# WATS: Calibrating Graph Neural Networks with Wavelet-Aware Temperature Scaling

arXiv: https://arxiv.org/abs/2506.23782 · HTML: https://mlsanity.com/paper/2506.23782/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 26 of its 53 references that are in the map.
- First posted on arXiv 30 Jun 2025.

## Builds on (most cited first, 26 of 26)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Inductive Representation Learning on Large Graphs](https://mlsanity.com/paper/1706.02216/) (2017)
- [On Calibration of Modern Neural Networks](https://mlsanity.com/paper/1706.04599/) (2017)
- [Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning](https://mlsanity.com/paper/1506.02142/) (2015)
- [Pitfalls of Graph Neural Network Evaluation](https://mlsanity.com/paper/1811.05868/) (2018)
- [Link Prediction Based on Graph Neural Networks](https://mlsanity.com/paper/1802.09691/) (2018)
- [Graph Neural Networks for Social Recommendation](https://mlsanity.com/paper/1902.07243/) (2019)
- [Conformalized Quantile Regression](https://mlsanity.com/paper/1905.03222/) (2019)
- [Conformal Prediction Under Covariate Shift](https://mlsanity.com/paper/1904.06019/) (2019)
- [Deep Gaussian Embedding of Graphs: Unsupervised Inductive Learning via Ranking](https://mlsanity.com/paper/1707.03815/) (2017)
- [Mix-n-Match: Ensemble and Compositional Methods for Uncertainty Calibration in Deep Learning](https://mlsanity.com/paper/2003.07329/) (2020)
- [Motif-based Graph Self-Supervised Learning for Molecular Property Prediction](https://mlsanity.com/paper/2110.00987/) (2021)
- [GraphSMOTE: Imbalanced Node Classification on Graphs with Graph Neural Networks](https://mlsanity.com/paper/2103.08826/) (2021)
- [Graph Wavelet Neural Network](https://mlsanity.com/paper/1904.07785/) (2019)
- [Learning Structural Node Embeddings Via Diffusion Wavelets](https://mlsanity.com/paper/1710.10321/) (2017)
- [Be Confident! Towards Trustworthy Graph Neural Networks via Confidence Calibration](https://mlsanity.com/paper/2109.14285/) (2021)
- [How Framelets Enhance Graph Neural Networks](https://mlsanity.com/paper/2102.06986/) (2021)
- [What Makes Graph Neural Networks Miscalibrated?](https://mlsanity.com/paper/2210.06391/) (2022)
- [SimCalib: Graph Neural Network Calibration based on Similarity between Nodes](https://mlsanity.com/paper/2312.11858/) (2023)
- [On Calibration of Graph Neural Networks for Node Classification](https://mlsanity.com/paper/2206.01570/) (2022)
- [Feature Clipping for Uncertainty Calibration](https://mlsanity.com/paper/2410.19796/) (2024)
- [Generalized Equivariance and Preferential Labeling for GNN Node Classification](https://mlsanity.com/paper/2102.11485/) (2021)
- [Reducing Overconfidence Predictions for Autonomous Driving Perception](https://mlsanity.com/paper/2202.07825/) (2022)
- [Geometric Multimodal Deep Learning with Multi-Scaled Graph Wavelet Convolutional Network](https://mlsanity.com/paper/2111.13361/) (2021)
- [GETS: Ensemble Temperature Scaling for Calibration in Graph Neural Networks](https://mlsanity.com/paper/2410.09570/) (2024)

## Built on by (most cited first, 2 of 2)

- [When does distribution shift break graph neural networks calibration?](https://mlsanity.com/paper/2607.10804/) (2026)
- [HoTS: Homophily-Aware Temperature Scaling for Graph Neural Network Calibration](https://mlsanity.com/paper/2609.32426/) (2026)

## Abstract (arXiv)

Graph Neural Networks (GNNs) have demonstrated strong predictive performance on relational data; however, their confidence estimates often misalign with actual predictive correctness, posing significant limitations for deployment in safety-critical settings. While existing graph-aware calibration methods seek to mitigate this limitation, they primarily depend on coarse one-hop statistics, such as neighbor-predicted confidence, or latent node embeddings, thereby neglecting the fine-grained structural heterogeneity inherent in graph topology. In this work, we propose Wavelet-Aware Temperature Scaling (WATS), a post-hoc calibration framework that assigns node-specific temperatures based on tunable heat-kernel graph wavelet features. Specifically, WATS harnesses the scalability and topology sensitivity of graph wavelets to refine confidence estimates, all without necessitating model retraining or access to neighboring logits or predictions. Extensive evaluations across seven benchmark datasets with varying graph structures and two GNN backbones demonstrate that WATS achieves the lowest Expected Calibration Error (ECE) among all compared methods, outperforming both classical and graph-specific baselines by up to 42.3% in ECE and reducing calibration variance by 17.24% on average compared with graph-specific methods. Moreover, WATS remains computationally efficient, scaling well across graphs of diverse sizes and densities. Code will be released based on publication.