Theoretical limitations of a Hopfield network for crossbar switching

It has been reported through simulations that Hopfield networks for crossbar switching almost always achieve the maximum throughput. It has therefore appeared that Hopfield networks of high-speed computation by parallel processing could possibly be used for crossbar switching. However, it has not been determined whether they can always achieve the maximum throughput. In the paper, the capabilities and limitations of a Hopfield network for crossbar switching are considered. The Hopfield network considered in the paper is generated from the most familiar and seemingly the most powerful neural representation of crossbar switching. Based on a theoretical analysis of the network dynamics, we show what switching control the Hopfield network can or cannot produce. Consequently, we are able to show that a Hopfield network cannot always achieve the maximum throughput.