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On the Number of Limit Cycles in Diluted Neural Networks
Journal of Statistical Physics ( IF 1.6 ) Pub Date : 2020-11-05 , DOI: 10.1007/s10955-020-02664-3
Sungmin Hwang , Enrico Lanza , Giorgio Parisi , Jacopo Rocchi , Giancarlo Ruocco , Francesco Zamponi

We consider the storage properties of temporal patterns, i.e. cycles of finite lengths, in neural networks represented by (generally asymmetric) spin glasses defined on random graphs. Inspired by the observation that dynamics on sparse systems have more basins of attractions than the dynamics of densely connected ones, we consider the attractors of a greedy dynamics in sparse topologies, considered as proxy for the stored memories. We enumerate them using numerical simulation and extend the analysis to large systems sizes using belief propagation. We find that the logarithm of the number of such cycles is a non monotonic function of the mean connectivity and we discuss the similarities with biological neural networks describing the memory capacity of the hippocampus.

中文翻译:

关于稀释神经网络中的极限环数

我们考虑时间模式的存储特性,即有限长度的循环,在由随机图上定义的(通常是不对称的)自旋眼镜表示的神经网络中。受到稀疏系统动力学比密集连接系统动力学具有更多吸引力盆地的观察的启发,我们考虑稀疏拓扑中贪婪动力学的吸引子,被视为存储记忆的代理。我们使用数值模拟枚举它们,并使用置信传播将分析扩展到大型系统。我们发现这种循环次数的对数是平均连通性的非单调函数,我们讨论了与描述海马记忆容量的生物神经网络的相似性。
更新日期:2020-11-05
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