Title: AdaKernel: Learning Adaptive Kernel Parameters for Spatiotemporal Graph Neural Networks

Abstract:

Graph Neural Networks (GNNs) rely heavily on modeling spatial dependencies for effective spatiotemporal data analysis. However, conventional approaches are limited by their dependence on distance-based kernels with fixed, predefined parameters, which constrains the model's capacity. While generic adaptive mechanisms, such as Graph Attention Networks, provide greater flexibility, they frequently struggle to capture the underlying geometric structure, often yielding inferior results compared to distance-based models in data-sparse environments. In response to these challenges, this study revisits the issue of kernel parameterization, providing a theoretical proof that misspecified kernel parameters inevitably lead to approximation errors within GNNs.

To address this limitation, we introduce AdaKernel, a straightforward yet potent method that enables the neural network to learn adaptive kernel parameters. Distinct from techniques that attempt to reconstruct graph structures entirely from scratch, AdaKernel employs a structure-preserving strategy. It focuses on optimizing the scale of physical interactions rather than discarding them. Comprehensive experiments conducted across Kriging, Imputation, and Forecasting tasks show that AdaKernel consistently enhances the performance of various GNN architectures. It also surpasses model-agnostic adaptive baselines, confirming that precisely learned kernel parameters are more effective than both fixed priors and fully latent graph structures.

Source: arXiv Generated at: 2026-06-02 00:00:00 UTC