Abstract
The performance of Hebbian-type associative memories (HAMs) in the presence of faulty interconnections is examined, and equations for predicting network reliability are developed. Several HAM operating modes, i.e. zero or nonzero autoconnections (ZA or NZA), bipolar or unipolar network inputs, asynchronous or synchronous operation, have been investigated. Networks with NZA and bipolar inputs have the best performance in both capacity and reliability. An equation relating the probability of direct one-step convergence, <e1 xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">P</e1> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">dc</sub> , to the percentage of failed connections is derived. For a connection failure rate of up to 50%, this equation can estimate <e1 xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">P</e1> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">dc </sub> accurately. The reliability becomes poorer when the network size increases; hence, reducing the percentage of failed connections becomes very important in physical implementations of large networks. Also, as the number of stored vectors increases, the network reliability decreases. Asynchronous-mode and synchronous-mode operation have the same <e1 xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">P</e1> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">dc</sub> and reliability when there are no error bits in the probe vector, but networks operating in the asynchronous mode have higher P <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">dc</sub> and better reliability when the number of input errors increases. Reliability measures for second-order HAMs are also investigated
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