Since the papers really don't go into any detail on convolution networks, I figured I'd take a small stab at what they from what I've picked up. Basically, they're multilayer neural networks that get full translation invariance, and partial scale and rotation invariance. They do so by sharing weights. Normally to get a network that detects an object anywhere in an image, you'd need training data of that object in each location. Here they used shared weights from each location (and scale?), so that when the weights are changed for one location they're changed everywhere, giving networks the power of convolution without massive amounts of additional training. (Take all this with a grain of salt, since it's not something I know much about.)

It seems like the principle here, of pulling neighbors together and pushing non-neighbors apart to achieve dimensionality reduction is quite powerful - and also used elsewhere.

I'm reminded of Kohonen networks, another neural network sometimes used for dimensionality reduction, but with the differences (as I
understand) of:
a) generally only attracting neighbors (and not repelling non-neighbors)
b) tending to work in unsupervised environments
c) having 'neighbors' defined by the structure of the manifold you're trying to fit to the data, rather than by labels