> I don't understand how taking a series of data and applying a random rotation could mathemetically lead every time to "simpler" geometry.

Let's pick a simpler compression problem where changing the frame of reference improves packing.

There's a neat trick in the context of floating point numbers.

The values do not always compress when they are stored exactly as given.

[0.1, 0.2, 0.3, 0.4, 0.5]

Maybe I can encode them in 15 bytes instead of 20 as float32.

Up the frame of reference to be decibels instead of bels and we can encode them as sequential values without storing exponent or sign again.

Changing the frame of reference, makes the numbers "more alike" than they were originally.

But how do you pick a good frame of reference is all heuristics and optimization gradients.