论文标题
空间相关性对Hopfield神经网络和密集的关联记忆的影响
Effect of spatial correlations on Hopfield Neural Network and Dense Associative Memories
论文作者
论文摘要
Hopfield模型是可以获得分析结果的少数神经网络之一。但是，其中大多数是在随机不相关模式的假设下得出的，而在现实生活中，要存储的数据显示出非平凡的相关性。在本文中，我们研究了hopfield网络在无效温度下的检索能力如何受我们馈送的数据中的空间相关性的影响。特别是，我们用作模式，以在反温度$β$下存储线性ISING模型的配置。利用信号到噪声技术，我们在Hopfield网络的负载和Ising温度中获得了一个相图，可以观察到模糊相位和检索区域。值得注意的是，随着内部模式内部模式的空间相关性的增加，Hopfield网络的临界负载减小，这一结果也通过数值模拟证实。然后将分析推广到具有任意奇数相互作用的密集缔合记忆，为此我们获得类似的结果。
Hopfield model is one of the few neural networks for which analytical results can be obtained. However, most of them are derived under the assumption of random uncorrelated patterns, while in real life applications data to be stored show non-trivial correlations. In the present paper we study how the retrieval capability of the Hopfield network at null temperature is affected by spatial correlations in the data we feed to it. In particular, we use as patterns to be stored the configurations of a linear Ising model at inverse temperature $β$. Exploiting the signal to noise technique we obtain a phase diagram in the load of the Hopfield network and the Ising temperature where a fuzzy phase and a retrieval region can be observed. Remarkably, as the spatial correlation inside patterns is increased, the critical load of the Hopfield network diminishes, a result also confirmed by numerical simulations. The analysis is then generalized to Dense Associative Memories with arbitrary odd-body interactions, for which we obtain analogous results.
