# Pointspectrum: Equivariance Meets Laplacian Filtering for Graph Representation Learning

arXiv: https://arxiv.org/abs/2109.02358 · HTML: https://mlsanity.com/paper/2109.02358/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 26 of its 35 references that are in the map.
- First posted on arXiv 6 Sep 2021.

## Builds on (most cited first, 26 of 26)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Delving Deep into Rectifiers: Surpassing Human-Level Performance on ImageNet Classification](https://mlsanity.com/paper/1502.01852/) (2015)
- [Non-local Neural Networks](https://mlsanity.com/paper/1711.07971/) (2017)
- [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)
- [Simplifying Graph Convolutional Networks](https://mlsanity.com/paper/1902.07153/) (2019)
- [Deep Sets](https://mlsanity.com/paper/1703.06114/) (2017)
- [Variational Graph Auto-Encoders](https://mlsanity.com/paper/1611.07308/) (2016)
- [Deep Graph Infomax](https://mlsanity.com/paper/1809.10341/) (2018)
- [Representation Learning on Graphs with Jumping Knowledge Networks](https://mlsanity.com/paper/1806.03536/) (2018)
- [Measuring and Relieving the Over-smoothing Problem for Graph Neural Networks from the Topological View](https://mlsanity.com/paper/1909.03211/) (2019)
- [PairNorm: Tackling Oversmoothing in GNNs](https://mlsanity.com/paper/1909.12223/) (2019)
- [GNNGuard: Defending Graph Neural Networks against Adversarial Attacks](https://mlsanity.com/paper/2006.08149/) (2020)
- [Universal Invariant and Equivariant Graph Neural Networks](https://mlsanity.com/paper/1905.04943/) (2019)
- [Attributed Graph Clustering: A Deep Attentional Embedding Approach](https://mlsanity.com/paper/1906.06532/) (2019)
- [Universal approximations of invariant maps by neural networks](https://mlsanity.com/paper/1804.10306/) (2018)
- [Towards Deeper Graph Neural Networks with Differentiable Group Normalization](https://mlsanity.com/paper/2006.06972/) (2020)
- [Attributed Graph Clustering via Adaptive Graph Convolution](https://mlsanity.com/paper/1906.01210/) (2019)
- [Adaptive Graph Encoder for Attributed Graph Embedding](https://mlsanity.com/paper/2007.01594/) (2020)
- [Inductive Matrix Completion Based on Graph Neural Networks](https://mlsanity.com/paper/1904.12058/) (2019)
- [Adversarially Regularized Graph Autoencoder for Graph Embedding](https://mlsanity.com/paper/1802.04407/) (2018)
- [On Universal Equivariant Set Networks](https://mlsanity.com/paper/1910.02421/) (2019)
- [End to end learning and optimization on graphs](https://mlsanity.com/paper/1905.13732/) (2019)
- [Graph InfoClust: Leveraging cluster-level node information for unsupervised graph representation learning](https://mlsanity.com/paper/2009.06946/) (2020)
- [Universal approximations of permutation invariant/equivariant functions by deep neural networks](https://mlsanity.com/paper/1903.01939/) (2019)
- [Is a Single Vector Enough? Exploring Node Polysemy for Network Embedding](https://mlsanity.com/paper/1905.10668/) (2019)

## Abstract (arXiv)

Graph Representation Learning (GRL) has become essential for modern graph data mining and learning tasks. GRL aims to capture the graph's structural information and exploit it in combination with node and edge attributes to compute low-dimensional representations. While Graph Neural Networks (GNNs) have been used in state-of-the-art GRL architectures, they have been shown to suffer from over smoothing when many GNN layers need to be stacked. In a different GRL approach, spectral methods based on graph filtering have emerged addressing over smoothing; however, up to now, they employ traditional neural networks that cannot efficiently exploit the structure of graph data. Motivated by this, we propose PointSpectrum, a spectral method that incorporates a set equivariant network to account for a graph's structure. PointSpectrum enhances the efficiency and expressiveness of spectral methods, while it outperforms or competes with state-of-the-art GRL methods. Overall, PointSpectrum addresses over smoothing by employing a graph filter and captures a graph's structure through set equivariance, lying on the intersection of GNNs and spectral methods. Our findings are promising for the benefits and applicability of this architectural shift for spectral methods and GRL.