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Because by definition compression discards all information that isn't relevant to the training goal, and by definition the training goal isn't what you want to generalize to (otherwise there is no generalization happening).
The most compressed model that does X is only capable of doing X. If it could do more then you could compress further.
I think I might be mistaking your point about compression with the "representation" needed to do good compression. It's just that for me if my brain is making skill programs to handle new situations, the ability to represent efficiently information seems like an important feature
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