(to be clear this is not me arguing for any particular merits of llm-based compression, but) you appear to have conflated one particular nondeterministic llm-based compression scheme that you imagined with all possible such schemes, many of which would easily fit any reasonable definitions of lossless and deterministic by losslessly doing deterministic things using the probability distributions output by an llm at each step along the input sequence to be compressed.

With a temperature of zero, LLM output will always be the same. Then it becomes a matter of getting it to output the exact replica of the input: if we can do that, it will always produce it, and the fact it can also be used as a bullshit machine becomes irrelevant.

With the usual interface it’s probably inefficient: giving just a prompt alone might not produce the output we need, or it might be larger than the thing we’re trying to compress. However, if we also steer the decisions along the way, we can probably give a small prompt that gets the LLM going, and tweak its decision process to get the tokens we want. We can then store those changes alongside the prompt. (This is a very hand-wavy concept, I know.)