Correct me if I'm wrong, but watermarking is only possible, if the model has a limited set of input you can provide (affects for the output) and a limited set o

Correct me if I'm wrong, but watermarking is only possible, if the model has a limited set of input you can provide (affects for the output) and a limited set of output it produces, and it should be completely deterministic. And you should pre-calculate all possible combinations. And this should be also the case for every possible LLMs; then you can compare which LLMs could produce which outputs based on what inputs. Then there is some certainty that this output is produced by this LLM and this another LLM might produce it as well with these inputs. So... impossible?