SPDM: Geometry-Modulated State Space Modeling with Manifold Constraints for Time Series Forecasting
Multivariate time series forecasting requires capturing the continuously evolving correlation structure among interacting variables. Existing state-space models process time series by scanning tokenized temporal or spatial sequences, discarding the evolutionary geometric structure. We address this limitation by introducing manifold constraints into state-space modeling: treating the cross-variable correlation structure as a continuous trajectory on the symmetric positive definite manifold, whose Riemannian geometric features, tangent space linearity, and Frechet mean centrality act as a principled geometric regularizer that guides and stabilizes the selective scanning dynamics of SSMs. We...
| Authors | Xingsheng Chen, Siu-Ming Yiu |
|---|---|
| Primary category | cs.LG |
| Published | 6 June 2026 |
| Last updated at source | 6 June 2026 |
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