用小波框架构建时序模型，提升瞬态信号的定位能力
WaveSSM: Multiscale State-Space Models for Non-stationary Signal Attention
- 基于小波框架设计多尺度状态空间模型，实现时间局部化
- 在PTB-XL和语音命令数据集上优于S4等基线模型
- 适合处理具有瞬态特征的生理信号与音频数据
状态空间模型（SSMs）已成为长序列建模的强大基础，其中HiPPO框架表明连续时间投影算子可导出稳定且内存高效的动态系统，以编码输入信号的历史。然而，现有基于投影的SSMs通常依赖具有全局时间支持的多项式基，其归纳偏置与具有局部或瞬态结构的信号不匹配。本文提出WaveSSM，一类基于小波框架构建的SSM。关键观察是：小波框架在时间维度上具有局部支持，对需要精确定位的任务尤为有益。实验证明，在相同条件下，WaveSSM在包含瞬态动态的真实世界数据集上优于正交基对手（如S4），包括在PTB-XL数据集上的生理信号和在Speech Commands数据集上的原始音频。
原文摘要 · Abstract (English)
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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