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If you are taking a truncated SVD, the math says that it is the best representation of that data for a given truncation size, and will even give you a measure of how good that representation is. But picking how good you need often ends up being a kind of annoying and fuzzy heuristic thing. In addition, some data just gives you better singular values, and so fundamentally compresses better.

I guess the brain probably is dealing (in a hugely non-mathematical way -- it is just an analogy!) with a similar sort of thing. Somehow we pick some memories to keep in great detail -- either because they seem to be very valuable, or because they just seem to compress nicely.

It is a bit funny that one name for this sort of thing is a "singular experience."




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