Originally Posted by GeekGal

I don't know what it relearns when the battery (normal car battery) is disconnected and reconnected, beyond certain things -- when I disconnected my low voltage battery to do a P.I.E. radio plug install, I had to press my brake pedal to full travel after plugging the battery back in -- standard behavior documented in the manual for when the battery's been disconnected (teaches the vehicle the full travel of the brake pedal, again, and clears a standard "Check Brake System" or similar message from the message center.) The sunroof has to be retrained similarly, at least per the manual (I didn't have to on mine) so it opens the correct amount.

I didn't notice any changes in the vehicle's FE or driving characteristics but the manual did say to drive it a bit after reconnecting so it could "relearn" various things.

The Ford Mustang forums which I occasionally follow since my brother and father have new Mustangs also refer to this 1k to 3k learning and improved fuel economy behavior in their vehicles. I'm no mechanic but it was something about the vehicles running "rich" for the first 1k-3k miles, and after that break-in running less so resulting in some MPG gains.