Leg press involves no co-ordination, squat does.
So naturally you increase dramatically to start with, as you do with any exercise because of neurological adaption, but when co-ordination involves its even greater.
The most hilarious improvements are with front squats, where I first had to start with about 20% of my back squat weight because my co-ordination was so poor with them, and then was about 75% in 2 weeks. Front squats are now my favorite exercise too