On the intractability of loading pyramidal architectures

It is known that loading (i.e. training) general neural architectures, when the tasks (training sets) are also general, is NP-complete. In this paper, an architecture class called `pyramidal networks´ is considered. Such architectures are relevant to research in weightless neural models. It is shown that it is NP-complete to decide whether or not there exists a configuration of node functions whose output is consistent with a given training set. It is also shown that this problem can be solved in polynomial time if the width of these architectures is bounded by a logarithmic growth function (in the length of the input pattern). The theoretical results obtained in this work can be used as guidelines in designing neural models