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

Atsushi Takabatake; Takaharu Yaguchi

ICML 2026poster0 citations

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

Abstract

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.

BibTeX

@inproceedings{
takabatake2026state,
title={State Space Model with Continuous Limit of Hi{PPO} Matrix: Eigenvalue Analysis and Explicit Solution Formula},
author={Atsushi Takabatake and Takaharu Yaguchi},
booktitle={Forty-third International Conference on Machine Learning},
year={2026},
url={https://openreview.net/forum?id=eeRgTFtEjv}
}