WaveSSM: Multiscale State-Space Models for Non-stationary Signal Attention
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.
The following analysis is generated by AI and may contain errors. It is separate from the authors’ abstract and is not peer review.
Research summary
The main contribution of this paper is the introduction of WaveSSM, a novel wavelet-based state-space model that significantly enhances the modeling of non-stationary signals by leveraging localized temporal representations. This work addresses critical limitations in existing models, providing a robust framework for future research and applications in sequence modeling.
Methodology
The methodology introduced in WaveSSM is innovative, leveraging wavelet frames to construct state-space models that address the limitations of traditional polynomial bases in capturing localized and transient structures in sequential data. The authors provide a rigorous theoretical foundation for their approach, detailing the construction of the wavelet-based SSMs and the stability considerations necessary for their implementation. The use of the SaFARi framework to generalize the HiPPO formulation is a significant contribution, as it allows for a broader application of SSMs beyond orthogonal bases. The paper also discusses the numerical stability of the proposed models, which is critical for practical applications.
Results & evaluation
The experimental evaluation is thorough, with the authors testing WaveSSM on a variety of real-world datasets, including physiological signals and audio classification tasks. The results demonstrate that WaveSSM outperforms existing SSMs like S4 under controlled conditions, particularly in scenarios involving transient dynamics. The paper provides clear comparisons and metrics, showcasing the advantages of the proposed method over traditional approaches. However, the paper could benefit from additional experiments on more diverse datasets to further validate the robustness of the model.
Reproducibility
The paper includes sufficient details regarding the methodology and experiments, which would allow for reproducibility. However, the absence of a public code repository or demo URL limits the ease with which other researchers can replicate the findings. Clear hyperparameter settings and experimental protocols are provided, but access to the implementation would enhance reproducibility.
Limitations
One identified limitation is the model's performance in very long-context scenarios, where WaveSSM exhibits challenges similar to those faced by traditional SSMs. Additionally, while the paper claims improvements in transient signal modeling, it does not extensively address potential trade-offs in computational efficiency compared to other state-of-the-art models. The paper could also explore the implications of the model's complexity on real-time applications.
Broader impact
The potential applications of WaveSSM are significant, particularly in fields requiring precise modeling of non-stationary signals, such as biomedical signal processing and audio analysis. The ability to effectively capture transient dynamics could lead to advancements in areas like healthcare diagnostics and speech recognition, ultimately benefiting society by improving the accuracy and efficiency of these technologies. The main contribution of this paper is the introduction of WaveSSM, a novel wavelet-based state-space model that significantly enhances the modeling of non-stationary signals by leveraging localized temporal representations. This work addresses critical limitations in existing models, providing a robust framework for future research and applications in sequence modeling.
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