# Understanding and Mitigating Under-Confidence in GNNs from the Final Layer

arXiv: https://arxiv.org/abs/2505.11335 · HTML: https://mlsanity.com/paper/2505.11335/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 39 of its 61 references that are in the map.
- First posted on arXiv 16 May 2025.

## Builds on (most cited first, 30 of 39)

- [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)
- [Representation Learning on Graphs with Jumping Knowledge Networks](https://mlsanity.com/paper/1806.03536/) (2018)
- [Simple and Deep Graph Convolutional Networks](https://mlsanity.com/paper/2007.02133/) (2020)
- [Geom-GCN: Geometric Graph Convolutional Networks](https://mlsanity.com/paper/2002.05287/) (2020)
- [Graph Neural Networks for Social Recommendation](https://mlsanity.com/paper/1902.07243/) (2019)
- [Graph Structure Learning for Robust Graph Neural Networks](https://mlsanity.com/paper/2005.10203/) (2020)
- [Beyond temperature scaling: Obtaining well-calibrated multiclass probabilities with Dirichlet calibration](https://mlsanity.com/paper/1910.12656/) (2019)
- [Beyond Low-frequency Information in Graph Convolutional Networks](https://mlsanity.com/paper/2101.00797/) (2021)
- [A critical look at the evaluation of GNNs under heterophily: Are we really making progress?](https://mlsanity.com/paper/2302.11640/) (2023)
- [Deep Gaussian Embedding of Graphs: Unsupervised Inductive Learning via Ranking](https://mlsanity.com/paper/1707.03815/) (2017)
- [Graph Self-Supervised Learning: A Survey](https://mlsanity.com/paper/2103.00111/) (2021)
- [A Note on Over-Smoothing for Graph Neural Networks](https://mlsanity.com/paper/2006.13318/) (2020)
- [A Survey on Oversmoothing in Graph Neural Networks](https://mlsanity.com/paper/2303.10993/) (2023)
- [Uncertainty Aware Semi-Supervised Learning on Graph Data](https://mlsanity.com/paper/2010.12783/) (2020)
- [Be Confident! Towards Trustworthy Graph Neural Networks via Confidence Calibration](https://mlsanity.com/paper/2109.14285/) (2021)
- [Graph Posterior Network: Bayesian Predictive Uncertainty for Node Classification](https://mlsanity.com/paper/2110.14012/) (2021)
- [Uncertainty Quantification over Graph with Conformalized Graph Neural Networks](https://mlsanity.com/paper/2305.14535/) (2023)
- [Energy-based Out-of-Distribution Detection for Graph Neural Networks](https://mlsanity.com/paper/2302.02914/) (2023)
- [Intra Order-preserving Functions for Calibration of Multi-Class Neural Networks](https://mlsanity.com/paper/2003.06820/) (2020)
- [Cluster-guided Contrastive Graph Clustering Network](https://mlsanity.com/paper/2301.01098/) (2023)
- [Graph Trend Filtering Networks for Recommendations](https://mlsanity.com/paper/2108.05552/) (2021)
- [What Makes Graph Neural Networks Miscalibrated?](https://mlsanity.com/paper/2210.06391/) (2022)
- [FP-GNN: a versatile deep learning architecture for enhanced molecular property prediction](https://mlsanity.com/paper/2205.03834/) (2022)
- [A Survey on Graph Neural Networks for Knowledge Graph Completion](https://mlsanity.com/paper/2007.12374/) (2020)
- [CONVERT:Contrastive Graph Clustering with Reliable Augmentation](https://mlsanity.com/paper/2308.08963/) (2023)
- [On the Benefits of Attribute-Driven Graph Domain Adaptation](https://mlsanity.com/paper/2502.06808/) (2025)
- [Structure-Preserving Graph Representation Learning](https://mlsanity.com/paper/2209.00793/) (2022)

## Built on by (most cited first, 6 of 6)

- [OFFSET: Segmentation-based Focus Shift Revision for Composed Image Retrieval](https://mlsanity.com/paper/2507.05631/) (2025)
- [HUD: Hierarchical Uncertainty-Aware Disambiguation Network for Composed Video Retrieval](https://mlsanity.com/paper/2512.02792/) (2025)
- [ConeSep: Cone-based Robust Noise-Unlearning Compositional Network for Composed Image Retrieval](https://mlsanity.com/paper/2604.20358/) (2026)
- [TEMA: Anchor the Image, Follow the Text for Multi-Modification Composed Image Retrieval](https://mlsanity.com/paper/2604.21806/) (2026)
- [IMAGINE: Adaptive Schema-Imagery Enhanced Composition for Composed Video Retrieval](https://mlsanity.com/paper/2606.08144/) (2026)
- [Global-Graph Guided and Local-Graph Weighted Contrastive Learning for Unified Clustering on Incomplete and Noise Multi-View Data](https://mlsanity.com/paper/2512.21516/) (2025)

## Abstract (arXiv)

Graph Neural Networks (GNNs) have demonstrated remarkable effectiveness on graph-based tasks. However, their predictive confidence is often miscalibrated, typically exhibiting under-confidence, which harms the reliability of their decisions. Existing calibration methods for GNNs normally introduce additional calibration components, which fail to capture the intrinsic relationship between the model and the prediction confidence, resulting in limited theoretical guarantees and increased computational overhead. To address this issue, we propose a simple yet efficient graph calibration method. We establish a unified theoretical framework revealing that model confidence is jointly governed by class-centroid-level and node-level calibration at the final layer. Based on this insight, we theoretically show that reducing the weight decay of the final-layer parameters alleviates GNN under-confidence by acting on the class-centroid level, while node-level calibration acts as a finer-grained complement to class-centroid-level calibration, which encourages each test node to be closer to its predicted class prototype in the final-layer representations. Extensive experiments validate the superiority of our method. The code is released at https://github.com/huangJC0429/SCAR.