Seifter Jared, Reggia James A
University of Pennsylvania.
Artif Life. 2015 Winter;21(1):55-71. doi: 10.1162/ARTL_a_00152. Epub 2014 Dec 16.
The idea that there is an edge of chaos, a region in the space of dynamical systems having special meaning for complex living entities, has a long history in artificial life. The significance of this region was first emphasized in cellular automata models when a single simple measure, λCA, identified it as a transitional region between order and chaos. Here we introduce a parameter λNN that is inspired by λCA but is defined for recurrent neural networks. We show through a series of systematic computational experiments that λNN generally orders the dynamical behaviors of randomly connected/weighted recurrent neural networks in the same way that λCA does for cellular automata. By extending this ordering to larger values of λNN than has typically been done with λCA and cellular automata, we find that a second edge-of-chaos region exists on the opposite side of the chaotic region. These basic results are found to hold under different assumptions about network connectivity, but vary substantially in their details. The results show that the basic concept underlying the lambda parameter can usefully be extended to other types of complex dynamical systems than just cellular automata.
存在混沌边缘的观点，即在动力系统空间中对复杂生物实体具有特殊意义的一个区域，在人工生命领域有着悠久的历史。当一种单一的简单度量λCA将其识别为有序与混沌之间的过渡区域时，该区域的重要性在细胞自动机模型中首次得到强调。在此，我们引入一个受λCA启发但为递归神经网络定义的参数λNN。我们通过一系列系统的计算实验表明，λNN通常以与λCA对细胞自动机相同的方式对随机连接/加权递归神经网络的动力学行为进行排序。通过将这种排序扩展到比通常对λCA和细胞自动机所做的更大的λNN值，我们发现在混沌区域的另一侧存在第二个混沌边缘区域。这些基本结果在关于网络连通性的不同假设下成立，但在细节上有很大差异。结果表明，λ参数背后的基本概念可以有效地扩展到除细胞自动机之外的其他类型的复杂动力系统。
