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Losslessly, because that's easier to test.
When you're recalling a memory, do you remember the position of every blade of grass, or the exact angle of the Sun?

Humans, the only extant example of a general intelligence, don't do lossless compression at all.

I don't think you get to AGI by trying to compress noise.

Lossless compression requires the recognition of patterns in the data. And a smart way to use those patterns to perform the actual compression.