A Convergence rate for translation-invariant kernels Theorem 2

A list of different activation functions and their associated kernels is provided in Table 3. ( t 1) Analytic formulas in more general cases may not exist and they would need to be replaced by successive integrals. The successive integrals can still be explicitly defined. Eq. (28) describes the asymptotic kernel limit for any This independence hypothesis is required in Eq. (18) and Eq. However, this assumption is unrealistic for practical Reservoir Computing. This is valid for several activation functions, the ones presented in Table 3.