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The more general point is that generalization requires you to store seemingly useless information at training time (info that doesn't help your training objective), that will become useful in the future (when generalization actually happens). That's the opposite of compression.
Now, obviously, generalization requires abstraction, which requires erasing irrelevant details, so your high-generalization system will be doing *some* amount of compression. But it will be storing lots of seemingly useless info as well.
Is this why you argue in the paper that it is a necessity for a generalizable system to have a cost. Like it can't get away from storing useless info?
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