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).
WaLRUS: Wavelets for Long-range Representation Using SSMs
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abstract
State-Space Models (SSMs) have proven to be powerful tools for modeling long-range dependencies in sequential data. While the recent method known as HiPPO has demonstrated strong performance, and formed the basis for machine learning models S4 and Mamba, it remains limited by its reliance on closed-form solutions for a few specific, well-behaved bases. The SaFARi framework generalized this approach, enabling the construction of SSMs from arbitrary frames, including non-orthogonal and redundant ones, thus allowing an infinite diversity of possible "species" within the SSM family. In this paper, we introduce WaLRUS (Wavelets for Long-range Representation Using SSMs), a new implementation of SaFARi built from Daubechies wavelets.
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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).