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Are there well known non-frequency-domain compression techniques (lossy or lossless) that exploit information sparsity? Like the first image could be segmented as in the second image, and only the 4 non-empty rectangles stored. That sort of approach.
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Non-frequency domain because it seems to me preserving feature legibility is a useful property. I can say “rectangle id 14 contains a smiley”
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Example of why it’s useful: you can navigate (inefficiently) directly on a compressed map if it’s not in some other conformal space. Like knowing only the highways topology. Shortest path point to point in the highway graph won’t be real shortest path but it will avoid obstacles.
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Replying to @vgr and @meditationstuff
(the robots move on a graph connecting the centroids of the open rectangles so you get weird artifacts)
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I’m trying to think this through for time perception in narrative memory, not actually implement it. For example our brains seem to store emotionally charged events in great detail (so recalled time perception slows per David Eagleman experiments) but yada-yada over white space.
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Good statement of the problem, which I’d compress further to “explainable compressions.” Specifically ones that in the limit recover the raw ontology of explanation. The way a caricature admits a “facial” explanation of a face similar to a photograph.
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Replying to @vgr
the task is to store a smaller representation, and for that mapping to be interpretable?
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For time, slow/fast time perception is still ontologically *time* perception. We don’t suddenly switch to frequency based perception when thinking about, for eg., 10,000 years of yada-yada history. Cyclic theories of history seem clearly like a different compression ontology.
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I tried to replicate a lossless compression paper from like fifteen years ago that looked for "motifs" in non-frequency-domain. Not a well known technique but there's stuff out there, fwiw. Not sure about well known.
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Heh I implemented the segmentation approach sketched above to store maps lossily for some robot path planning stuff 15y ago. Could get really extreme compressions (like 95%) on some maps, but the tradeoff is the path planning got more inefficient
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