# The Transferability of Downsamped Sparse Graph Convolutional Networks

arXiv: https://arxiv.org/abs/2408.17274 · HTML: https://mlsanity.com/paper/2408.17274/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 6 of its 21 references that are in the map.
- First posted on arXiv 30 Aug 2024.

## Builds on (most cited first, 6 of 6)

- [FastGCN: Fast Learning with Graph Convolutional Networks via Importance Sampling](https://mlsanity.com/paper/1801.10247/) (2018)
- [Graphon Neural Networks and the Transferability of Graph Neural Networks](https://mlsanity.com/paper/2006.03548/) (2020)
- [Generalization Guarantee of Training Graph Convolutional Networks with Graph Topology Sampling](https://mlsanity.com/paper/2207.03584/) (2022)
- [Limits, approximation and size transferability for GNNs on sparse graphs via graphops](https://mlsanity.com/paper/2306.04495/) (2023)
- [A Survey on Graph Neural Network Acceleration: Algorithms, Systems, and Customized Hardware](https://mlsanity.com/paper/2306.14052/) (2023)
- [Modeling Sparse Graph Sequences and Signals Using Generalized Graphons](https://mlsanity.com/paper/2312.08124/) (2023)

## Abstract (arXiv)

To accelerate the training of graph convolutional networks (GCNs) on real-world large-scale sparse graphs, downsampling methods are commonly employed as a preprocessing step. However, the effects of graph sparsity and topological structure on the transferability of downsampling methods have not been rigorously analyzed or theoretically guaranteed, particularly when the topological structure is affected by graph sparsity. In this paper, we introduce a novel downsampling method based on a sparse random graph model and derive an expected upper bound for the transfer error. Our findings show that smaller original graph sizes, higher expected average degrees, and increased sampling rates contribute to reducing this upper bound. Experimental results validate the theoretical predictions. By incorporating both sparsity and topological similarity into the model, this study establishes an upper bound on the transfer error for downsampling in the training of large-scale sparse graphs and provides insight into the influence of topological structure on transfer performance.