Say, if you compress some data using these LLMs, how hard it is to decompress the data again without access to the LLM used to perform the compression? Is the compression “algorithm” used by the LLM will be the same for all runs (which means you probably can reverse engineer it to created a decompressor program), or will it be different every time it compress new data?

It probably is more like the LLM is able to „pack the truck much more efficiently“ and decompression should be the same.

But I agree that the likely use-case of uploading all your files to the cloud, having it compress your files, and downloading the result which is a few kb smaller isn’t really practical time efficient or even needed at all.

Correct me if I'm wrong, but don't algorithms like Huffman or even Shannon-Fano code with blocks already pack the files as efficiently as possible? It's impossible to compress a file beyond it's entropy, and those algorithms get pretty damn close to it.

Correct me if I’m wrong

Well actually, yes, I’m sorry to have to tell you are wrong. Shannon-Fano coding is suboptimal for prefix codes and Huffman coding, while optimal for prefix-based coding, is not necessarily the most efficient compression method for any given data (and often isn’t).

Huffman can be optimal given certain strict constraints, but those constraints don’t always occur in natural/real- world data.

The best compression method (whether lossless or lossy) depends greatly on the nature of the data to be compressed. Patterns and biases can make certain methods much more efficient (or more practical) in some cases, when they might be useless elsewhere or in general. This is why data is often transformed before compression, using a reversible transformation that “encourages” certain desirable statistical characteristics in the data, so the compression method can better exploit them.

For example, compression software (e.g. gzip) may perform a Burrows-Wheeler transform and other encodings before applying Huffman coding to get a better compression ratio. If Huffman coding was an optimal compression method for all possible data, this would be a redundant! Often, E.g. in medical imaging, audio/video data, the data is best analysed in a different domain to better reveal the underlying patterns and redundancies in the data so they cam be easily exploited by compression. E.g. frequency domain instead of time/spatial domain.