论文标题
非线性复发网络的内存和预测能力
Memory and forecasting capacities of nonlinear recurrent networks
论文作者
论文摘要
最初针对具有独立输入的回声状态和线性网络引入的内存能力概念，被推广到具有固定但依赖输入的非线性复发网络。输入中依赖性的存在使网络预测能力的引入很自然，从而衡量使用网络状态预测时间序列值的可能性。记忆和预测能力的通用界限是根据非线性复发网络的神经元数量和自动增强函数或输入的光谱密度提出的。这些界限将文献中众所周知的估计值概括为依赖的输入设置。最后，对于具有独立输入的线性循环网络的特定情况，证明内存能力由关联的可控性矩阵的等级给出，这一事实长期以来一直假定为不存在社区证明的事实。
The notion of memory capacity, originally introduced for echo state and linear networks with independent inputs, is generalized to nonlinear recurrent networks with stationary but dependent inputs. The presence of dependence in the inputs makes natural the introduction of the network forecasting capacity, that measures the possibility of forecasting time series values using network states. Generic bounds for memory and forecasting capacities are formulated in terms of the number of neurons of the nonlinear recurrent network and the autocovariance function or the spectral density of the input. These bounds generalize well-known estimates in the literature to a dependent inputs setup. Finally, for the particular case of linear recurrent networks with independent inputs it is proved that the memory capacity is given by the rank of the associated controllability matrix, a fact that has been for a long time assumed to be true without proof by the community.
