# SimCalib: Graph Neural Network Calibration based on Similarity between Nodes

arXiv: https://arxiv.org/abs/2312.11858 · HTML: https://mlsanity.com/paper/2312.11858/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- Builds on 28 of its 42 references that are in the map.
- First posted on arXiv 19 Dec 2023.

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

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [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)
- [Simple and Scalable Predictive Uncertainty Estimation using Deep Ensembles](https://mlsanity.com/paper/1612.01474/) (2016)
- [Prototypical Networks for Few-shot Learning](https://mlsanity.com/paper/1703.05175/) (2017)
- [A Simple Unified Framework for Detecting Out-of-Distribution Samples and Adversarial Attacks](https://mlsanity.com/paper/1807.03888/) (2018)
- [Pitfalls of Graph Neural Network Evaluation](https://mlsanity.com/paper/1811.05868/) (2018)
- [Evidential Deep Learning to Quantify Classification Uncertainty](https://mlsanity.com/paper/1806.01768/) (2018)
- [Graph Neural Networks for Social Recommendation](https://mlsanity.com/paper/1902.07243/) (2019)
- [Empirical Evaluation of Rectified Activations in Convolutional Network](https://mlsanity.com/paper/1505.00853/) (2015)
- [Unlabeled Data Improves Adversarial Robustness](https://mlsanity.com/paper/1905.13736/) (2019)
- [Beyond temperature scaling: Obtaining well-calibrated multiclass probabilities with Dirichlet calibration](https://mlsanity.com/paper/1910.12656/) (2019)
- [Adversarially Robust Generalization Requires More Data](https://mlsanity.com/paper/1804.11285/) (2018)
- [Probabilistic Backpropagation for Scalable Learning of Bayesian Neural Networks](https://mlsanity.com/paper/1502.05336/) (2015)
- [Mix-n-Match: Ensemble and Compositional Methods for Uncertainty Calibration in Deep Learning](https://mlsanity.com/paper/2003.07329/) (2020)
- [Flipout: Efficient Pseudo-Independent Weight Perturbations on Mini-Batches](https://mlsanity.com/paper/1803.04386/) (2018)
- [Calibration of Neural Networks using Splines](https://mlsanity.com/paper/2006.12800/) (2020)
- [Be Confident! Towards Trustworthy Graph Neural Networks via Confidence Calibration](https://mlsanity.com/paper/2109.14285/) (2021)
- [Intra Order-preserving Functions for Calibration of Multi-Class Neural Networks](https://mlsanity.com/paper/2003.06820/) (2020)
- [When and How Mixup Improves Calibration](https://mlsanity.com/paper/2102.06289/) (2021)
- [What Makes Graph Neural Networks Miscalibrated?](https://mlsanity.com/paper/2210.06391/) (2022)
- [Towards Trustworthy Predictions from Deep Neural Networks with Fast Adversarial Calibration](https://mlsanity.com/paper/2012.10923/) (2020)
- [Are Graph Neural Networks Miscalibrated?](https://mlsanity.com/paper/1905.02296/) (2019)
- [Spectral clustering in the Gaussian mixture block model](https://mlsanity.com/paper/2305.00979/) (2023)
- [A Graph Is More Than Its Nodes: Towards Structured Uncertainty-Aware Learning on Graphs](https://mlsanity.com/paper/2210.15575/) (2022)
- [Graph Neural Network Framework for Security Assessment Informed by Topological Measures](https://mlsanity.com/paper/2301.12988/) (2023)

## Built on by (most cited first, 10 of 10)

- [Similarity-Navigated Conformal Prediction for Graph Neural Networks](https://mlsanity.com/paper/2405.14303/) (2024)
- [Understanding and Mitigating Under-Confidence in GNNs from the Final Layer](https://mlsanity.com/paper/2505.11335/) (2025)
- [GETS: Ensemble Temperature Scaling for Calibration in Graph Neural Networks](https://mlsanity.com/paper/2410.09570/) (2024)
- [WATS: Calibrating Graph Neural Networks with Wavelet-Aware Temperature Scaling](https://mlsanity.com/paper/2506.23782/) (2025)
- [Sheaf Graph Neural Networks via PAC-Bayes Spectral Optimization](https://mlsanity.com/paper/2508.00357/) (2025)
- [Towards Precise Prediction Uncertainty in GNNs: Refining GNNs with Topology-grouping Strategy](https://mlsanity.com/paper/2412.14223/) (2024)
- [Enhance GNNs with Reliable Confidence Estimation via Adversarial Calibration Learning](https://mlsanity.com/paper/2503.18235/) (2025)
- [Better Not to Propagate: Understanding Edge Uncertainty and Over-smoothing in Signed Graph Neural Networks](https://mlsanity.com/paper/2408.04895/) (2024)
- [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 exhibited impressive performance in modeling graph data as exemplified in various applications. Recently, the GNN calibration problem has attracted increasing attention, especially in cost-sensitive scenarios. Previous work has gained empirical insights on the issue, and devised effective approaches for it, but theoretical supports still fall short. In this work, we shed light on the relationship between GNN calibration and nodewise similarity via theoretical analysis. A novel calibration framework, named SimCalib, is accordingly proposed to consider similarity between nodes at global and local levels. At the global level, the Mahalanobis distance between the current node and class prototypes is integrated to implicitly consider similarity between the current node and all nodes in the same class. At the local level, the similarity of node representation movement dynamics, quantified by nodewise homophily and relative degree, is considered. Informed about the application of nodewise movement patterns in analyzing nodewise behavior on the over-smoothing problem, we empirically present a possible relationship between over-smoothing and GNN calibration problem. Experimentally, we discover a correlation between nodewise similarity and model calibration improvement, in alignment with our theoretical results. Additionally, we conduct extensive experiments investigating different design factors and demonstrate the effectiveness of our proposed SimCalib framework for GNN calibration by achieving state-of-the-art performance on 14 out of 16 benchmarks.