Supplementary Material: Stationary Activations for Uncertainty Calibration in Deep Learning

This supplementary document is organized as follows. This covariance function can be equally presented as a spectral density function, as discussed in the main paper (Wiener-Khinchin theorem). From the Fourier-duality, the spectral density function of Eq. (11) can be recovered by the Fourier Starting from Eq. (13), we can now do the spectral factorization by manipulating the G ( i ω), (17) which is the form we use in the main paper. Following Eq. (17), we can collect the transfer function of the corresponding stable part (see discussion From the empirical results in Figure 1 it is clear that the Matérn activations of form Eq. (20) approach Thus we provide the following high-level proof. The effect of the decay envelope is clearly visible when moving along the diagonal.