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

arXiv: https://arxiv.org/abs/2606.01283 · HTML: https://mlsanity.com/paper/2606.01283/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 28 of its 49 references that are in the map.
- First posted on arXiv 31 May 2026.

## Builds on (most cited first, 28 of 28)

- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Neural Message Passing for Quantum Chemistry](https://mlsanity.com/paper/1704.01212/) (2017)
- [Relational inductive biases, deep learning, and graph networks](https://mlsanity.com/paper/1806.01261/) (2018)
- [Spatio-Temporal Graph Convolutional Networks: A Deep Learning Framework for Traffic Forecasting](https://mlsanity.com/paper/1709.04875/) (2017)
- [Attention is not Explanation](https://mlsanity.com/paper/1902.10186/) (2019)
- [Graph WaveNet for Deep Spatial-Temporal Graph Modeling](https://mlsanity.com/paper/1906.00121/) (2019)
- [Adaptive Graph Convolutional Recurrent Network for Traffic Forecasting](https://mlsanity.com/paper/2007.02842/) (2020)
- [GMAN: A Graph Multi-Attention Network for Traffic Prediction](https://mlsanity.com/paper/1911.08415/) (2019)
- [Graph Neural Network-Based Anomaly Detection in Multivariate Time Series](https://mlsanity.com/paper/2106.06947/) (2021)
- [BRITS: Bidirectional Recurrent Imputation for Time Series](https://mlsanity.com/paper/1805.10572/) (2018)
- [Discrete Graph Structure Learning for Forecasting Multiple Time Series](https://mlsanity.com/paper/2101.06861/) (2021)
- [Dynamic Graph Convolutional Recurrent Network for Traffic Prediction: Benchmark and Solution](https://mlsanity.com/paper/2104.14917/) (2021)
- [Spatial-Temporal Identity: A Simple yet Effective Baseline for Multivariate Time Series Forecasting](https://mlsanity.com/paper/2208.05233/) (2022)
- [Spatio-Temporal Graph Neural Networks for Predictive Learning in Urban Computing: A Survey](https://mlsanity.com/paper/2303.14483/) (2023)
- [Gaussian Process Kernels for Pattern Discovery and Extrapolation](https://mlsanity.com/paper/1302.4245/) (2013)
- [Exploring Progress in Multivariate Time Series Forecasting: Comprehensive Benchmarking and Heterogeneity Analysis](https://mlsanity.com/paper/2310.06119/) (2023)
- [Inductive Graph Neural Networks for Spatiotemporal Kriging](https://mlsanity.com/paper/2006.07527/) (2020)
- [Learning to Reconstruct Missing Data from Spatiotemporal Graphs with Sparse Observations](https://mlsanity.com/paper/2205.13479/) (2022)
- [Network of Tensor Time Series](https://mlsanity.com/paper/2102.07736/) (2021)
- [Networked Time Series Imputation via Position-aware Graph Enhanced Variational Autoencoders](https://mlsanity.com/paper/2305.18612/) (2023)
- [Kriging Convolutional Networks](https://mlsanity.com/paper/2306.09463/) (2023)
- [Spatial Aggregation and Temporal Convolution Networks for Real-time Kriging](https://mlsanity.com/paper/2109.12144/) (2021)
- [INCREASE: Inductive Graph Representation Learning for Spatio-Temporal Kriging](https://mlsanity.com/paper/2302.02738/) (2023)
- [Multivariate Time Series Forecasting with Latent Graph Inference](https://mlsanity.com/paper/2203.03423/) (2022)
- [KITS: Inductive Spatio-Temporal Kriging with Increment Training Strategy](https://mlsanity.com/paper/2311.02565/) (2023)
- [TraverseNet: Unifying Space and Time in Message Passing for Traffic Forecasting](https://mlsanity.com/paper/2109.02474/) (2021)
- [Decoupling Long- and Short-Term Patterns in Spatiotemporal Inference](https://mlsanity.com/paper/2109.09506/) (2021)
- [NodeTrans: A Graph Transfer Learning Approach for Traffic Prediction](https://mlsanity.com/paper/2207.01301/) (2022)

## Abstract (arXiv)

Modeling spatial dependencies is central to spatiotemporal data analysis using Graph Neural Networks (GNNs). Traditional methods rely on distance-based kernels with predefined parameters, which restricts model capacity. Although generic adaptive mechanisms (e.g., Graph Attention Networks) offer flexibility, they often fail to capture the underlying geometric structure, performing worse than distance-based models in data-sparse scenarios. Addressing this, we revisit the kernel parameterization problem and theoretically prove that misspecified kernel parameters introduce unavoidable approximation errors in GNNs. To overcome this, we propose AdaKernel, a simple yet effective approach that learns adaptive kernel parameters within the neural network. Unlike methods that learn graph structures from scratch, AdaKernel adopts a structure-preserving strategy that optimizes the scale of physical interactions rather than discarding them. Extensive experiments on Kriging, Imputation, and Forecasting demonstrate that AdaKernel consistently improves various GNN architectures and outperforms model-agnostic adaptive baselines, validating that accurately learned kernel parameters are superior to both fixed priors and fully latent graph structures.