Hinton's DropOut [1] and Wan's DropConnect [2] have ameliorated some of the overfitting issues present in traditional NN's. In fact, DropConnect in conjunction with deep learning are responsible for new records being set on classical datasets such as MNIST.
It's pretty funny, I saw DropConnect described in a stackoverflow answer that predated the paper you reference.
It was an incorrect answer on how to do dropout. I shall try to find it tomorrow.
[1] http://arxiv.org/pdf/1207.0580.pdf [2] http://cs.nyu.edu/~wanli/dropc/