arXiv：cs.LG（机器学习，全量分类）· Alexandre Bloch, Benjamin Walker, Jo\"el Mouterde, Sam Morley, Samuel N. Cohen, Terry Lyons·· 15 小时前AI 评分38
用指数加权签名扩展 SSM：EWS 在长时序分类上取得最高平均准确率
Extending SSMs with the Exponentially Weighted Signature
AI 导读
研究者提出指数加权签名（EWS），一种对路径迭代积分、并以可学习生成器的矩阵指数对每个增量按经过时钟时间加权的连续时间模型，可证明其满足线性受控微分方程、保持签名的群结构与通用性，并支持并行扫描。
正文
Abstract:We introduce the exponentially weighted signature (EWS), a continuous-time model that computes iterated integrals of a path, where each increment is weighted by the matrix exponential of a learnable generator over elapsed clock time. We prove that it solves a linear controlled differential equation, keeps the group-like structure and the universality of the signature, and satisfies a modified Chen identity, enabling a parallel scan. At depth one the EWS is a state-space model (SSM), and we map linear time-invariant SSMs, Mamba channels and Mamba-$2$ heads to it in closed form. The EWS extends SSMs through an arbitrary matrix generator, a clock that generalises the step size to causal functionals of the input, and higher truncation depths that are non-linear in the path within a single layer. Empirically, the EWS achieves the highest average accuracy and rank on six long time-series classification datasets, where depth generally helps. Learned clocks prove necessary for state tracking on formal language tasks, and at depth one, the EWS matches or exceeds competing SSMs on regression and forecasting with far fewer parameters.
| Comments: | 47 pages, 1 figure |
| Subjects: | Machine Learning (stat.ML); Machine Learning (cs.LG) |
| Cite as: | arXiv:2603.19198 [stat.ML] |
| (or arXiv:2603.19198v3 [stat.ML] for this version) | |
| https://doi.org/10.48550/arXiv.2603.19198 arXiv-issued DOI via DataCite |
Submission history
From: Alexandre Bloch [view email]
[v1]
Thu, 19 Mar 2026 17:51:20 UTC (579 KB)
[v2]
Mon, 28 Sep 2026 16:54:50 UTC (75 KB)
[v3]
Wed, 30 Sep 2026 20:25:54 UTC (75 KB)
来源：arXiv：cs.LG（机器学习，全量分类） · arxiv.org