# Distribution Knowledge Embedding for Graph Pooling

arXiv: https://arxiv.org/abs/2109.14333 · HTML: https://mlsanity.com/paper/2109.14333/

## Key facts

- Cited by 19 papers in the map (data through 14 Oct 2026).
- Builds on 28 of its 51 references that are in the map.
- First posted on arXiv 29 Sep 2021.

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

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [How Powerful are Graph Neural Networks?](https://mlsanity.com/paper/1810.00826/) (2018)
- [A Comprehensive Survey on Graph Neural Networks](https://mlsanity.com/paper/1901.00596/) (2019)
- [Open Graph Benchmark: Datasets for Machine Learning on Graphs](https://mlsanity.com/paper/2005.00687/) (2020)
- [Convolutional Neural Networks on Graphs with Fast Localized Spectral Filtering](https://mlsanity.com/paper/1606.09375/) (2016)
- [Hierarchical Graph Representation Learning with Differentiable Pooling](https://mlsanity.com/paper/1806.08804/) (2018)
- [Convolutional Networks on Graphs for Learning Molecular Fingerprints](https://mlsanity.com/paper/1509.09292/) (2015)
- [TUDataset: A collection of benchmark datasets for learning with graphs](https://mlsanity.com/paper/2007.08663/) (2020)
- [Graph U-Nets](https://mlsanity.com/paper/1905.05178/) (2019)
- [Self-Attention Graph Pooling](https://mlsanity.com/paper/1904.08082/) (2019)
- [ASAP: Adaptive Structure Aware Pooling for Learning Hierarchical Graph Representations](https://mlsanity.com/paper/1911.07979/) (2019)
- [Accurate Learning of Graph Representations with Graph Multiset Pooling](https://mlsanity.com/paper/2102.11533/) (2021)
- [Hierarchical Graph Pooling with Structure Learning](https://mlsanity.com/paper/1911.05954/) (2019)
- [Beyond Bilinear: Generalized Multimodal Factorized High-order Pooling for Visual Question Answering](https://mlsanity.com/paper/1708.03619/) (2017)
- [Factorizable Graph Convolutional Networks](https://mlsanity.com/paper/2010.05421/) (2020)
- [Towards Faster Training of Global Covariance Pooling Networks by Iterative Matrix Square Root Normalization](https://mlsanity.com/paper/1712.01034/) (2017)
- [Memory-Based Graph Networks](https://mlsanity.com/paper/2002.09518/) (2020)
- [Anonymous Walk Embeddings](https://mlsanity.com/paper/1805.11921/) (2018)
- [Is Second-order Information Helpful for Large-scale Visual Recognition?](https://mlsanity.com/paper/1703.08050/) (2017)
- [Topology-Aware Graph Pooling Networks](https://mlsanity.com/paper/2010.09834/) (2020)
- [Deep CNNs Meet Global Covariance Pooling: Better Representation and Generalization](https://mlsanity.com/paper/1904.06836/) (2019)
- [Pooling Architecture Search for Graph Classification](https://mlsanity.com/paper/2108.10587/) (2021)
- [Second-Order Pooling for Graph Neural Networks](https://mlsanity.com/paper/2007.10467/) (2020)
- [Hierarchical Adaptive Pooling by Capturing High-order Dependency for Graph Representation Learning](https://mlsanity.com/paper/2104.05960/) (2021)
- [Bregman Divergences for Infinite Dimensional Covariance Matrices](https://mlsanity.com/paper/1403.4334/) (2014)
- [Hierarchical Graph Capsule Network](https://mlsanity.com/paper/2012.08734/) (2020)
- [Hierarchical Gaussian Descriptors with Application to Person Re-Identification](https://mlsanity.com/paper/1706.04318/) (2017)
- [More About Covariance Descriptors for Image Set Coding: Log-Euclidean Framework based Kernel Matrix Representation](https://mlsanity.com/paper/1909.07273/) (2019)

