Reservoir Computing (RC) has become popular in recent years due to its fast
and efficient computational capabilities. Standard RC has been shown to be
equivalent in the asymptotic limit to Recurrent Kernels, which helps in
analyzing its expressive power. However, many well-established RC paradigms,
such as Leaky RC, Sparse RC, and Deep RC, are yet to be analyzed in such a way.
This study aims to fill this gap by providing an empirical analysis of the
equivalence of specific RC architectures with their corresponding Recurrent
Kernel formulation. We conduct a convergence study by varying the activation
function implemented in each architecture. Our study also sheds light on the
role of sparse connections in RC architectures and propose an optimal sparsity
level that depends on the reservoir size. Furthermore, our systematic analysis
shows that in Deep RC models, convergence is better achieved with successive
reservoirs of decreasing sizes.

通过对特定的 RC 体系结构和其对应的递归核公式的等效性进行实证分析，本研究填补了基于泄漏型 RC、稀疏 RC 和深层 RC 等众多已建立的 RC 范式尚未进行该等效性分析的空白。我们通过变化各个体系结构中实施的激活函数进行了收敛性研究。我们的研究还揭示了稀疏连接在 RC 体系结构中的作用，并提出了与水库尺寸有关的最佳稀疏程度。此外，我们的系统分析表明，在深层 RC 模型中，通过逐渐减小水库大小的连续水库可以更好地实现收敛。