# Graph Cross Networks with Vertex Infomax Pooling

arXiv: https://arxiv.org/abs/2010.01804 · HTML: https://mlsanity.com/paper/2010.01804/

## Key facts

- Cited by 31 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 5 Oct 2020.

## Built on by (most cited first, 30 of 31)

- [UniGNN: a Unified Framework for Graph and Hypergraph Neural Networks](https://mlsanity.com/paper/2105.00956/) (2021)
- [Graph Pooling for Graph Neural Networks: Progress, Challenges, and Opportunities](https://mlsanity.com/paper/2204.07321/) (2022)
- [On Positional and Structural Node Features for Graph Neural Networks on Non-attributed Graphs](https://mlsanity.com/paper/2107.01495/) (2021)
- [Improving Subgraph Recognition with Variational Graph Information Bottleneck](https://mlsanity.com/paper/2112.09899/) (2021)
- [Skeleton-Parted Graph Scattering Networks for 3D Human Motion Prediction](https://mlsanity.com/paper/2208.00368/) (2022)
- [Online Multi-Agent Forecasting with Interpretable Collaborative Graph Neural Network](https://mlsanity.com/paper/2107.00894/) (2021)
- [Comprehensive Graph Gradual Pruning for Sparse Training in Graph Neural Networks](https://mlsanity.com/paper/2207.08629/) (2022)
- [Graph Pooling via Coarsened Graph Infomax](https://mlsanity.com/paper/2105.01275/) (2021)
- [Probabilistic Graph Rewiring via Virtual Nodes](https://mlsanity.com/paper/2405.17311/) (2024)
- [Maximum Entropy Weighted Independent Set Pooling for Graph Neural Networks](https://mlsanity.com/paper/2107.01410/) (2021)
- [Hierarchical graph neural nets can capture long-range interactions](https://mlsanity.com/paper/2107.07432/) (2021)
- [Incomplete Multi-view Clustering via Cross-view Relation Transfer](https://mlsanity.com/paper/2112.00739/) (2021)
- [Brain Graph Super-Resolution Using Adversarial Graph Neural Network with Application to Functional Brain Connectivity](https://mlsanity.com/paper/2105.00425/) (2021)
- [A Comprehensive Graph Pooling Benchmark: Effectiveness, Robustness and Generalizability](https://mlsanity.com/paper/2406.09031/) (2024)
- [Diversified Multiscale Graph Learning with Graph Self-Correction](https://mlsanity.com/paper/2103.09754/) (2021)
- [Structure-Aware Hierarchical Graph Pooling using Information Bottleneck](https://mlsanity.com/paper/2104.13012/) (2021)
- [Detecting Arbitrary Order Beneficial Feature Interactions for Recommender Systems](https://mlsanity.com/paper/2206.13764/) (2022)
- [Learning Graph Representation by Aggregating Subgraphs via Mutual Information Maximization](https://mlsanity.com/paper/2103.13125/) (2021)
- [On Exploring Node-feature and Graph-structure Diversities for Node Drop Graph Pooling](https://mlsanity.com/paper/2306.12726/) (2023)
- [Graph Parsing Networks](https://mlsanity.com/paper/2402.14393/) (2024)
- [Supervised Contrastive Learning with Structure Inference for Graph Classification](https://mlsanity.com/paper/2203.07691/) (2022)
- [A Class-Aware Representation Refinement Framework for Graph Classification](https://mlsanity.com/paper/2209.00936/) (2022)
- [Models and Benchmarks for Representation Learning of Partially Observed Subgraphs](https://mlsanity.com/paper/2209.00508/) (2022)
- [Self-Supervised Node Representation Learning via Node-to-Neighbourhood Alignment](https://mlsanity.com/paper/2302.04626/) (2023)
- [Seeing All From a Few: Nodes Selection Using Graph Pooling for Graph Clustering](https://mlsanity.com/paper/2105.05320/) (2021)
- [Careful Selection and Thoughtful Discarding: Graph Explicit Pooling Utilizing Discarded Nodes](https://mlsanity.com/paper/2311.12644/) (2023)
- [TimeGraphs: Graph-based Temporal Reasoning](https://mlsanity.com/paper/2401.03134/) (2024)
- [Context Pooling: Query-specific Graph Pooling for Generic Inductive Link Prediction in Knowledge Graphs](https://mlsanity.com/paper/2507.07595/) (2025)
- [Rate-Distortion Optimized Communication for Collaborative Perception](https://mlsanity.com/paper/2509.21994/) (2025)
- [Joint Learning of Hierarchical Community Structure and Node Representations: An Unsupervised Approach](https://mlsanity.com/paper/2201.09086/) (2022)

## Abstract (arXiv)

We propose a novel graph cross network (GXN) to achieve comprehensive feature learning from multiple scales of a graph. Based on trainable hierarchical representations of a graph, GXN enables the interchange of intermediate features across scales to promote information flow. Two key ingredients of GXN include a novel vertex infomax pooling (VIPool), which creates multiscale graphs in a trainable manner, and a novel feature-crossing layer, enabling feature interchange across scales. The proposed VIPool selects the most informative subset of vertices based on the neural estimation of mutual information between vertex features and neighborhood features. The intuition behind is that a vertex is informative when it can maximally reflect its neighboring information. The proposed feature-crossing layer fuses intermediate features between two scales for mutual enhancement by improving information flow and enriching multiscale features at hidden layers. The cross shape of the feature-crossing layer distinguishes GXN from many other multiscale architectures. Experimental results show that the proposed GXN improves the classification accuracy by 2.12% and 1.15% on average for graph classification and vertex classification, respectively. Based on the same network, the proposed VIPool consistently outperforms other graph-pooling methods.