# From Spectral Graph Convolutions to Large Scale Graph Convolutional Networks

arXiv: https://arxiv.org/abs/2207.05669 · HTML: https://mlsanity.com/paper/2207.05669/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 13 of its 21 references that are in the map.
- First posted on arXiv 12 Jul 2022.

## Builds on (most cited first, 13 of 13)

- [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)
- [Inductive Representation Learning on Large Graphs](https://mlsanity.com/paper/1706.02216/) (2017)
- [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)
- [Link Prediction Based on Graph Neural Networks](https://mlsanity.com/paper/1802.09691/) (2018)
- [GraphSAINT: Graph Sampling Based Inductive Learning Method](https://mlsanity.com/paper/1907.04931/) (2019)
- [FastGCN: Fast Learning with Graph Convolutional Networks via Importance Sampling](https://mlsanity.com/paper/1801.10247/) (2018)
- [Cluster-GCN: An Efficient Algorithm for Training Deep and Large Graph Convolutional Networks](https://mlsanity.com/paper/1905.07953/) (2019)
- [SIGN: Scalable Inception Graph Neural Networks](https://mlsanity.com/paper/2004.11198/) (2020)
- [Graph Learning: A Survey](https://mlsanity.com/paper/2105.00696/) (2021)
- [Spectral-based Graph Convolutional Network for Directed Graphs](https://mlsanity.com/paper/1907.08990/) (2019)
- [Graph Fairing Convolutional Networks for Anomaly Detection](https://mlsanity.com/paper/2010.10274/) (2020)

## Abstract (arXiv)

Graph Convolutional Networks (GCNs) have been shown to be a powerful concept that has been successfully applied to a large variety of tasks across many domains over the past years. In this work we study the theory that paved the way to the definition of GCN, including related parts of classical graph theory. We also discuss and experimentally demonstrate key properties and limitations of GCNs such as those caused by the statistical dependency of samples, introduced by the edges of the graph, which causes the estimates of the full gradient to be biased. Another limitation we discuss is the negative impact of minibatch sampling on the model performance. As a consequence, during parameter update, gradients are computed on the whole dataset, undermining scalability to large graphs. To account for this, we research alternative methods which allow to safely learn good parameters while sampling only a subset of data per iteration. We reproduce the results reported in the work of Kipf et al. and propose an implementation inspired to SIGN, which is a sampling-free minibatch method. Eventually we compare the two implementations on a benchmark dataset, proving that they are comparable in terms of prediction accuracy for the task of semi-supervised node classification.