W4S4 initializes S4 state space models with WaLRUS wavelet frames and reports better delay reconstruction and classification accuracy than HiPPO-based S4, with frozen (A,B).
SaFARi: State-Space Models for Frame-Agnostic Representation
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abstract
State-Space Models (SSMs) have re-emerged as a powerful tool for online function approximation, 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 the best of a few limited options. In this paper, we present a generalized method for building an SSM with any frame or basis, rather than being restricted to polynomials. This framework encompasses the approach known as HiPPO, but also permits an infinite diversity of other possible "species" within the SSM architecture. We dub this approach SaFARi: SSMs for Frame-Agnostic Representation.
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W4S4: WaLRUS Meets S4 for Long-Range Sequence Modeling
W4S4 initializes S4 state space models with WaLRUS wavelet frames and reports better delay reconstruction and classification accuracy than HiPPO-based S4, with frozen (A,B).