Reduction of synapses in the Hopfield autoassociative memory

The auto-associative Hopfield network is a set of neurons in which the output of each neuron is the input of all other neurons, i.e. the inter-neuronal connections graph of the Hopfield network is complete. The large number of inter-neuronal connections is one of the problems of the Hopfield networks hardware implementation. A solution is the reduction (exclusion) of insignificant connections. In this paper, based on the analogy with oscillator networks, the connections number reducing effect on the auto-associative Hopfield network behavior is investigated. It is shown that the exclusion of connections with weights whose absolute values are strictly less than the maximum for a given neuron substantially improves the operation quality of the Hopfield network trained according to the Hebb's rule. As the dimension of the stored vectors increases, not only the chimeras disappear but the permissible input data noise level also increases. At the same time, the network connections number is reduced by 13–17 times. The reduction of connections in the Hopfield network, trained by the projection method, worsens its functioning quality, namely: in the network output data, there are distortions even while the reference vectors are entered. With the stored vectors dimension increasing, the allowable noise level for the reduced Hopfield–Hebb networks approaches the corresponding index for the Hopfield projection networks. Thus, given the much smaller number of connections in the reduced Hopfield–Hebb networks, these networks can successfully compete with the Hopfield projection networks for a sufficiently large stored vectors dimension.