Excellent use of memory
I have noticed that if I render an image with Cycles at 500 x 500 and compare the GPU memory used to render at 5000 x 5000, there is no increase. This is quite surprising and impressive considering other GPU renderers I know always increase memory usage depending on image size.
Credit for this goes to the Cycles developers as this is the way it is built for Blender.
As long as you are doing a non-progressive-refine render, the GPU only cares about one tile at a time. This means that you can set the full render resolution to any size at all and it will not increase GPU memory usage.