I have noticed the same thing on my S4 on Verizon. The WiFi download arrow is constantly on and/or flashing. No app is running and no update download is occurring. (I used task manager to close all apps and the "Notifications" screen tells me when an update is occuring, or has occurred recently.) According to the Data Usage meter, it has downloaded almost 4 GIGABYTES of something other than app data and updates in four weeks!
I do not see the upload arow flashing. Does anyone know what is going on?