I am going off the explanation in the declaude page (and related papers). But I see now anthropic mentions Aaronson's distortion-free watermarking.
Random watermarking functions colour the tokens based on (small) contexts and a secret key. Given watermarking functions are randomly chosen every single time they are used (so essentially not deterministically seeded by the context and secret key), then indeed the completion distributions are unchanged. However, they are deterministically chosen, a given string of text will always have the same corresponding watermarking functions. Tokens scored high by the function see an increased probability of being the chosen completion, those scored low see a reduced probability. I dont see it is different from merely talking about it as green/red and the points hold?
Random watermarking functions colour the tokens based on (small) contexts and a secret key. Given watermarking functions are randomly chosen every single time they are used (so essentially not deterministically seeded by the context and secret key), then indeed the completion distributions are unchanged. However, they are deterministically chosen, a given string of text will always have the same corresponding watermarking functions. Tokens scored high by the function see an increased probability of being the chosen completion, those scored low see a reduced probability. I dont see it is different from merely talking about it as green/red and the points hold?