# Self-organization Preserved Graph Structure Learning with Principle of Relevant Information

arXiv: https://arxiv.org/abs/2301.00015 · HTML: https://mlsanity.com/paper/2301.00015/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 24 of its 47 references that are in the map.
- First posted on arXiv 30 Dec 2022.

## Builds on (most cited first, 24 of 24)

- [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)
- [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)
- [Pitfalls of Graph Neural Network Evaluation](https://mlsanity.com/paper/1811.05868/) (2018)
- [Geom-GCN: Geometric Graph Convolutional Networks](https://mlsanity.com/paper/2002.05287/) (2020)
- [DropEdge: Towards Deep Graph Convolutional Networks on Node Classification](https://mlsanity.com/paper/1907.10903/) (2019)
- [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)
- [Adversarial Attacks on Neural Networks for Graph Data](https://mlsanity.com/paper/1805.07984/) (2018)
- [Graph Structure Learning for Robust Graph Neural Networks](https://mlsanity.com/paper/2005.10203/) (2020)
- [Iterative Deep Graph Learning for Graph Neural Networks: Better and Robust Node Embeddings](https://mlsanity.com/paper/2006.13009/) (2020)
- [Adversarial Attack and Defense on Graph Data: A Survey](https://mlsanity.com/paper/1812.10528/) (2018)
- [Graph Information Bottleneck for Subgraph Recognition](https://mlsanity.com/paper/2010.05563/) (2020)
- [SLAPS: Self-Supervision Improves Structure Learning for Graph Neural Networks](https://mlsanity.com/paper/2102.05034/) (2021)
- [Graph Structure Learning with Variational Information Bottleneck](https://mlsanity.com/paper/2112.08903/) (2021)
- [SUGAR: Subgraph Neural Network with Reinforcement Pooling and Self-Supervised Mutual Information Mechanism](https://mlsanity.com/paper/2101.08170/) (2021)
- [Layer aggregation and reducibility of multilayer interconnected networks](https://mlsanity.com/paper/1405.0425/) (2014)
- [Position-aware Structure Learning for Graph Topology-imbalance by Relieving Under-reaching and Over-squashing](https://mlsanity.com/paper/2208.08302/) (2022)
- [Principle of Relevant Information for Graph Sparsification](https://mlsanity.com/paper/2206.00118/) (2022)
- [Fast Incremental von Neumann Graph Entropy Computation: Theory, Algorithm, and Applications](https://mlsanity.com/paper/1805.11769/) (2018)
- [Multiscale Principle of Relevant Information for Hyperspectral Image Classification](https://mlsanity.com/paper/1907.06022/) (2019)
- [Ego-based Entropy Measures for Structural Representations](https://mlsanity.com/paper/2003.00553/) (2020)

## Built on by (most cited first, 8 of 8)

- [Hyperbolic Geometric Graph Representation Learning for Hierarchy-imbalance Node Classification](https://mlsanity.com/paper/2304.05059/) (2023)
- [From Latent Graph to Latent Topology Inference: Differentiable Cell Complex Module](https://mlsanity.com/paper/2305.16174/) (2023)
- [DeepRicci: Self-supervised Graph Structure-Feature Co-Refinement for Alleviating Over-squashing](https://mlsanity.com/paper/2401.12780/) (2024)
- [DSLR: Diversity Enhancement and Structure Learning for Rehearsal-based Graph Continual Learning](https://mlsanity.com/paper/2402.13711/) (2024)
- [GaGSL: Global-augmented Graph Structure Learning via Graph Information Bottleneck](https://mlsanity.com/paper/2411.04356/) (2024)
- [Probability Passing for Graph Neural Networks: Graph Structure and Representations Joint Learning](https://mlsanity.com/paper/2407.10688/) (2024)
- [Boolean Product Graph Neural Networks](https://mlsanity.com/paper/2409.14001/) (2024)
- [Differentiable Lifting for Topological Neural Networks](https://mlsanity.com/paper/2608.01160/) (2026)

## Abstract (arXiv)

Most Graph Neural Networks follow the message-passing paradigm, assuming the observed structure depicts the ground-truth node relationships. However, this fundamental assumption cannot always be satisfied, as real-world graphs are always incomplete, noisy, or redundant. How to reveal the inherent graph structure in a unified way remains under-explored. We proposed PRI-GSL, a Graph Structure Learning framework guided by the Principle of Relevant Information, providing a simple and unified framework for identifying the self-organization and revealing the hidden structure. PRI-GSL learns a structure that contains the most relevant yet least redundant information quantified by von Neumann entropy and Quantum Jensen-Shannon divergence. PRI-GSL incorporates the evolution of quantum continuous walk with graph wavelets to encode node structural roles, showing in which way the nodes interplay and self-organize with the graph structure. Extensive experiments demonstrate the superior effectiveness and robustness of PRI-GSL.