Associative memory in a network of ‘spiking’ neurons

Abstract

The Hopfield network provides a simple model of an associative memory in a neuronal structure. It is, however, based on highly artificial assumptions, especially the use of formal two-state neurons or graded-response neurons. The authors address the question of what happens if formal neurons are replaced by a model of ‘spiking’ neurons. They do so in two steps. First, they show how to include refractoriness and noise into a simple threshold model of neuronal spiking. The spike trains resulting from such a model reproduce the distribution of interspike intervals and gain functions found in real neurons. In a second step they connect the model neurons so as to form a large associative memory system. The spike transmission is described by a synaptic kernel which includes axonal delays, ‘Hebbian’ synaptic efficacies, and a realistic postsynaptic response. The collective behaviour of the system is predicted by a set of dynamical equations which are exact in the limit of a large and fully connected network that has to store a finite number of patterns. The authors show that in a stationary retrieval state the statistics of the spiking dynamics is completely wiped out and the system reduces to a network of graded-response neurons. In the case of an oscillatory retrieval state, however, the spiking noise and the internal time constants of the neurons become important and determine the behaviour of the system.