A Stationarity-and-Coupling Criterion for Training-Free Time-Lagged Spectral Embeddings of Multivariate Time Series
arXiv:2606.13823v1 Announce Type: new Abstract: We study training-free fixed-length descriptors for multivariate time series and ask not merely whether such a descriptor performs well, but when it can be expected to work at all. Our object of study is $D(\tau)$, built from a time-lagged correlation matrix truncated at the Marchenko-Pastur edge so that only signal-bearing eigenvalues survive and classified by cosine similarity to class centroids with zero learned parameters. The central contribution is not the descriptor but a falsifiable applicability criterion for it. Working from a stationar
The paper tackles a fundamental challenge in time series analysis for complex systems, driven by the increasing need for robust, training-free methods in AI and control applications.
Developing reliable training-free descriptors for multivariate time series is critical for real-time analytics, autonomous systems, and scientific discovery where training data is limited or costs are prohibitive.
This research provides a falsifiable criterion for the applicability of a specific time-lagged spectral embedding method, enabling more predictable deployment and understanding of its limitations rather than solely focusing on performance.
- · AI researchers
- · Autonomous systems developers
- · Financial modeling platforms
- · Industrial IoT analytics
- · High-cost, high-compute training models
More efficient and reliable analysis of complex, real-time data streams across various domains.
Accelerated development of AI agents and automated decision-making systems that rely on understanding dynamic environments without continuous retraining.
Reduced barriers to entry for AI deployment in computationally constrained or data-scarce environments, potentially democratizing advanced analytics.
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Read at arXiv cs.LG