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arXiv 2204.04520cond-mat.dis-nnphysics.bio-ph
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存储和检索不匹配记忆模式的广义Hopfield模型

A generalized Hopfield model to store and retrieve mismatched memory patterns

Luca Leuzzi, Alberto Patti, Federico Ricci-Tersenghi

备注：
18 pages, 27 figures
发表信息：
J. Stat. Mech. (2022) 073301
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摘要：

我们研究了一类Hopfield模型，其中记忆由高斯变量和二元变量的混合表示，神经元是伊辛自旋。我们研究了当两类变量在模式中的相对权重变化时，这类模型的性质。我们定量地确定如何检索阶段挤压为零的内存模式包含一个较大的部分不匹配的变量。由于记忆是纯粹的高斯检索丢失任何积极的存储容量。它示出，这是因为在高斯的情况下的自由能的球对称性。引入两种不同的记忆模式的自旋配置之间的重叠和每个贡献的模式从两种变量可以观察到的高斯部分的模式作为一个噪音，检索更加困难。通过Monte Carlo数值模拟研究了系统的吸引域、恢复精度和存储容量。我们发现，即使在网络容量缩小到零的限制，（少数）检索状态保持一个大的吸引力和大的不匹配的模式重叠的盆地。因此，网络可以用于检索，但容量非常小。

英文摘要：

We study a class of Hopfield models where the memories are represented by a mixture of Gaussian and binary variables and the neurons are Ising spins. We study the properties of this family of models as the relative weight of the two kinds of variables in the patterns varies. We quantitatively determine how the retrieval phase squeezes towards zero as the memory patterns contain a larger fraction of mismatched variables. As the memory is purely Gaussian retrieval is lost for any positive storage capacity. It is shown that this comes about because of the spherical symmetry of the free energy in the Gaussian case. Introducing two different memory pattern overlaps between spin configurations and each contribution to the pattern from the two kinds of variables one can observe that the Gaussian parts of the patterns act as a noise, making retrieval more difficult. The basins of attraction of the states, the accuracy of the retrieval and the storage capacity are studied by means of Monte Carlo numerical simulations. We uncover that even in the limit where the network capacity shrinks to zero, the (few) retrieval states maintain a large basin of attraction and large overlaps with the mismatched patterns. So the network can be used for retrieval, but with a very small capacity.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

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