# Self-Supervised Node Representation Learning via Node-to-Neighbourhood Alignment

arXiv: https://arxiv.org/abs/2302.04626 · HTML: https://mlsanity.com/paper/2302.04626/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 51 of its 64 references that are in the map.
- First posted on arXiv 9 Feb 2023.

## Builds on (most cited first, 30 of 51)

- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [A Simple Framework for Contrastive Learning of Visual Representations](https://mlsanity.com/paper/2002.05709/) (2020)
- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Representation Learning with Contrastive Predictive Coding](https://mlsanity.com/paper/1807.03748/) (2018)
- [Momentum Contrast for Unsupervised Visual Representation Learning](https://mlsanity.com/paper/1911.05722/) (2019)
- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [Inductive Representation Learning on Large Graphs](https://mlsanity.com/paper/1706.02216/) (2017)
- [Bootstrap your own latent: A new approach to self-supervised Learning](https://mlsanity.com/paper/2006.07733/) (2020)
- [How Powerful are Graph Neural Networks?](https://mlsanity.com/paper/1810.00826/) (2018)
- [A Comprehensive Survey on Graph Neural Networks](https://mlsanity.com/paper/1901.00596/) (2019)
- [Exploring Simple Siamese Representation Learning](https://mlsanity.com/paper/2011.10566/) (2020)
- [Convolutional Neural Networks on Graphs with Fast Localized Spectral Filtering](https://mlsanity.com/paper/1606.09375/) (2016)
- [node2vec: Scalable Feature Learning for Networks](https://mlsanity.com/paper/1607.00653/) (2016)
- [Barlow Twins: Self-Supervised Learning via Redundancy Reduction](https://mlsanity.com/paper/2103.03230/) (2021)
- [DeepWalk: Online Learning of Social Representations](https://mlsanity.com/paper/1403.6652/) (2014)
- [Simplifying Graph Convolutional Networks](https://mlsanity.com/paper/1902.07153/) (2019)
- [Contrastive Multiview Coding](https://mlsanity.com/paper/1906.05849/) (2019)
- [Learning deep representations by mutual information estimation and maximization](https://mlsanity.com/paper/1808.06670/) (2018)
- [Deep Graph Infomax](https://mlsanity.com/paper/1809.10341/) (2018)
- [Deeper Insights into Graph Convolutional Networks for Semi-Supervised Learning](https://mlsanity.com/paper/1801.07606/) (2018)
- [VICReg: Variance-Invariance-Covariance Regularization for Self-Supervised Learning](https://mlsanity.com/paper/2105.04906/) (2021)
- [Pitfalls of Graph Neural Network Evaluation](https://mlsanity.com/paper/1811.05868/) (2018)
- [Relational Knowledge Distillation](https://mlsanity.com/paper/1904.05068/) (2019)
- [Representation Learning on Graphs with Jumping Knowledge Networks](https://mlsanity.com/paper/1806.03536/) (2018)
- [MINE: Mutual Information Neural Estimation](https://mlsanity.com/paper/1801.04062/) (2018)
- [Contrastive Multi-View Representation Learning on Graphs](https://mlsanity.com/paper/2006.05582/) (2020)
- [FastGCN: Fast Learning with Graph Convolutional Networks via Importance Sampling](https://mlsanity.com/paper/1801.10247/) (2018)
- [Multi-scale Attributed Node Embedding](https://mlsanity.com/paper/1909.13021/) (2019)
- [Deep Graph Contrastive Representation Learning](https://mlsanity.com/paper/2006.04131/) (2020)

## Built on by (most cited first, 2 of 2)

- [Structural Entropy Guided Probabilistic Coding](https://mlsanity.com/paper/2412.08841/) (2024)
- [LEED: Local Embedding Evolution Distance for over-smoothing estimation and virtual node selection in GNN](https://mlsanity.com/paper/2608.09596/) (2026)

## Abstract (arXiv)

Self-supervised node representation learning aims to learn node representations from unlabelled graphs that rival the supervised counterparts. The key towards learning informative node representations lies in how to effectively gain contextual information from the graph structure. In this work, we present simple-yet-effective self-supervised node representation learning via aligning the hidden representations of nodes and their neighbourhood. Our first idea achieves such node-to-neighbourhood alignment by directly maximizing the mutual information between their representations, which, we prove theoretically, plays the role of graph smoothing. Our framework is optimized via a surrogate contrastive loss and a Topology-Aware Positive Sampling (TAPS) strategy is proposed to sample positives by considering the structural dependencies between nodes, which enables offline positive selection. Considering the excessive memory overheads of contrastive learning, we further propose a negative-free solution, where the main contribution is a Graph Signal Decorrelation (GSD) constraint to avoid representation collapse and over-smoothing. The GSD constraint unifies some of the existing constraints and can be used to derive new implementations to combat representation collapse. By applying our methods on top of simple MLP-based node representation encoders, we learn node representations that achieve promising node classification performance on a set of graph-structured datasets from small- to large-scale.