# LiftPool: Lifting-based Graph Pooling for Hierarchical Graph Representation Learning

arXiv: https://arxiv.org/abs/2204.12881 · HTML: https://mlsanity.com/paper/2204.12881/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 19 of its 30 references that are in the map.
- First posted on arXiv 27 Apr 2022.

## Builds on (most cited first, 19 of 19)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [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)
- [Neural Machine Translation by Jointly Learning to Align and Translate](https://mlsanity.com/paper/1409.0473/) (2014)
- [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)
- [Dynamic Graph CNN for Learning on Point Clouds](https://mlsanity.com/paper/1801.07829/) (2018)
- [Convolutional Neural Networks on Graphs with Fast Localized Spectral Filtering](https://mlsanity.com/paper/1606.09375/) (2016)
- [Spectral Networks and Locally Connected Networks on Graphs](https://mlsanity.com/paper/1312.6203/) (2013)
- [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)
- [Graph U-Nets](https://mlsanity.com/paper/1905.05178/) (2019)
- [Self-Attention Graph Pooling](https://mlsanity.com/paper/1904.08082/) (2019)
- [Deep Convolutional Networks on Graph-Structured Data](https://mlsanity.com/paper/1506.05163/) (2015)
- [Order Matters: Sequence to sequence for sets](https://mlsanity.com/paper/1511.06391/) (2015)
- [CayleyNets: Graph Convolutional Neural Networks with Complex Rational Spectral Filters](https://mlsanity.com/paper/1705.07664/) (2017)
- [Graph Neural Networks with convolutional ARMA filters](https://mlsanity.com/paper/1901.01343/) (2019)
- [ASAP: Adaptive Structure Aware Pooling for Learning Hierarchical Graph Representations](https://mlsanity.com/paper/1911.07979/) (2019)

## Built on by (most cited first, 3 of 3)

- [A Comprehensive Graph Pooling Benchmark: Effectiveness, Robustness and Generalizability](https://mlsanity.com/paper/2406.09031/) (2024)
- [LGRPool: Hierarchical Graph Pooling Via Local-Global Regularisation](https://mlsanity.com/paper/2504.08530/) (2025)
- [Mitigating Context Bias in Domain Adaptation for Object Detection using Mask Pooling](https://mlsanity.com/paper/2505.18446/) (2025)

## Abstract (arXiv)

Graph pooling has been increasingly considered for graph neural networks (GNNs) to facilitate hierarchical graph representation learning. Existing graph pooling methods commonly consist of two stages, i.e., selecting the top-ranked nodes and removing the rest nodes to construct a coarsened graph representation. However, local structural information of the removed nodes would be inevitably dropped in these methods, due to the inherent coupling of nodes (location) and their features (signals). In this paper, we propose an enhanced three-stage method via lifting, named LiftPool, to improve hierarchical graph representation by maximally preserving the local structural information in graph pooling. LiftPool introduces an additional stage of graph lifting before graph coarsening to preserve the local information of the removed nodes and decouple the processes of node removing and feature reduction. Specifically, for each node to be removed, its local information is obtained by subtracting the global information aggregated from its neighboring preserved nodes. Subsequently, this local information is aligned and propagated to the preserved nodes to alleviate information loss in graph coarsening. Furthermore, we demonstrate that the proposed LiftPool is localized and permutation-invariant. The proposed graph lifting structure is general to be integrated with existing downsampling-based graph pooling methods. Evaluations on benchmark graph datasets show that LiftPool substantially outperforms the state-of-the-art graph pooling methods in the task of graph classification.