Spatiotemporal Kronecker Covariance Neural Networks

Researchers introduced the Kronecker coVariance Neural Network (KVNN), a temporal graph neural network that represents the spatiotemporal covariance matrix as a sum of Kronecker products to decouple spatial and temporal dependencies, according to the arXiv paper 2609.25326v1. KVNNs perform filtering on spatial and temporal components, admit a rigorous spectral analysis, and are provably stable to finite-sample estimation errors, addressing the limitations of spatiotemporal Principal Component Analysis (ST-PCA). Across five real-world datasets, KVNNs achieved strong forecasting performance while often requiring significantly fewer trainable parameters than competitive methods and remaining consistent under estimation noise.

arXiv:2609.25326v1 Announce Type: new Abstract: Multivariate time series contain complex patterns that span across both space and time. While covariance-based statistical tools like spatiotemporal Principal Component Analysis ST-PCA help identify these patterns, they are limited to linear operations and prone to estimation errors with limited data. Recent covariance-based spatiotemporal neural networks offer more stable, non-linear alternatives, but they ignore correlations across different time steps. To solve this, we introduce the Kronecker coVariance Neural Network KVNN , a temporal graph neural network that represents the spatiotemporal covariance matrix via a sum of Kronecker products where spatial and temporal dependencies are decoupled. By implementing filtering operations on spatial and temporal components, KVNNs achieve expressive processing capabilities, admit a rigorous spectral analysis, and are provably stable to finite-sample estimation errors, ultimately addressing all of ST-PCA's limitations. We show on five real-world datasets that KVNNs achieve strong forecasting performance, often requiring significantly fewer trainable parameters than competitive methods, and are consistent under estimation noise.