There are also billions of possible Yes/No questions you can ask that won't get unique answers.

The LLM proper will never answer "yes" or "no". It will answer something like "Yes - 99.75%; No - 0.0007%; Blue - 0.0000007%; This - 0.000031%" etc , for all possible tokens. It is this complete response that is apparently unique.

With regular LLM interactions, the inference server then takes this output and actually picks one of these responses using the probabilities. Obviously, that is a lossy and non-injective process.

If the authors are correct (I'm not equipped to judge) then there must be additional output which is thrown away before the user is presented with their yes/no, which can be used to recover the prompt.

It would be pretty cool if this were true. One could annotate results with this metadata as a way of citing sources.