At first, i found the paper very theoretical, and did not clearly understand the intention behind deriving different networks and approximation schemes from the variational principle defined in equation (1). Later experimental results on two different types of problems ( 2-dimensional additive funtion, 2-dimensional Gabor function ) clearly showed that different networks and approximation schemes work better on one type of problems than the other, and the difference in these methods is in the stabilizer used in the equation (1), which represent different a priori assumptions about smoothness.

One usefull lesson to take home from this paper, i think, is that trying one of these methods on a particular problem may not be enough; however careful thinking about the problem (a priori knowledge) may lead to a wise choice between these methods.