Are remapped Xbox buttons stored on the controller?

Via the Xbox Accessories app, it appears that you can remap the buttons on your Xbox one controller (awesome!).

Question: Would the newly remapped button scheme be stored directly on the controller? Or on the Xbox/PC? In other words, if I remap the buttons, and then use the controller with a different Xbox/PC, will my remapped button scheme come along with me to the new system? Is the behavior any different with the Elite controller?

I don't think it stores any information on gamepad itself.

You can imagine something like this:

• Standard: Xbox Game Pad A > Receiver > Xbox Console > Yeap that's an A.
• With Xbox Accessories app: Xbox Game Pad A > Receiver > Wait a second I should check my own profile. Nope it's not A, it's B (says the app) > Xbox Console > Yeap that's a B!

It's just a profiler app. But let's say you're using another console with Xbox Accessories not installed, how can it manage this signal binding?