# In-n-Out: Calibrating Graph Neural Networks for Link Prediction

arXiv: https://arxiv.org/abs/2403.04605 · HTML: https://mlsanity.com/paper/2403.04605/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 33 references that are in the map.
- First posted on arXiv 7 Mar 2024.

## Builds on (most cited first, 16 of 16)

- [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)
- [How Powerful are Graph Neural Networks?](https://mlsanity.com/paper/1810.00826/) (2018)
- [Neural Message Passing for Quantum Chemistry](https://mlsanity.com/paper/1704.01212/) (2017)
- [Fast Graph Representation Learning with PyTorch Geometric](https://mlsanity.com/paper/1903.02428/) (2019)
- [Variational Graph Auto-Encoders](https://mlsanity.com/paper/1611.07308/) (2016)
- [Link Prediction Based on Graph Neural Networks](https://mlsanity.com/paper/1802.09691/) (2018)
- [Multi-scale Attributed Node Embedding](https://mlsanity.com/paper/1909.13021/) (2019)
- [FedGNN: Federated Graph Neural Network for Privacy-Preserving Recommendation](https://mlsanity.com/paper/2102.04925/) (2021)
- [Equivariant and Stable Positional Encoding for More Powerful Graph Neural Networks](https://mlsanity.com/paper/2203.00199/) (2022)
- [Be Confident! Towards Trustworthy Graph Neural Networks via Confidence Calibration](https://mlsanity.com/paper/2109.14285/) (2021)
- [Uncertainty Quantification over Graph with Conformalized Graph Neural Networks](https://mlsanity.com/paper/2305.14535/) (2023)
- [Message passing all the way up](https://mlsanity.com/paper/2202.11097/) (2022)
- [What Makes Graph Neural Networks Miscalibrated?](https://mlsanity.com/paper/2210.06391/) (2022)
- [Are Graph Neural Networks Miscalibrated?](https://mlsanity.com/paper/1905.02296/) (2019)
- [Heterogeneous Graph Neural Networks for Large-Scale Bid Keyword Matching](https://mlsanity.com/paper/2111.00926/) (2021)

## Built on by (most cited first, 3 of 3)

- [Uncertainty Quantification on Graph Learning: A Survey](https://mlsanity.com/paper/2404.14642/) (2024)
- [Lightweight Inference-Time Personalization for Frozen Knowledge Graph Embeddings](https://mlsanity.com/paper/2512.22398/) (2025)
- [The Confidence Trap: Calibration Attacks for Graph Neural Networks](https://mlsanity.com/paper/2606.08467/) (2026)

## Abstract (arXiv)

Deep neural networks are notoriously miscalibrated, i.e., their outputs do not reflect the true probability of the event we aim to predict. While networks for tabular or image data are usually overconfident, recent works have shown that graph neural networks (GNNs) show the opposite behavior for node-level classification. But what happens when we are predicting links? We show that, in this case, GNNs often exhibit a mixed behavior. More specifically, they may be overconfident in negative predictions while being underconfident in positive ones. Based on this observation, we propose IN-N-OUT, the first-ever method to calibrate GNNs for link prediction. IN-N-OUT is based on two simple intuitions: i) attributing true/false labels to an edge while respecting a GNNs prediction should cause but small fluctuations in that edge's embedding; and, conversely, ii) if we label that same edge contradicting our GNN, embeddings should change more substantially. An extensive experimental campaign shows that IN-N-OUT significantly improves the calibration of GNNs in link prediction, consistently outperforming the baselines available -- which are not designed for this specific task.