### Dynamics of an auto-associative neural network model with arbitrary connectivity and noise in the threshold

Hiro-Fumi Yanai, Yasuji Sawada, and Shuji Yoshizawa

### abstract

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The method of statistical neurodynamics is used to analyse retrieval dynamics of an auto-associative neural network model. The model has arbitrarily specified connectivity and static noises are added to threshold values. The method is based only on probability and approximation calculations. Connections between neurons are determined by a version of the Hebb rule (correlation-type rule), and some of them are removed at random. It is shown that the capacity of the network per connection is a monotone decreasing function of connectivity if there are no noises in the threshold. When there are noises in the threshold there exists an optimal value of the sparsity of connections which yields the maximum capacity for a fixed noise level. In addition, effects of systematic removal of connections in contrast with random removal, i.e. structured models, are discussed. It is shown that a wide range of neural network models, such as a bidirectional associative memory network or a layered network, are special cases of an auto-associative neural network with structured connections, so that the systematic discussion is possible from the point of view proposed here.
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