The fact that the best compression algorithms are, in the LLM setting, still catastrophically bad at prediction suggests that the overlap between compression and prediction is weak at best.
This shows that prediction algorithms (AI models) are also very good at compression, but compression algorithms (like the ones used in gzip) are not likewise very good at prediction. Which is evidence that compression is necessary but not sufficient for prediction.
For example, LLM pretraining datasets are on the order of tens or hundreds of terabytes. If an LLM-based code for that data is ~twice as efficient as gzip, you could afford to transmit the weights of even a very large LLM and still come out ahead.
In other words: LLMs actually are excellent compressors of their training sets in the formal information-theoretic sense.
