加权模式作为改进Hopfield模型的工具
Weighted Patterns as a Tool for Improving the Hopfield Model
摘要：
我们推广的标准Hopfield模型的情况下，当一个权重被分配给每个输入模式。权重可以解释为网络输入处模式出现的频率。在统计物理方法的框架下，我们得到了鞍点方程，使我们能够检查网络的记忆。在不等权重的情况下，我们的模型不会由于内存溢出而导致内存的灾难性破坏（这是标准Hopfield模型的典型特征）。真实记忆仅由权重超过由权重分布确定的临界值的模式组成。我们得到的算法，使我们能够找到这个临界值的任意分布的权重，并详细分析了一些特定的权重分布。它示出的记忆减少的情况下相比，标准的Hopfield模型。然而，在我们的模型中，网络可以在线学习，而不会对记忆造成灾难性的破坏。
英文摘要：
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.
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