# Towards Sparse Hierarchical Graph Classifiers

arXiv: https://arxiv.org/abs/1811.01287 · HTML: https://mlsanity.com/paper/1811.01287/

## Key facts

- Cited by 100 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 3 Nov 2018.

## Built on by (most cited first, 30 of 100)

- [Weisfeiler and Lehman Go Topological: Message Passing Simplicial Networks](https://mlsanity.com/paper/2103.03212/) (2021)
- [Accurate Learning of Graph Representations with Graph Multiset Pooling](https://mlsanity.com/paper/2102.11533/) (2021)
- [DiffWire: Inductive Graph Rewiring via the Lov'asz Bound](https://mlsanity.com/paper/2206.07369/) (2022)
- [SUGAR: Subgraph Neural Network with Reinforcement Pooling and Self-Supervised Mutual Information Mechanism](https://mlsanity.com/paper/2101.08170/) (2021)
- [Understanding Pooling in Graph Neural Networks](https://mlsanity.com/paper/2110.05292/) (2021)
- [Reconstruction for Powerful Graph Representations](https://mlsanity.com/paper/2110.00577/) (2021)
- [Ordered Subgraph Aggregation Networks](https://mlsanity.com/paper/2206.11168/) (2022)
- [Graph Coarsening with Neural Networks](https://mlsanity.com/paper/2102.01350/) (2021)
- [Graph Pooling for Graph Neural Networks: Progress, Challenges, and Opportunities](https://mlsanity.com/paper/2204.07321/) (2022)
- [How Framelets Enhance Graph Neural Networks](https://mlsanity.com/paper/2102.06986/) (2021)
- [Learning Pedestrian Group Representations for Multi-modal Trajectory Prediction](https://mlsanity.com/paper/2207.09953/) (2022)
- [A graph convolutional autoencoder approach to model order reduction for parametrized PDEs](https://mlsanity.com/paper/2305.08573/) (2023)
- [SpeqNets: Sparsity-aware Permutation-equivariant Graph Networks](https://mlsanity.com/paper/2203.13913/) (2022)
- [Cell Attention Networks](https://mlsanity.com/paper/2209.08179/) (2022)
- [Explaining the Explainers in Graph Neural Networks: a Comparative Study](https://mlsanity.com/paper/2210.15304/) (2022)
- [ReGVD: Revisiting Graph Neural Networks for Vulnerability Detection](https://mlsanity.com/paper/2110.07317/) (2021)
- [Bending Graphs: Hierarchical Shape Matching using Gated Optimal Transport](https://mlsanity.com/paper/2202.01537/) (2022)
- [Equivariant Graph Hierarchy-Based Neural Networks](https://mlsanity.com/paper/2202.10643/) (2022)
- [Aero-Nef: Neural Fields for Rapid Aircraft Aerodynamics Simulations](https://mlsanity.com/paper/2407.19916/) (2024)
- [Graph coarsening: From scientific computing to machine learning](https://mlsanity.com/paper/2106.11863/) (2021)
- [Learning 3D Particle-based Simulators from RGB-D Videos](https://mlsanity.com/paper/2312.05359/) (2023)
- [TopoGCL: Topological Graph Contrastive Learning](https://mlsanity.com/paper/2406.17251/) (2024)
- [Search to Fine-tune Pre-trained Graph Neural Networks for Graph-level Tasks](https://mlsanity.com/paper/2308.06960/) (2023)
- [KGPool: Dynamic Knowledge Graph Context Selection for Relation Extraction](https://mlsanity.com/paper/2106.00459/) (2021)
- [Tensor-view Topological Graph Neural Network](https://mlsanity.com/paper/2401.12007/) (2024)
- [A Survey on Malware Detection with Graph Representation Learning](https://mlsanity.com/paper/2303.16004/) (2023)
- [Revisiting Point Cloud Simplification: A Learnable Feature Preserving Approach](https://mlsanity.com/paper/2109.14982/) (2021)
- [Topological Pooling on Graphs](https://mlsanity.com/paper/2303.14543/) (2023)
- [Boosting Graph Pooling with Persistent Homology](https://mlsanity.com/paper/2402.16346/) (2024)
- [Multi-Level Attention Pooling for Graph Neural Networks: Unifying Graph Representations with Multiple Localities](https://mlsanity.com/paper/2103.01488/) (2021)

## Abstract (arXiv)

Recent advances in representation learning on graphs, mainly leveraging graph convolutional networks, have brought a substantial improvement on many graph-based benchmark tasks. While novel approaches to learning node embeddings are highly suitable for node classification and link prediction, their application to graph classification (predicting a single label for the entire graph) remains mostly rudimentary, typically using a single global pooling step to aggregate node features or a hand-designed, fixed heuristic for hierarchical coarsening of the graph structure. An important step towards ameliorating this is differentiable graph coarsening---the ability to reduce the size of the graph in an adaptive, data-dependent manner within a graph neural network pipeline, analogous to image downsampling within CNNs. However, the previous prominent approach to pooling has quadratic memory requirements during training and is therefore not scalable to large graphs. Here we combine several recent advances in graph neural network design to demonstrate that competitive hierarchical graph classification results are possible without sacrificing sparsity. Our results are verified on several established graph classification benchmarks, and highlight an important direction for future research in graph-based neural networks.