# Convolutional Neural Networks on Graphs with Fast Localized Spectral Filtering

**Authors:** Michaël Defferrard, Xavier Bresson, Pierre Vandergheynst  
**arXiv:** [1606.09375](https://arxiv.org/abs/1606.09375)  
**Date:** 2016-06-30  
**Summary page:** https://www.summarizepaper.com/en/paper/1606.09375v3/

## Key points

- Authors aim to extend the application of CNNs from regular grids to irregular domains represented by graphs
- Proposed formulation of CNNs based on spectral graph theory
- Mathematical framework provides background and efficient numerical schemes for designing fast localized convolutional filters on graphs
- Technique maintains linear computational complexity and constant learning complexity as traditional CNNs
- Applicable to any graph structure
- Validated through experiments on MNIST and 20NEWS datasets
- Results demonstrate effective learning of local, stationary, and compositional features on graphs

## Summary

In their work titled "Convolutional Neural Networks on Graphs with Fast Localized Spectral Filtering," authors Michaël Defferrard, Xavier Bresson, and Pierre Vandergheynst aim to extend the application of convolutional neural networks (CNNs) from low-dimensional regular grids to high-dimensional irregular domains represented by graphs. These irregular domains include social networks, brain connectomes, and word embeddings. To achieve this, the authors propose a formulation of CNNs based on spectral graph theory. This mathematical framework provides the necessary background and efficient numerical schemes for designing fast localized convolutional filters on graphs. Importantly, their technique maintains the same linear computational complexity and constant learning complexity as traditional CNNs while being applicable to any graph structure. The authors validate their approach through experiments conducted on MNIST and 20NEWS datasets. The results demonstrate that their novel deep learning system can effectively learn local, stationary, and compositional features on graphs. Overall, this work presents a significant advancement in generalizing CNNs to high-dimensional irregular domains represented by graphs. By leveraging spectral graph theory which enables efficient computation of localized convolutional filters while maintaining the universality of application across various graph structures; this technique maintains the same linear computational complexity and constant learning complexity as traditional CNNs. The experiments conducted on MNIST and 20NEWS datasets demonstrate that this novel deep learning system can effectively learn local, stationary, and compositional features on graphs.