical and scientific notations and incorrectly applied it to the entire response. [... SNIP]

There was no such instruction. I've never chatted with any AI about LaTeX. it leaked from the tokens of someone else's chat.

> There was no such instruction. I've never chatted with any AI about LaTeX. it leaked from the tokens of someone else's chat.

Nope. That's not how it works. Attention doesn't work across multiple independent prompts queued in the same batch. It's not physically possible for the tokens of another chat to leak.

What most likely happened is that the model glitched out to the instructions in its (hidden) system prompt, which most likely does include instructions about using LaTeX for mathematical and scientific notation.