SPDM: Geometry-Modulated State Space Modeling with Manifold Constraints for Time Series Forecasting
arXiv:2606.09917v1 Announce Type: new Abstract: 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 linear
This paper presents a novel approach to time series forecasting by incorporating geometric principles into state-space modeling, reflecting an ongoing trend in AI research to enhance model performance through more sophisticated mathematical foundations.
Improved multivariate time series forecasting can lead to more accurate predictions in various complex systems, impacting fields from finance and climate modeling to supply chain logistics and potentially even autonomous systems.
The explicit incorporation of manifold constraints and Riemannian geometry into state-space models provides a new theoretical and practical avenue for analyzing complex, evolving correlations in time series data.
- · AI researchers
- · Data scientists
- · Financial modeling firms
- · Logistics and supply chain companies
- · Developers of less geometrically sophisticated time series models
- · Sectors reliant on simpler forecasting methods
Enhances the accuracy and robustness of predictive models for systems with interdependent variables.
Could lead to the development of more advanced AI agents capable of higher-fidelity real-world temporal reasoning.
May contribute to the foundational algorithms for future autonomous systems and complex adaptive control, reducing unforeseen errors in dynamic environments.
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Read at arXiv cs.LG