A new explanation of geometric nature of the reservoir computing phenomenon
is presented. Reservoir computing is understood in the literature as the
possibility of approximating input/output systems with randomly chosen
recurrent neural systems and a trained linear readout layer. Light is shed on
this phenomenon by constructing what is called strongly universal reservoir
systems as random projections of a family of state-space systems that generate
Volterra series expansions. This procedure yields a state-affine reservoir
system with randomly generated coefficients in a dimension that is
logarithmically reduced with respect to the original system. This reservoir
system is able to approximate any element in the fading memory filters class
just by training a different linear readout for each different filter. Explicit
expressions for the probability distributions needed in the generation of the
projected reservoir system are stated and bounds for the committed
approximation error are provided.

本文提出了新的几何解释，解释了库沃塞蓝计算的现象，将其构建为强普适性水库系统；随机投影所有状态空间系统的家族，以产生 Volterra 级数扩展，生成随机系数的状态仿射水库系统能够通过为每个不同的滤波器训练一个不同的线性输出来近似任何消退存储过滤器类中的元素。