  A feed-forward neural net with adaptable synaptic weights and fixed, zero or
non-zero threshold potentials is studied, in the presence of a global feedback
signal that can only have two values, depending on whether the output of the
network in reaction to its input is right or wrong.
  It is found, on the basis of four biologically motivated assumptions, that
only two forms of learning are possible, Hebbian and Anti-Hebbian learning.
Hebbian learning should take place when the output is right, while there should
be Anti-Hebbian learning when the output is wrong.
  For the Anti-Hebbian part of the learning rule a particular choice is made,
which guarantees an adequate average neuronal activity without the need of
introducing, by hand, control mechanisms like extremal dynamics. A network with
realistic, i.e., non-zero threshold potentials is shown to perform its task of
realizing the desired input-output relations best if it is sufficiently
diluted, i.e. if only a relatively low fraction of all possible synaptic
connections is realized.
