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.