# Hierarchical Adaptive Pooling by Capturing High-order Dependency for Graph Representation Learning

arXiv: https://arxiv.org/abs/2104.05960 · HTML: https://mlsanity.com/paper/2104.05960/

## Key facts

- Cited by 15 papers in the map (data through 14 Oct 2026).
- Builds on 28 of its 57 references that are in the map.
- First posted on arXiv 13 Apr 2021.

## Builds on (most cited first, 28 of 28)

- [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)
- [Categorical Reparameterization with Gumbel-Softmax](https://mlsanity.com/paper/1611.01144/) (2016)
- [Open Graph Benchmark: Datasets for Machine Learning on Graphs](https://mlsanity.com/paper/2005.00687/) (2020)
- [Modeling Relational Data with Graph Convolutional Networks](https://mlsanity.com/paper/1703.06103/) (2017)
- [Beyond a Gaussian Denoiser: Residual Learning of Deep CNN for Image Denoising](https://mlsanity.com/paper/1608.03981/) (2016)
- [Spectral Networks and Locally Connected Networks on Graphs](https://mlsanity.com/paper/1312.6203/) (2013)
- [Gated Graph Sequence Neural Networks](https://mlsanity.com/paper/1511.05493/) (2015)
- [Hierarchical Graph Representation Learning with Differentiable Pooling](https://mlsanity.com/paper/1806.08804/) (2018)
- [Graph U-Nets](https://mlsanity.com/paper/1905.05178/) (2019)
- [Self-Attention Graph Pooling](https://mlsanity.com/paper/1904.08082/) (2019)
- [Composition-based Multi-Relational Graph Convolutional Networks](https://mlsanity.com/paper/1911.03082/) (2019)
- [Order Matters: Sequence to sequence for sets](https://mlsanity.com/paper/1511.06391/) (2015)
- [Graph Matching Networks for Learning the Similarity of Graph Structured Objects](https://mlsanity.com/paper/1904.12787/) (2019)
- [ASAP: Adaptive Structure Aware Pooling for Learning Hierarchical Graph Representations](https://mlsanity.com/paper/1911.07979/) (2019)
- [Graph Convolutional Networks with EigenPooling](https://mlsanity.com/paper/1904.13107/) (2019)
- [SimGNN: A Neural Network Approach to Fast Graph Similarity Computation](https://mlsanity.com/paper/1808.05689/) (2018)
- [Comparative Study of CNN and RNN for Natural Language Processing](https://mlsanity.com/paper/1702.01923/) (2017)
- [Hierarchical Graph Pooling with Structure Learning](https://mlsanity.com/paper/1911.05954/) (2019)
- [Rethinking pooling in graph neural networks](https://mlsanity.com/paper/2010.11418/) (2020)
- [Semi-Supervised Graph Classification: A Hierarchical Graph Perspective](https://mlsanity.com/paper/1904.05003/) (2019)
- [Topology-Aware Graph Pooling Networks](https://mlsanity.com/paper/2010.09834/) (2020)
- [Second-Order Pooling for Graph Neural Networks](https://mlsanity.com/paper/2007.10467/) (2020)
- [iPool -- Information-based Pooling in Hierarchical Graph Neural Networks](https://mlsanity.com/paper/1907.00832/) (2019)
- [Deep learning in bioinformatics: introduction, application, and perspective in big data era](https://mlsanity.com/paper/1903.00342/) (2019)

## Built on by (most cited first, 15 of 15)

- [Graph Pooling for Graph Neural Networks: Progress, Challenges, and Opportunities](https://mlsanity.com/paper/2204.07321/) (2022)
- [Calibrated One-class Classification for Unsupervised Time Series Anomaly Detection](https://mlsanity.com/paper/2207.12201/) (2022)
- [Higher-order Clustering and Pooling for Graph Neural Networks](https://mlsanity.com/paper/2209.03473/) (2022)
- [Distribution Knowledge Embedding for Graph Pooling](https://mlsanity.com/paper/2109.14333/) (2021)
- [Cluster-wise Graph Transformer with Dual-granularity Kernelized Attention](https://mlsanity.com/paper/2410.06746/) (2024)
- [Impact of Domain Knowledge and Multi-Modality on Intelligent Molecular Property Prediction: A Systematic Survey](https://mlsanity.com/paper/2402.07249/) (2024)
- [Curvature-based Pooling within Graph Neural Networks](https://mlsanity.com/paper/2308.16516/) (2023)
- [MaxCutPool: differentiable feature-aware Maxcut for pooling in graph neural networks](https://mlsanity.com/paper/2409.05100/) (2024)
- [Edge but not Least: Cross-View Graph Pooling](https://mlsanity.com/paper/2109.11796/) (2021)
- [Tackling Provably Hard Representative Selection via Graph Neural Networks](https://mlsanity.com/paper/2205.10403/) (2022)
- [BN-Pool: Bayesian Nonparametric Pooling for Graphs](https://mlsanity.com/paper/2501.09821/) (2025)
- [SMGRL: Scalable Multi-resolution Graph Representation Learning](https://mlsanity.com/paper/2201.12670/) (2022)
- [Multi-Scale Protein Structure Modelling with Geometric Graph U-Nets](https://mlsanity.com/paper/2512.06752/) (2025)
- [Learning from Historical Activations in Graph Neural Networks](https://mlsanity.com/paper/2601.01123/) (2026)
- [Revisiting the Generalization of Neural Graph Edit Distance Models](https://mlsanity.com/paper/2610.04644/) (2026)

## Abstract (arXiv)

Graph neural networks (GNN) have been proven to be mature enough for handling graph-structured data on node-level graph representation learning tasks. However, the graph pooling technique for learning expressive graph-level representation is critical yet still challenging. Existing pooling methods either struggle to capture the local substructure or fail to effectively utilize high-order dependency, thus diminishing the expression capability. In this paper we propose HAP, a hierarchical graph-level representation learning framework, which is adaptively sensitive to graph structures, i.e., HAP clusters local substructures incorporating with high-order dependencies. HAP utilizes a novel cross-level attention mechanism MOA to naturally focus more on close neighborhood while effectively capture higher-order dependency that may contain crucial information. It also learns a global graph content GCont that extracts the graph pattern properties to make the pre- and post-coarsening graph content maintain stable, thus providing global guidance in graph coarsening. This novel innovation also facilitates generalization across graphs with the same form of features. Extensive experiments on fourteen datasets show that HAP significantly outperforms twelve popular graph pooling methods on graph classification task with an maximum accuracy improvement of 22.79%, and exceeds the performance of state-of-the-art graph matching and graph similarity learning algorithms by over 3.5% and 16.7%.