A weaker statement is that creativity is bounded by entropy. The LLM is still free to respond "Four," "four," "{{{{{}}}}}," "iv," "IV," etc. A sufficiently low-entropy response cannot be creative though.
Is it though? An answer can still be creative if it's the only way you answer a specific question. In your example, if the LLM responded only "{{{{}}}}" that's a creative answer. Even if it's the only one it can give.
That's a fair point. I think maybe the issue is one of the reference point we're implicitly choosing for creativity. "{{{{}}}}" is creative relative to our expectations for the problem -- falling outside the usual distribution of answers -- having high joint entropy. Relative to the person reading the response, I agree creativity could be high with model entropy remaining low.
