State Space Model with Continuous Limit of HiPPO Matrix: Eigenvalue Analysis and Explicit Solution Formula

As a lightweight model for sequence processing, an LSSL that uses the HiPPO matrix has been proposed. In this paper, as the continuous limit of the HiPPO Matrix, we propose Continuized-HiPPO Operator. Furthermore, as examples of advantages obtained by using this operator, we show that one can analyze the asymptotic behavior of eigenvalues of a matrix related to the HiPPO matrix, and that the LSSL induced by the continuous limit Continuized-HiPPO Operator admits an explicit solution.