For instance, consider the distribution of strings drawn from the language '0+'. Now consider the same for the language '[01]+'. A compressor looking at only the strings of the first language within those of the second can do a much better job if it does not have to account for future data.
This also relates distantly to the idea of overfitting in machine learning.
But the Hutter prize (of which I'm a big fan) is for ever-more-optimal compressors, and in fact many of the solutions don't generalise to other input data without stripping out various tricks.
Most of the neural compressors are trying to squeeze every last bit out by sacrificing runtime. You can speed them up a fair bit and they're pretty good. fast-cmix with a small priming corpus will probably be about twice as compact as something like lzma or brotli.
The crucial idea is that once you do that and start optimizing for compression, at some point more compression on the training dataset can lead to worse predictions on the futures you care for. Which is very incompatible with the poster statement.
In that case all bets are off for all machine learning algorithms anyway. If the changes are not arbitrarily different then some of the lost performance can be recovered.
You talk about generalization a lot, but perhaps you are not aware that the technical term is defined under the assumption that test and train distribution are the same.
This means that training data isn't that helpful to top of the line compressors. eg. Fabrice Bellards nncp that's currently the record holding compressor for enwik9 is an LLM that learns on the fly. It's 628KB as shipped (LLM code complexity is high) and it wins on data sets gigabytes in size due to it's ability to create the training data on the fly. No pre-trained LLM comes close when you measure it as above (program size + compressed result).
So it's really not worth that much concern. There's a reason we all say AI is compression and we dismiss comments like the above. They don't pan out. No one's shipping significant dictionaries or pre-trained data. You want to win competitive compression? You'd better have raw code that learns on the fly and is naturally generalizable.
Predictors don't have to give you some corpus-average probability. They can give probabilities adjusted per symbol. The probability could even be exactly 1 for some symbol when the predictor is absolutely certain (and then it costs 0 bits to encode).
If you had a magic oracle predictor that already knew all the data you wanted to send, you'd have perfect compression.
At some level, nothing is representative of all future "problems".
I think as far as corner cases is concerned, people can optimize for what they think matters. Larger models, higher sensitivities, better filtering.
Beyond this, I don't know what you're peeved by. There's no manifesto, there's no claiming that any particular method to prediction is perfect yet.
This is a great experiment. Do some world building offline about Smergle the Keen finding the Hoopla of Kynashiusous. Then ask ChatGPT what reagents would have been more effective in breaking through the borantiastic door than squeeble stomach juices.
Of course we know the answer - it will either drop into a 'I have only been trained on data before blah blah blah' or 'I cannot talk about current world leaders' or 'I have not been trained on your hackneyed and unpublished romantasy saga, why don't you tell me about it?'
On the other hand, if it is aware of the general concepts of your concept, and has bridging concepts for related topics it has been trained upon, it might try to apply the general concepts to a specific but different scenario.
Also sparked the thought that the assumption only holds if the future looks like the present.