# SMGRL: Scalable Multi-resolution Graph Representation Learning

arXiv: https://arxiv.org/abs/2201.12670 · HTML: https://mlsanity.com/paper/2201.12670/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 25 of its 49 references that are in the map.
- First posted on arXiv 29 Jan 2022.

## Builds on (most cited first, 25 of 25)

- [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)
- [Open Graph Benchmark: Datasets for Machine Learning on Graphs](https://mlsanity.com/paper/2005.00687/) (2020)
- [node2vec: Scalable Feature Learning for Networks](https://mlsanity.com/paper/1607.00653/) (2016)
- [DeepWalk: Online Learning of Social Representations](https://mlsanity.com/paper/1403.6652/) (2014)
- [Predict then Propagate: Graph Neural Networks meet Personalized PageRank](https://mlsanity.com/paper/1810.05997/) (2018)
- [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)
- [A Note on Over-Smoothing for Graph Neural Networks](https://mlsanity.com/paper/2006.13318/) (2020)
- [Network Embedding as Matrix Factorization: Unifying DeepWalk, LINE, PTE, and node2vec](https://mlsanity.com/paper/1710.02971/) (2017)
- [Graph Neural Networks with convolutional ARMA filters](https://mlsanity.com/paper/1901.01343/) (2019)
- [Cooperative Game Theory Approaches for Network Partitioning](https://mlsanity.com/paper/1707.03587/) (2017)
- [Implicit Graph Neural Networks](https://mlsanity.com/paper/2009.06211/) (2020)
- [Scaling Up Graph Neural Networks Via Graph Coarsening](https://mlsanity.com/paper/2106.05150/) (2021)
- [GNN-FiLM: Graph Neural Networks with Feature-wise Linear Modulation](https://mlsanity.com/paper/1906.12192/) (2019)
- [HARP: Hierarchical Representation Learning for Networks](https://mlsanity.com/paper/1706.07845/) (2017)
- [Spectrally approximating large graphs with smaller graphs](https://mlsanity.com/paper/1802.07510/) (2018)
- [Graph Coarsening with Neural Networks](https://mlsanity.com/paper/2102.01350/) (2021)
- [A Unifying Framework for Spectrum-Preserving Graph Sparsification and Coarsening](https://mlsanity.com/paper/1902.09702/) (2019)
- [MILE: A Multi-Level Framework for Scalable Graph Embedding](https://mlsanity.com/paper/1802.09612/) (2018)
- [Hierarchical Message-Passing Graph Neural Networks](https://mlsanity.com/paper/2009.03717/) (2020)
- [Hierarchical Adaptive Pooling by Capturing High-order Dependency for Graph Representation Learning](https://mlsanity.com/paper/2104.05960/) (2021)
- [GOSH: Embedding Big Graphs on Small Hardware](https://mlsanity.com/paper/2008.12336/) (2020)

## Built on by (most cited first, 1 of 1)

- [Probabilistic Graph Rewiring via Virtual Nodes](https://mlsanity.com/paper/2405.17311/) (2024)

## Abstract (arXiv)

Graph convolutional networks (GCNs) allow us to learn topologically-aware node embeddings, which can be useful for classification or link prediction. However, they are unable to capture long-range dependencies between nodes without adding additional layers -- which in turn leads to over-smoothing and increased time and space complexity. Further, the complex dependencies between nodes make mini-batching challenging, limiting their applicability to large graphs. We propose a Scalable Multi-resolution Graph Representation Learning (SMGRL) framework that enables us to learn multi-resolution node embeddings efficiently. Our framework is model-agnostic and can be applied to any existing GCN model. We dramatically reduce training costs by training only on a reduced-dimension coarsening of the original graph, then exploit self-similarity to apply the resulting algorithm at multiple resolutions. The resulting multi-resolution embeddings can be aggregated to yield high-quality node embeddings that capture both long- and short-range dependencies. Our experiments show that this leads to improved classification accuracy, without incurring high computational costs.