发表机构
Imperial College London（伦敦帝国理工学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
LogSig-SSM通过多尺度对数签名压缩长序列为令牌，结合选择性SSM，实现高效且鲁棒的时间序列建模，在多个基准上性能优异且训练更快、内存更省。
AI 中文摘要
时间序列数据通常以高频且不规则的方式采样，并表现出长程依赖性，这使得长期建模变得困难。连续时间模型如神经受控微分方程（NCDE）和神经粗糙微分方程（NRDE）能够处理不规则采样，但它们在长序列上扩展性差。选择性状态空间模型（SSM）如Mamba在序列长度上呈线性扩展，但在单个块内跨隐藏维度的循环混合能力有限。我们提出了LogSig-SSM（状态空间模型的对数签名压缩），该方法首先使用多尺度窗口化对数签名将长多变量时间序列压缩为较短的令牌序列，然后使用选择性SSM骨干处理这些令牌。LogSig-SSM具有可扩展性，并对不规则采样具有鲁棒性，结合了捕获高阶跨通道交互的对数签名令牌与建模长程依赖性的选择性SSM。该模型还允许连续时间解释，即由基于对数签名的输入驱动的NCDE/NRDE式系统，其中选择性引起潜在动态的输入相关重新缩放。在四个基准测试中，即UEA上的长序列分类、PPG-DaLiA上的高频生理回归、多变量天气预报以及PhysioNet Sepsis上的不规则采样临床预测，LogSig-SSM优于或匹配强SSM和连续时间基线，同时在最长序列上训练速度比Mamba快高达30倍，GPU内存使用量减少高达37倍。
英文摘要
Time-series data are often sampled irregularly at high frequencies and exhibit long-range dependencies, which makes long-horizon modelling difficult. Continuous-time models such as neural controlled differential equations (NCDEs) and neural rough differential equations (NRDEs) can handle irregular sampling, but they scale poorly to long sequences. Selective state-space models (SSMs) such as Mamba scale linearly with sequence length, but they provide limited recurrent mixing across hidden dimensions within a single block. We propose LogSig-SSM (Log-Signature Compression for State-Space Models), which first compresses long multivariate time series into a shorter sequence of tokens using multi-scale windowed log-signatures, and then processes these tokens with a selective SSM backbone. LogSig-SSM is scalable and robust to irregular sampling, combining log-signature tokens that capture higher-order cross-channel interactions with a selective SSM that models long-range dependencies. The model also admits a continuous-time interpretation as an NCDE/NRDE-style system driven by a log-signature-based input, in which selectivity induces an input-dependent rescaling of the latent dynamics. Across four benchmarks, namely long-sequence classification on UEA, high-frequency physiological regression on PPG-DaLiA, multivariate weather forecasting, and irregularly sampled clinical prediction on PhysioNet Sepsis, LogSig-SSM outperforms or matches strong SSM and continuous-time baselines while training up to $30\times$ faster and using up to $37\times$ less GPU memory than Mamba on the longest sequences.
CommentsAccepted at NeurIPS 2026. 23 pages, 2 figures, 15 tables
