Yeah, still, I wouldn’t claim “as no human would end up falling into that”, given that it may not be that unlikely to find at least one human who displays similar writing the more humans you involve.

No, it is actually statistically impossible for a human to replicate this on sufficiently long runs of text.

This is not about replicating writing like a model. This is basically about guessing which words to pick from the list of suitable words based on a rule that you don't know (because the key is secret).

To reduce this to the simplest possible example, imagine you are writing a "text" from just two letters: "a" and "b". Let's say for convenience that the text is supposed to be random. So the text would look something like "ababaaabbababbbabababaabbbabaababbaaabbabaabbaaaaabaaabbbaabaabababbabbbbbbbbabbabaabbbbbbbaabbabaab"

(generated with '''.join(random.choice(['a', 'b']) for i in range(0, 50)))

The watermarking works as follows: the model owner holds a key, and then uses that key to influence the random choices between "a" and "b" somehow, in a context-dependent way. The actual algorithm is quite complicated, but for simplicity let's just say we have a secret pattern which biases the random choice towards it. In order to see the exaggerated results, let's say the secret key is "aaaabbbb" (of course this is a bad secret key, once again just an example), and that the bias is strong (let's say 80%). So this would mean that the first four letters in our text are more likely to be "a", the next four letters are more likely to be "b", then the next four letters are more likely to be "a", and so on.

Then the text would look something like "aaaabaabaabaabbbabaaaabbaaaababbbaaaabbbabaabbbbaaabaabbaaaaabbbabababbaaaaabbbbaaabbbbbaaaaababaaba".

(generated with ''.join(random.choice(['a', 'b'] + ([key[i % len(key)]] * 3)) for i in range(0, 100)))

You can see visually that the secret key has affected the text. Of course in this example even if you didn't know the secret key you could probably figure it out, in reality the algorithm is way more complicated than that, relying on cryptography, so you wouldn't be able to know the secret key or see that the string has been biased at all.

If the text is long enough, and you know the secret key, you can guarantee that the text was generated with it. In our examples, the letters in the text match our key 77% of the time. The probability of an actual random algorithm generating a text like that is already very low, despite the base entropy being only 100 bits. If my math is correct, for our example the p-value is 2.7 * 10⁻⁸, or about 0.00000027%. I would bet a hungy that the text was generated by our watermarking algorithm, with odds like these!

Of course we did exaggerate the bias and our base algorithm was random. In reality the bias is smaller, the algorithm for determining the likelihoods of possible next tokens is very complicated (it's the LLM itself), and the algorithm for determining which token to bias is also way more complicated (involving cryptography and real secret keys). That said, hopefully it should help you understand why, for sufficiently long texts, this fingerprinting is just not possible to be replicated by humans.