  We generalize the standard Hopfield model to the case when a weight is
assigned to each input pattern. The weight can be interpreted as the frequency
of the pattern occurrence at the input of the network. In the framework of the
statistical physics approach we obtain the saddle-point equation allowing us to
examine the memory of the network. In the case of unequal weights our model
does not lead to the catastrophic destruction of the memory due to its
overfilling (that is typical for the standard Hopfield model). The real memory
consists only of the patterns with weights exceeding a critical value that is
determined by the weights distribution. We obtain the algorithm allowing us to
find this critical value for an arbitrary distribution of the weights, and
analyze in detail some particular weights distributions. It is shown that the
memory decreases as compared to the case of the standard Hopfield model.
However, in our model the network can learn online without the catastrophic
destruction of the memory.
