Abstract
We describe a modified attractor neural network in which neuronal dynamics takes place on a time scale of the absolute refractory period but the mean temporal firing rate of any neuron in the network is lower by an arbitrary factor that characterizes the strength of the effective inhibition. It operates by encoding information on the excitatory neurons only and assuming the inhibitory neurons to be faster and to inhibit the excitatory ones by an effective postsynaptic potential that is expressed in terms of the activity of the excitatory neurons themselves. Retrieval is identified as a nonergodic behavior of the network whose consecutive states have a significantly enhanced activity rate for the neurons that should be active in a stored pattern and a reduced activity rate for the neurons that are inactive in the memorized pattern. In contrast to the Hopfield model the network operates away from fixed points and under the strong influence of noise. As a consequence, of the neurons that should be active in a pattern, only a small fraction is active in any given time cycle and those are randomly distributed, leading to reduced temporal rates. We argue that this model brings neural network models much closer to biological reality. We present the results of detailed analysis of the model as well as simulations.
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