SaFARi: State-Space Models for Frame-Agnostic Representation

State-Space Models (SSMs) have re-emerged as a powerful tool for online function approx-imation, and as the backbone of machine learning models for long-range dependent data. However, to date, only a few polynomial bases have been explored for this purpose, and the state-of-the-art implementations were built upon a few limited options. In this paper, we present a generalized method for building an SSM with any frame or basis. This framework encompasses the approach known as HiPPO, but also permits an infinite diversity of other possible “species” of SSM, paving the way for improved performance of SSM-based machine learning models. We dub this approach SaFARi: SSMs for Frame-Agnostic Representation.