Real-time computation at the edge of chaos in recurrent neural networks
Real-time computation at the edge of chaos in recurrent neural networks
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DOI：
10.1162/089976604323057443
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发表时间：
2004-07-01
影响因子：
2.9
通讯作者：
Natschl채ger, T
中科院分区：
文献类型：
--
作者：
Bertschinger, N;Natschl채ger, T
根据连通性的不同，简单计算单元的递归网络可以表现出非常不同类型的动力学，从完全有序到混沌。我们分析了由随时间变化的输入信号驱动的随机连接的阈值门网络所表现出的动态（有序或混沌）的类型如何取决于描述连接矩阵分布的参数。特别是，我们计算的临界边界参数空间中的有序到混沌动力学的过渡发生。采用最近开发的实时计算分析框架，我们表明，只有在临界边界附近，这样的网络可以执行复杂的时间序列计算。因此，这一结果有力地支持了这样的假设，即能够进行复杂计算任务的动力系统应该在混沌边缘附近运行，即从有序到混沌动力学的过渡。
Depending on the connectivity, recurrent networks of simple computational units can show very different types of dynamics, ranging from totally ordered to chaotic. We analyze how the type of dynamics (ordered or chaotic) exhibited by randomly connected networks of threshold gates driven by a time-varying input signal depends on the parameters describing the distribution of the connectivity matrix. In particular, we calculate the critical boundary in parameter space where the transition from ordered to chaotic dynamics takes place. Employing a recently developed framework for analyzing real-time computations, we show that only near the critical boundary can such networks perform complex computations on time series. Hence, this result strongly supports conjectures that dynamical systems that are capable of doing complex computational tasks should operate near the edge of chaos, that is, the transition from ordered to chaotic dynamics.