# HoTS: Homophily-Aware Temperature Scaling for Graph Neural Network Calibration

arXiv: https://arxiv.org/abs/2609.32426 · HTML: https://mlsanity.com/paper/2609.32426/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 25 of its 39 references that are in the map.
- First posted on arXiv 26 Sep 2026.

## Builds on (most cited first, 25 of 25)

- [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)
- [Open Graph Benchmark: Datasets for Machine Learning on Graphs](https://mlsanity.com/paper/2005.00687/) (2020)
- [Pitfalls of Graph Neural Network Evaluation](https://mlsanity.com/paper/1811.05868/) (2018)
- [Revisiting Semi-Supervised Learning with Graph Embeddings](https://mlsanity.com/paper/1603.08861/) (2016)
- [Geom-GCN: Geometric Graph Convolutional Networks](https://mlsanity.com/paper/2002.05287/) (2020)
- [Beyond temperature scaling: Obtaining well-calibrated multiclass probabilities with Dirichlet calibration](https://mlsanity.com/paper/1910.12656/) (2019)
- [A critical look at the evaluation of GNNs under heterophily: Are we really making progress?](https://mlsanity.com/paper/2302.11640/) (2023)
- [Mix-n-Match: Ensemble and Compositional Methods for Uncertainty Calibration in Deep Learning](https://mlsanity.com/paper/2003.07329/) (2020)
- [Is Homophily a Necessity for Graph Neural Networks?](https://mlsanity.com/paper/2106.06134/) (2021)
- [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)
- [What Makes Graph Neural Networks Miscalibrated?](https://mlsanity.com/paper/2210.06391/) (2022)
- [Adaptive Temperature Scaling for Robust Calibration of Deep Neural Networks](https://mlsanity.com/paper/2208.00461/) (2022)
- [Contextual Stochastic Block Model: Sharp Thresholds and Contiguity](https://mlsanity.com/paper/2011.09841/) (2020)
- [Are Graph Neural Networks Miscalibrated?](https://mlsanity.com/paper/1905.02296/) (2019)
- [On Performance Discrepancies Across Local Homophily Levels in Graph Neural Networks](https://mlsanity.com/paper/2306.05557/) (2023)
- [Optimal Inference in Contextual Stochastic Block Models](https://mlsanity.com/paper/2306.07948/) (2023)
- [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)
- [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)
- [Post-Calibration Reliability Reranking of Relevance Decisions via Label-wise Monotone Projection](https://mlsanity.com/paper/2608.10406/) (2026)

## Abstract (arXiv)

For graph node classification, calibrated class probabilities are needed when confidence scores, usually the maximum predicted class probability, are used to rank predictions, defer uncertain nodes to human review, or control risk. Existing post-hoc calibrators either apply one global temperature or use graph-aware modules without a principled structural form. We study how local graph structure should enter node-level calibration. Our first results show that a logit-only temperature rule is insufficient when nodes with identical logits but different local homophily require different optimal temperatures. We then analyze a population-concentration contextual stochastic block model with Gaussian features and a one-layer linear GCN. Under equidistant class means, the Bayes posterior over class-template scores is a temperature-scaled softmax whose inverse-temperature is governed by a homophily-dependent signal strength. In the positive-signal homophilic regime, the resulting temperature decreases approximately inversely with normalized local homophily. This law motivates Homophily-aware Temperature Scaling (HoTS), a simple post-hoc calibrator that assigns each node a positive scalar temperature from entropy-based logit concentration and estimated local homophily. HoTS has three temperature parameters, preserves the predicted class, and learns the strength of the structural correction from calibration data. Across 18 node-classification benchmarks, two GNN backbones, and eight calibration baselines, HoTS achieves the best mean Expected Calibration Error (ECE) of 4.79%, the best average rank, and the most reliable confidence ranking in selective classification. Code is available at https://github.com/inu0104/HoTS.