The best way to make your mind remember the proper swing is to teach it slowly, practice making quality swings in slow motion so that your mind memorizes the correct movement
Straight back and straight through putting is very effective when putting inside fifteen feet and requires that you keep the putter face square to the target line throughout the entire stroke
Working on your swing in slow motion will allow you to analyze what you are doing on each part of the swing, which will help you fix your flaws but also get away from swinging segmentally