WaveSSM: Multiscale State-Space Models for Non-stationary Signal Attention
Ruben Solozabal, Velibor Bojkovic, Hilal AlQuabeh, Klea Ziu, Kentaro Inui, Martin Takac
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.
BibTeX
@inproceedings{
solozabal2026wavessm,
title={Wave{SSM}: Multiscale State-Space Models for Non-stationary Signal Attention},
author={Ruben Solozabal and Velibor Bojkovic and Hilal AlQuabeh and Klea Ziu and Kentaro Inui and Martin Tak{\'a}{\v{c}}},
booktitle={Forty-third International Conference on Machine Learning},
year={2026},
url={https://openreview.net/forum?id=8f5JVzcFvA}
}