To power features like Smart Stay (for keeping the screen on) and Smart Pause (for pausing videos when you're not looking), the GS4 uses sensors to detect your eyes. Take the load off of your phone by disabling Smart Screen. Go to the Input and Control section within the My Device tab of the Settings menu. Then press Smart Screen. From there, you can individually turn each Smart Screen feature off to save some power.
If you swipe down from the top of the screen and then press the grid icon in the top right corner, you can disable Smart stay and Smart scroll by tapping the respective icons.