# Discrete Curvature Graph Information Bottleneck

arXiv: https://arxiv.org/abs/2412.19993 · HTML: https://mlsanity.com/paper/2412.19993/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 25 references that are in the map.
- First posted on arXiv 28 Dec 2024.

## Builds on (most cited first, 18 of 18)

- [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)
- [Categorical Reparameterization with Gumbel-Softmax](https://mlsanity.com/paper/1611.01144/) (2016)
- [Pitfalls of Graph Neural Network Evaluation](https://mlsanity.com/paper/1811.05868/) (2018)
- [On Variational Bounds of Mutual Information](https://mlsanity.com/paper/1905.06922/) (2019)
- [Understanding over-squashing and bottlenecks on graphs via curvature](https://mlsanity.com/paper/2111.14522/) (2021)
- [Graph Information Bottleneck](https://mlsanity.com/paper/2010.12811/) (2020)
- [Cooperative Game Theory Approaches for Network Partitioning](https://mlsanity.com/paper/1707.03587/) (2017)
- [Graph Information Bottleneck for Subgraph Recognition](https://mlsanity.com/paper/2010.05563/) (2020)
- [Towards Unsupervised Deep Graph Structure Learning](https://mlsanity.com/paper/2201.06367/) (2022)
- [Revisiting Over-smoothing and Over-squashing Using Ollivier-Ricci Curvature](https://mlsanity.com/paper/2211.15779/) (2022)
- [Graph Structure Learning with Variational Information Bottleneck](https://mlsanity.com/paper/2112.08903/) (2021)
- [ACE-HGNN: Adaptive Curvature Exploration Hyperbolic Graph Neural Network](https://mlsanity.com/paper/2110.07888/) (2021)
- [Hyperbolic Geometric Graph Representation Learning for Hierarchy-imbalance Node Classification](https://mlsanity.com/paper/2304.05059/) (2023)
- [DeepRicci: Self-supervised Graph Structure-Feature Co-Refinement for Alleviating Over-squashing](https://mlsanity.com/paper/2401.12780/) (2024)
- [Toward Enhanced Robustness in Unsupervised Graph Representation Learning: A Graph Information Bottleneck Perspective](https://mlsanity.com/paper/2201.08557/) (2022)

## Built on by (most cited first, 4 of 4)

- [Deeper with Riemannian Geometry: Overcoming Oversmoothing and Oversquashing for Graph Foundation Models](https://mlsanity.com/paper/2510.17457/) (2025)
- [An Out-Of-Distribution Membership Inference Attack Approach for Cross-Domain Graph Attacks](https://mlsanity.com/paper/2505.20074/) (2025)
- [Mitigating Message Imbalance in Fraud Detection with Dual-View Graph Representation Learning](https://mlsanity.com/paper/2507.06469/) (2025)
- [Geometric Evolution Graph Convolutional Networks: Enhancing Graph Representation Learning via Ricci Flow](https://mlsanity.com/paper/2603.26178/) (2026)

## Abstract (arXiv)

Graph neural networks(GNNs) have been demonstrated to depend on whether the node effective information is sufficiently passing. Discrete curvature (Ricci curvature) is used to study graph connectivity and information propagation efficiency with a geometric perspective, and has been raised in recent years to explore the efficient message-passing structure of GNNs. However, most empirical studies are based on directly observed graph structures or heuristic topological assumptions and lack in-depth exploration of underlying optimal information transport structures for downstream tasks. We suggest that graph curvature optimization is more in-depth and essential than directly rewiring or learning for graph structure with richer message-passing characterization and better information transport interpretability. From both graph geometry and information theory perspectives, we propose the novel Discrete Curvature Graph Information Bottleneck (CurvGIB) framework to optimize the information transport structure and learn better node representations simultaneously. CurvGIB advances the Variational Information Bottleneck (VIB) principle for Ricci curvature optimization to learn the optimal information transport pattern for specific downstream tasks. The learned Ricci curvature is used to refine the optimal transport structure of the graph, and the node representation is fully and efficiently learned. Moreover, for the computational complexity of Ricci curvature differentiation, we combine Ricci flow and VIB to deduce a curvature optimization approximation to form a tractable IB objective function. Extensive experiments on various datasets demonstrate the superior effectiveness and interpretability of CurvGIB.