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.

最初针对具有独立输入的回波状态和线性网络引入的存储容量概念已普遍推广到具有固定但相关输入的非线性递归网络。输入中存在依赖关系自然会引入网络预测功能，该功能可使用网络状态来度量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递归网络的神经元数量和自协方差函数或输入的频谱密度来表示的。这些界限将文献中众所周知的估计值推广到相关的输入设置。最后，