There is a way to do this same compression by utilizing the raw probability distributions that the LLM produces as output. Fabrice Bellard has some experiments with doing this with transformers: https://bellard.org/nncp/
The idea is that if you can produce an accurate probably distribution over the next bit/byte/token, then you can compress things with an entropy compressor (huffman encoding, range encoding, asymmetric numeral systems, etc). This comment is too small of a space to explain fully how they work, but it suffices to say that pretty much every good compression algorithm models probability distributions in some way.
The idea is that if you can produce an accurate probably distribution over the next bit/byte/token, then you can compress things with an entropy compressor (huffman encoding, range encoding, asymmetric numeral systems, etc). This comment is too small of a space to explain fully how they work, but it suffices to say that pretty much every good compression algorithm models probability distributions in some way.