A possible transformation of the fully connected neural nets into partially connected networks

Realizing a neural network (NN) with a large number of interconnections meets severe difficulties in the case of VLSI implementation. Therefore, solving tasks by NN containing a lot of nodes involves an acute realization problem. Thus, the minimization of the number of interconnections is a fundamental problem of NN research. The cellular approach, to solve problems by using partially connected networks in which each neuron `communicates´ with a certain number of neighbouring ones, or at least a noncellular method to reduce the number of interconnections regardless of the neighbouring configuration, is considered. Both concepts of minimization are depicted. There is no general method to transform the original problem to an equivalent one which can be solved by a cellular or partially connected network under some invariancy criteria guaranteeing the same solution as it was achieved by the original net. This paper provides a method and an exact procedure for accomplishing this optimization in the sense of minimizing the number of interconnections. However, the number of computations needed grows extremely fast with respect to the number of nodes, which prevents practical application to problems with large complexity