Analytic interdomain memory for efficient online HiPPO-SVGP

Online Gaussian processes are attractive for streaming prediction but exact inference is cubic and sparse online updates can forget early observations. Online HiPPO-SVGP addresses this issue using HiPPO-based interdomain inducing variables, but its interdomain kernel construction relies on temporal ODE recursion of Fourier-Legendre states. We study an analytic replacement for this construction in the one-dimensional HiPPO-LegS setting with stationary kernels. The method expresses the required sine/cosine-Legendre overlap integrals in closed form using spherical Bessel functions, allowing kernel quantities to be evaluated directly at the target horizon. Experiments on Solar Irradiance and COVID-19 mortality streams show comparable predictive performance to ODE-based OHSVGP, while runtime scaling confirms reduced dependence on ODE discretization steps.