## Built on by (most cited first, 19 of 19)

- [Graph Pooling for Graph Neural Networks: Progress, Challenges, and Opportunities](https://mlsanity.com/paper/2204.07321/) (2022)
- [FreeCustom: Tuning-Free Customized Image Generation for Multi-Concept Composition](https://mlsanity.com/paper/2405.13870/) (2024)
- [Improving Expressivity of GNNs with Subgraph-specific Factor Embedded Normalization](https://mlsanity.com/paper/2305.19903/) (2023)
- [Riemannian Multinomial Logistics Regression for SPD Neural Networks](https://mlsanity.com/paper/2305.11288/) (2023)
- [Understanding Matrix Function Normalizations in Covariance Pooling through the Lens of Riemannian Geometry](https://mlsanity.com/paper/2407.10484/) (2024)
- [A Lie Group Approach to Riemannian Batch Normalization](https://mlsanity.com/paper/2403.11261/) (2024)
- [Unveiling Global Interactive Patterns across Graphs: Towards Interpretable Graph Neural Networks](https://mlsanity.com/paper/2407.01979/) (2024)
- [Adversarial Erasing with Pruned Elements: Towards Better Graph Lottery Ticket](https://mlsanity.com/paper/2308.02916/) (2023)
- [Powerformer: A Section-adaptive Transformer for Power Flow Adjustment](https://mlsanity.com/paper/2401.02771/) (2024)
- [GNN-VPA: A Variance-Preserving Aggregation Strategy for Graph Neural Networks](https://mlsanity.com/paper/2403.04747/) (2024)
- [Geometry-Aware Edge Pooling for Graph Neural Networks](https://mlsanity.com/paper/2506.11700/) (2025)
- [From GNNs to Trees: Multi-Granular Interpretability for Graph Neural Networks](https://mlsanity.com/paper/2505.00364/) (2025)
- [Message-passing selection: Towards interpretable GNNs for graph classification](https://mlsanity.com/paper/2306.02081/) (2023)
- [TextureDiffusion: Target Prompt Disentangled Editing for Various Texture Transfer](https://mlsanity.com/paper/2409.09610/) (2024)
- [Edge-Based Graph Component Pooling](https://mlsanity.com/paper/2409.11856/) (2024)
- [Mitigating Cascading Effects in Large Adversarial Graph Environments](https://mlsanity.com/paper/2404.14418/) (2024)
- [Learning a Mini-batch Graph Transformer via Two-stage Interaction Augmentation](https://mlsanity.com/paper/2407.09904/) (2024)
- [Learning from Historical Activations in Graph Neural Networks](https://mlsanity.com/paper/2601.01123/) (2026)
- [LieBN: Batch Normalization over Lie Groups](https://mlsanity.com/paper/2607.08783/) (2026)

## Abstract (arXiv)

Graph-level representation learning is the pivotal step for downstream tasks that operate on the whole graph. The most common approach to this problem heretofore is graph pooling, where node features are typically averaged or summed to obtain the graph representations. However, pooling operations like averaging or summing inevitably cause massive information missing, which may severely downgrade the final performance. In this paper, we argue what is crucial to graph-level downstream tasks includes not only the topological structure but also the distribution from which nodes are sampled. Therefore, powered by existing Graph Neural Networks (GNN), we propose a new plug-and-play pooling module, termed as Distribution Knowledge Embedding (DKEPool), where graphs are rephrased as distributions on top of GNNs and the pooling goal is to summarize the entire distribution information instead of retaining a certain feature vector by simple predefined pooling operations. A DKEPool network de facto disassembles representation learning into two stages, structure learning and distribution learning. Structure learning follows a recursive neighborhood aggregation scheme to update node features where structure information is obtained. Distribution learning, on the other hand, omits node interconnections and focuses more on the distribution depicted by all the nodes. Extensive experiments demonstrate that the proposed DKEPool significantly and consistently outperforms the state-of-the-art methods.