Hi, its problem when i rendering a head with hairs particles, eyebrows are bugged. But its all right on viewport rendering mode. Problem have only "brows" particle system.
Cycles Render. Blender 2.78b downloaded at blender.org
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I tested the .blend file and it appears in addition to hairs rendering incorrectly when hitting F12, upon return to the viewport the hairs are displaced randomly from original positions. After going into object edit mode and back the hairs are back to original positions.
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This is not relevant to GPU or CPU, you'll have such behavior in all render modes.
Your issue is caused by using interpolated children for particles without restricting area where they need to be interpolated for. This makes them to be interpolated across the whole surface.
Using weight paint or a 2K texture to limit particle system to will solve your problem.
Thanks for the report, but it is known behavior.