Neural networks have attracted much interest recently, and using parallel
architectures to simulate neural networks is a natural and necessary applica(cid:173) tion. The SIMD model of parallel computation is chosen, because systems of this type can be built with large numbers of processing elements. However, such systems are not naturally suited to generalized communication. A method is proposed that allows an implementation of neural network connections on massively parallel SIMD architectures. The key to this system is an algorithm that allows the formation of arbitrary connections between the "neurons". A feature is the ability to add new connections quickly. It also has error recov(cid:173) ery ability and is robust over a variety of network topologies. Simulations of the general connection system, and its implementation on the Connection Ma(cid:173) chine, indicate that the time and space requirements are proportional to the product of the average number of connections per neuron and the diameter of the interconnection network.