  In this paper, feedforward neural networks are presented that have nonlinear
weight functions based on look--up tables, that are specially smoothed in a
regularization called the diffusion. The idea of such a type of networks is
based on the hypothesis that the greater number of adaptive parameters per a
weight function might reduce the total number of the weight functions needed to
solve a given problem. Then, if the computational complexity of a propagation
through a single such a weight function would be kept low, then the introduced
neural networks might possibly be relatively fast.
  A number of tests is performed, showing that the presented neural networks
may indeed perform better in some cases than the classic neural networks and a
number of other learning machines.
