This is an anti-aliasing artifact. It has nothing to do with CPU vs GPU. If you are seeing it on exporting a raster image (JPG or PNG), make sure you use "Art Optimized".
This occurs when you have objects butting up against each other (as opposed to overlapping), and when a raster version is created, the file is rasterized object by object from the bottom up, and each object gets a a bit of anti-aliasing along the edges creating partially-transparent pixels that allow what's behind your art to slightly show through; in your case white. Depending on your export resolution, this effect will be more or less visible, but still there.
The "Art Optimized" setting does things a bit different where it renders your art at a higher resolution, THEN downsamples the complete image to your intended resolution, essentially eliminating the issue.
If you are seeing it on the screen, it's the same issue.
Note that this doesn't affect printing, as when these objects are sent to print to a high resolution device, like a printer or pre-press system, no antialiasing occurs and the objects show no gap at all. However if any flattening occurs at all in your PDF, you might "bake-in" the "gap"