top | item 45246900 (no title) sdl | 5 months ago So basically the map projection problem [1] in higher dimensions?[1] https://en.m.wikipedia.org/wiki/Map_projection discuss order hn newest niemandhier|5 months ago Worse. Map projection means that you cannot have a mapping that preserves elements of the internal geometry: angles and such.Violation of topology means that a surface wrongly is mapped to one intersecting itself: Think Klein Bottle.https://en.wikipedia.org/wiki/Klein_bottle bravura|5 months ago Can you share an actual example demonstrating this potential pathology?Like many things in ML, this might be a problem in theory but empirically it isn’t important, or is very low on the stack rank of issues with our models. load replies (1)
niemandhier|5 months ago Worse. Map projection means that you cannot have a mapping that preserves elements of the internal geometry: angles and such.Violation of topology means that a surface wrongly is mapped to one intersecting itself: Think Klein Bottle.https://en.wikipedia.org/wiki/Klein_bottle bravura|5 months ago Can you share an actual example demonstrating this potential pathology?Like many things in ML, this might be a problem in theory but empirically it isn’t important, or is very low on the stack rank of issues with our models. load replies (1)
bravura|5 months ago Can you share an actual example demonstrating this potential pathology?Like many things in ML, this might be a problem in theory but empirically it isn’t important, or is very low on the stack rank of issues with our models. load replies (1)
niemandhier|5 months ago
Violation of topology means that a surface wrongly is mapped to one intersecting itself: Think Klein Bottle.
https://en.wikipedia.org/wiki/Klein_bottle
bravura|5 months ago
Like many things in ML, this might be a problem in theory but empirically it isn’t important, or is very low on the stack rank of issues with our models.