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

• URL: http://arxiv.org/abs/2602.22266v1
• Date: Wed, 25 Feb 2026 06:27:22 GMT
• Title: WaveSSM: Multiscale State-Space Models for Non-stationary Signal Attention
• Authors: Ruben Solozabal, Velibor Bojkovic, Hilal Alquabeh, Klea Ziu, Kentaro Inui, Martin Takac,
• Abstract summary: State-space models (SSMs) have emerged as a powerful foundation for long-range sequence modeling.<n>We introduce emphWaveSSM, a collection of SSMs constructed over wavelet frames.<n>Our key observation is that wavelet frames yield a localized support on the temporal dimension, useful for tasks requiring precise localization.
• Score: 22.983737182781244
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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