标题： 加权模式作为改进霍普菲尔德模型的工具 显示英文标题

标题： Weighted Patterns as a Tool for Improving the Hopfield Model

摘要： 我们将标准的Hopfield模型推广到每个输入模式都有一个权重的情况。 该权重可以解释为该模式在网络输入中出现的频率。 在统计物理方法的框架下，我们得到了允许我们研究网络记忆的鞍点方程。 在权重不相等的情况下，由于过度填充导致的记忆灾难性破坏不会发生（这是标准Hopfield模型的典型特征）。 实际记忆仅包括权重超过由权重分布确定的临界值的模式。 我们得到了一种算法，可以找到任意权重分布下的这个临界值，并详细分析了一些特定的权重分布。 结果表明，与标准Hopfield模型的情况相比，记忆有所下降。 然而，在我们的模型中，网络可以在不导致记忆灾难性破坏的情况下在线学习。 显示英文摘要

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.