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

NeurIPS 2026 · Graph learning › GNN architectures · approach: GNN generalization theory · 0 citations (OpenAlex)

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Proposes HoTS, a post-hoc node-wise temperature scaling method whose temperature depends on entropy-based logit concentration and estimated local homophily, motivated by a CSBM Bayes analysis, and reports lowest mean ECE across 18 node-classification benchmarks.

Problem

Post-hoc calibration of GNN node-level confidence: a single global temperature ignores that nodes with identical logits but different local homophily have different reliability, and existing graph-aware calibrators lack a principled structural form.

Approach

Assigns each node a positive temperature T_i = T_base + beta*sqrt(2K log K (1-e_i)) / (|normalized estimated homophily|+eps)^alpha, with three learned parameters, motivated by a CSBM Bayes result that the optimal temperature decreases approximately inversely with normalized local homophily in the positive-signal homophilic regime.

Key results

• HoTS achieves the lowest mean ECE of 4.79% across 18 datasets and both backbones, versus 5.37% for HTS and 5.43% for CaGCN, and the best average rank of 3.33.
• On controlled CSBM sweeps, mean fitted temperature decreases with homophily with Pearson r = -0.846; the fitted exponent falls from 1.009 at zero noise to 0.182 at the largest noise level.
• In selective classification, HoTS gives the highest retained accuracy among prediction-preserving baselines at 6 of 7 coverage levels (e.g., 73.81% at 70% coverage vs 73.73% for TS).

Surprising findings

• On PubMed, CoraFull, Roman-Empire and tolokers, other calibrators (e.g., GATS, GETS, CaGCN) obtain lower ECE than HoTS.
• Fixing the homophily exponent to the oracle value alpha=1 increases mean ECE by 1.10 percentage points on real data, so the learned exponent matters.

Limitations

• The exact Bayes derivation holds only under an idealized CSBM with Gaussian features, equidistant means, uniform priors and a one-layer linear GCN; the implemented rule uses an absolute-value heuristic outside the positive-signal regime.
• The homophily-dependent law is a motivated surrogate rather than a derived pointwise optimum for learned logits.
• RBS and SimCalib were omitted from baselines because their public reference could not be located.

Experimental setup

Datasets: Cora CiteSeer PubMed Computers Photo CS Physics CoraFull Texas Cornell Wisconsin Chameleon

Benchmarks: Cora CiteSeer PubMed Computers Photo CS Physics CoraFull Texas Cornell Wisconsin Chameleon

Metrics: ECE NLL degree-stratified ECE average rank retained accuracy under selective classification

Baselines: Temperature Scaling Vector Scaling Ensemble Temperature Scaling HTS CaGCN GATS GETS WATS

Builds on: temperature scaling contextual stochastic block model GCN GAT

Closest papers by meaning

• GETS: Ensemble Temperature Scaling for Calibration in Graph Neural Networks (ICLR 2025 · similarity 0.91)
• Towards Precise Prediction Uncertainty in GNNs: Refining GNNs with Topology-grouping Strategy (AAAI 2025 · similarity 0.90)
• Understanding and Mitigating Under-Confidence in GNNs from the Final Layer (NeurIPS 2026 · similarity 0.89)
• SimCalib: Graph Neural Network Calibration Based on Similarity between Nodes (AAAI 2024 · similarity 0.88)
• A Unified Uncertainty Representation for Graph Neural Networks via Doubly-Spectral Stochastic Expansion (NeurIPS 2026 · similarity 0.88)
• What Is Missing For Graph Homophily? Disentangling Graph Homophily For Graph Neural Networks (NeurIPS 2024 · similarity 0.87)