If you've actually read the link regarding the DARPA Cognitive Research project, you will see that one of the things they were trying to figure out was how the brain could do what it does with such little power
I read it. It says IBM will have nine months for the first phase. That says to me that they're simply going to try building a really big neural network, most likely. Anything else would take far longer. Interesting to see what happens, but probably not a game-changer.
The problem with the "AI will advance geometrically" theory is that they've been saying that since the 60s and it hasn't happened. Fundamentally, the directions being explored by AI researchers will not lead to self-aware machines; merely improved Google search results and the like. You can accelerate all you want, but if you aren't pointing at a given destination, going really fast won't get you there.
It may be that we eventually figure out how to make intelligent machines, but it won't be as an inevitable result of the advancement of computers. If they do figure out how to model the human brain that might be a step in that direction, but it won't be the endgame.