It looks like x and y are the dimensions of your thingspace here. If you had a different thingspace, would you still be able to recover the same concept?
Yup! This is a very weird space to call a ‘thingspace’ but most transformations of it (anything that’s at least approximately injective, for example) will preserve the same concept.
Here’s what that same distribution I used above looks like if you plot the closed-form pushforward density analytically. In this picture it’s easier for the visual cortex to pick up on the patterns (although it would still be nontrivial for a human to figure out what should be colored red and what should be colored blue if you erased the colors).
It looks like x and y are the dimensions of your thingspace here. If you had a different thingspace, would you still be able to recover the same concept?
Yup! This is a very weird space to call a ‘thingspace’ but most transformations of it (anything that’s at least approximately injective, for example) will preserve the same concept.
Here’s what that same distribution I used above looks like if you plot the closed-form pushforward density analytically. In this picture it’s easier for the visual cortex to pick up on the patterns (although it would still be nontrivial for a human to figure out what should be colored red and what should be colored blue if you erased the colors).