It's looks like the same sign we can see in 6 Perception, and so I don't think it's actually part of the icon. Also, 10 Intelligence is definitely Nerd Rage!, which would actually make a lot of sense. But the good news is that, like a number of perks on the chart, my initial hunch about a 'Genius' related perk would seem to have been correct.
If you look at 5 Intelligence on the http://media2.giga.de/2015/07/Fallout4_Perks-rcm640x0.jpg chart, It looks very much like http://vignette3.wikia.nocookie.net/fallout/images/9/9c/EducatedFO3.png/revision/latest?cb=20101125051917. But if we look at it on the http://i.imgur.com/WBRA8Fv.jpg version, the icon is different from the original one. What's interesting about this is that the person shown in the icon does actually look like http://www.apredatorymind.com/Albert_Einstein_.jpg, and is wearing a lab coat. Also, in the top left of the icon, in place of the graduation hat seen in the previous version, we can instead see a dove flying towards Mr E, and in it's claws is what looks like a rolled up diploma.
What this would suggest in the first instance is that Educated now increases our rate of gaining XP far beyond that of maxing out the Intelligence stat, as a suggestion that we are able to learn faster due to advanced study and increased mental capability. But in addition to this, I have a very strong feeling that the first rank will also unlock unique dialogue options with scientifically minded NPCs, exactly as I had previously suggested. And also that if we are wearing a lab coat, we will be given unrestricted access to many areas of the game that would otherwise have been closed off to 'regular folk'. This would make the perk in many ways equivalent to joining the Mages Guild in the Elder Scrolls series, with access to unique items and equipment. Note that if this is correct, the restricted areas would still be accessible by other players, although they would have to use stealth, force, or some other method in order to gain entry.
One further point, the comment I made http://www.gamesas.com/topic/1529102-skills-perks-revised-edition/?p=24206026 about Einstien's General Theory of Relativity would have taken the form of an in-game Slow Time effect for use during real-time combat. Again, even though this would be unlikely to appear as a feature of the new Educated perk, I am more than certain that it would be made available in-game through one of the new or updated chems.