WaveSSM: Multiscale State-Space Models for Non-stationary Signal Attention

TL;DR

WaveSSM introduces wavelet-based state-space models that excel at modeling non-stationary signals with localized and transient features, outperforming traditional polynomial-based SSMs like S4 on real-world datasets.

Contribution

This work presents WaveSSM, a novel class of state-space models using wavelet frames for better localization in non-stationary signal modeling, improving over polynomial-based approaches.

Findings

WaveSSM outperforms S4 on physiological and audio datasets.

Wavelet frames provide better localization for transient signals.

Empirical results demonstrate improved accuracy in real-world tasks.

Abstract

State-space models (SSMs) have emerged as a powerful foundation for long-range sequence modeling, with the HiPPO framework showing that continuous-time projection operators can be used to derive stable, memory-efficient dynamical systems that encode the past history of the input signal. However, existing projection-based SSMs often rely on polynomial bases with global temporal support, whose inductive biases are poorly matched to signals exhibiting localized or transient structure. In this work, we introduce \emph{WaveSSM}, a collection of SSMs constructed over wavelet frames. Our key observation is that wavelet frames yield a localized support on the temporal dimension, useful for tasks requiring precise localization. Empirically, we show that on equal conditions, \textit{WaveSSM} outperforms orthogonal counterparts as S4 on real-world datasets with transient dynamics, including physiological signals on the PTB-XL dataset and raw audio on Speech Commands.