[kevin948]

Super cool stuff! Thanks for the article. I was wondering if someone had an opinion on an adjacent idea.

I've had Nash's infinitely collapsible sphere stuck in my head for some time: https://www.quantamagazine.org/mathematicians-identify-thres...

For purposes of nearest neighbors this seems like an incredibly interesting shape to inscribe into: The sphere, despite having spherical properties also maintains linear properties due to the corrugation. To me that means we can try to inscribe orthogonal properties into both of the spaces.

My understanding of these geometries isn't complex enough to make the connections, so my question is this: Do you think its feasible to use shapes with this 'corrugated' property to make better nearest neighbor compression? My intuition tells me that you can use the shape's linear nature to push apart independent components and inscribe the rest of the details into the spherical components. Or perhaps the opposite way.

Hopefully that made sense!

[extremelearning]

I don't have any intelligent comments on your question, but I wanted to say that I am a fan of Quanta magazine, but somehow had missed this really cool article. So thanks for pointing me to this fascinating field. ;)