Distribution of the activities in a diluted neural network

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Abstract
The dynamics of asymmetrically diluted neural networks can be solved exactly. In the present work, the distribution of the neural activities is calculated analytically for zero-temperature parallel dynamics. This distribution depends on the number of stored patterns and is a continuous function in the good retrieval phase. The continuous part of the distribution of activities is due to the asymmetry of the synapses since it is known that networks with symmetric interactions always have a distribution of activities which is a sum of a few delta functions. The expression for the distribution of activities is also given for a mixture of two patterns which have a non-zero overlap.