[adrian_b]

Which is why in this book the title of a paragraph is "Compression is an artificial intelligence problem".

However, I believe that is less useful to think that AI "finds an universal compression", than to think that the training of an AI model has the purpose to find a specific lossy data compression method, which is close to optimal for the input data that constitutes the training data set.

One could consider the training algorithm as a universal lossy data compression method, but this view is not useful in practice, because unlike a traditional lossy data compression algorithm, used e.g. for movie or picture compression, which you can use every day to compress many data sets, even in real time on an incoming data stream, the training of an AI model is a very long and expensive operation, which can be done only infrequently and which makes sense only for special important datasets, from which data will be frequently extracted by querying (i.e. AI inference) for a long time, to make worthwhile the compression, i.e. training, cost.

Moreover, for the best compression results the training of a new improved AI model does not consist only in determining the values of parameters (weights) of a fixed inference algorithm, but the structure of the inference algorithms is also tweaked for each new generation of models.

This is an additional reason that makes impractical to think about training as a universal compression algorithm (instead of a method for searching specific compression algorithms, which work for a given training set), because it is not a fixed algorithm, but a family of algorithms that evolves continuously, at least for now.

[mtdewcmu]

I think that the common meaning of AI has changed since this was written. This book was written at least 14 years ago, long before anyone had heard of an LLM. Matt Mahoney incorporated neural networks in his compressors. Afaik they weren't pretrained. They were adaptive and made one pass over the plaintext, simultaneously learning and predicting. Decoding worked similarly.

If you go and (re)read what he writes in relation to AI, which I just did, it's about exclusion. He excludes "Universal Compression" as impossible, Kolmogorov compression as uncomputable, and then he gets to Artificial Intelligence. Artificial Intelligence is an appropriate way to model data, since data is created by humans with human intelligence. And, AI doesn't violate mathematics the way Universal Compression and Kolmogorov solutions do. So therefore, Artificial Intelligence is what's left. That seems to be the argument.