There have been a few responses along the lines of 'not always' but what you say is indeed largely true. There is another thing that is worth considering and t

There have been a few responses along the lines of 'not always' but what you say is indeed largely true. There is another thing that is worth considering and that is the algorithms (and even the theory) that works well for compression of discrete sources are not well suited for compressing real numbers (floating point numbers aren't, but, they are the poor man's reals). On the theory side, this bothered Claude Shannon enough that he decided to revisit this later in his career to create rate distortion theory, he knew that there was some unfinished business in information theory. We do have sort of a chicken and egg problem here, especially when we want store a lot floating points for a ML workload. Learning how to compress and learning the underlying distribution are equivalent problems. If we have already learned the model, then yes we could compress the data well. But when we haven't, then by definition we wouldn't have the knowledge to do a good job of storing the data in a well compressed form. After we have acquired the knowledge to compress well, we don't really need the compressed data anymore to learn the model, we already have it. One way to address this would be to do both incrementally and simultaneously.