论文标题
关于稀释神经网络中极限周期的数量
On the number of limit cycles in diluted neural networks
论文作者
论文摘要
我们考虑在随机图上定义的（通常是不对称的）自旋玻璃（通常是不对称的）自旋玻璃的神经网络中时间模式的存储特性，即有限长度的循环。受到观察到稀疏系统的动力学比密集连接的动力学更多的景点的启发，我们考虑了稀疏拓扑中贪婪动态的吸引者，被认为是存储记忆的代理。我们使用数值模拟列举它们，并使用信念传播将分析扩展到大型系统大小。我们发现，这种循环数量的对数是平均连接性的非单调函数，我们与描述海马的记忆能力的生物神经网络讨论了相似性。
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.
