# Graph Neural Network-Inspired Kernels for Gaussian Processes in Semi-Supervised Learning

arXiv: https://arxiv.org/abs/2302.05828 · HTML: https://mlsanity.com/paper/2302.05828/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 30 of its 41 references that are in the map.
- First posted on arXiv 12 Feb 2023.

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

- [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)
- [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)
- [A Comprehensive Survey on Graph Neural Networks](https://mlsanity.com/paper/1901.00596/) (2019)
- [Neural Tangent Kernel: Convergence and Generalization in Neural Networks](https://mlsanity.com/paper/1806.07572/) (2018)
- [Fast Graph Representation Learning with PyTorch Geometric](https://mlsanity.com/paper/1903.02428/) (2019)
- [Open Graph Benchmark: Datasets for Machine Learning on Graphs](https://mlsanity.com/paper/2005.00687/) (2020)
- [Graph Neural Networks: A Review of Methods and Applications](https://mlsanity.com/paper/1812.08434/) (2018)
- [Model soups: averaging weights of multiple fine-tuned models improves accuracy without increasing inference time](https://mlsanity.com/paper/2203.05482/) (2022)
- [Deeper Insights into Graph Convolutional Networks for Semi-Supervised Learning](https://mlsanity.com/paper/1801.07606/) (2018)
- [Predict then Propagate: Graph Neural Networks meet Personalized PageRank](https://mlsanity.com/paper/1810.05997/) (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)
- [Wide Neural Networks of Any Depth Evolve as Linear Models Under Gradient Descent](https://mlsanity.com/paper/1902.06720/) (2019)
- [Deep Neural Networks as Gaussian Processes](https://mlsanity.com/paper/1711.00165/) (2017)
- [Multi-scale Attributed Node Embedding](https://mlsanity.com/paper/1909.13021/) (2019)
- [Understanding over-squashing and bottlenecks on graphs via curvature](https://mlsanity.com/paper/2111.14522/) (2021)
- [Gaussian Process Behaviour in Wide Deep Neural Networks](https://mlsanity.com/paper/1804.11271/) (2018)
- [Kernel Interpolation for Scalable Structured Gaussian Processes (KISS-GP)](https://mlsanity.com/paper/1503.01057/) (2015)
- [Bayesian Deep Convolutional Networks with Many Channels are Gaussian Processes](https://mlsanity.com/paper/1810.05148/) (2018)
- [Tensor Programs I: Wide Feedforward or Recurrent Neural Networks of Any Architecture are Gaussian Processes](https://mlsanity.com/paper/1910.12478/) (2019)
- [Neural Tangents: Fast and Easy Infinite Neural Networks in Python](https://mlsanity.com/paper/1912.02803/) (2019)
- [Deep Convolutional Networks as shallow Gaussian Processes](https://mlsanity.com/paper/1808.05587/) (2018)
- [Bayesian Semi-supervised Learning with Graph Gaussian Processes](https://mlsanity.com/paper/1809.04379/) (2018)
- [A multi-resolution approximation for massive spatial datasets](https://mlsanity.com/paper/1507.04789/) (2015)
- [Infinitely Wide Graph Convolutional Networks: Semi-supervised Learning via Gaussian Processes](https://mlsanity.com/paper/2002.12168/) (2020)
- [Hierarchically Compositional Kernels for Scalable Nonparametric Learning](https://mlsanity.com/paper/1608.00860/) (2016)
- [Linear-Cost Covariance Functions for Gaussian Random Fields](https://mlsanity.com/paper/1711.05895/) (2017)

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

- [Gaussian Process Limit Reveals Structural Benefits of Graph Transformers](https://mlsanity.com/paper/2603.17569/) (2026)
- [Infinite Width Graph Neural Networks for Node Regression/ Classification](https://mlsanity.com/paper/2310.08176/) (2023)
- [Flexible Infinite-Width Graph Convolutional Neural Networks](https://mlsanity.com/paper/2402.06525/) (2024)
- [Neighborhood Sampling Does Not Learn the Same Graph Neural Network](https://mlsanity.com/paper/2509.22868/) (2025)
- [Different Statistical Perspectives for Understanding Generalisation in Graph Neural Networks](https://mlsanity.com/paper/2605.25452/) (2026)
- [Lifting Finite-Sample Gaussian Approximation of Wide Neural Networks to Functional Convergence](https://mlsanity.com/paper/2610.18166/) (2026)

## Abstract (arXiv)

Gaussian processes (GPs) are an attractive class of machine learning models because of their simplicity and flexibility as building blocks of more complex Bayesian models. Meanwhile, graph neural networks (GNNs) emerged recently as a promising class of models for graph-structured data in semi-supervised learning and beyond. Their competitive performance is often attributed to a proper capturing of the graph inductive bias. In this work, we introduce this inductive bias into GPs to improve their predictive performance for graph-structured data. We show that a prominent example of GNNs, the graph convolutional network, is equivalent to some GP when its layers are infinitely wide; and we analyze the kernel universality and the limiting behavior in depth. We further present a programmable procedure to compose covariance kernels inspired by this equivalence and derive example kernels corresponding to several interesting members of the GNN family. We also propose a computationally efficient approximation of the covariance matrix for scalable posterior inference with large-scale data. We demonstrate that these graph-based kernels lead to competitive classification and regression performance, as well as advantages in computation time, compared with the respective GNNs.