# Graph Kernel Neural Networks

**Authors:** Luca Cosmo, Giorgia Minello, Michael Bronstein, Emanuele Rodolà, Luca Rossi, Andrea Torsello  
**arXiv:** [2112.07436](https://arxiv.org/abs/2112.07436)  
**Date:** 2021-12-14  
**Summary page:** https://www.summarizepaper.com/en/paper/2112.07436v1/

## Key points

- Paper introduces a novel approach to extending convolution operator for graphs
- Graphs pose a challenge due to their irregular structure
- Authors propose using graph kernels to address this issue
- Incorporating graph kernels into convolution operator enables structural model without computing input graph embedding
- Architecture is flexible in accommodating different types and numbers of graph kernels
- Offers interpretability through learned structural masks during training
- Extensive ablation study conducted to investigate impact of model hyperparameters
- Competitive performance demonstrated on standard graph classification datasets
- Enables application of convolutional operations on graphs using graph kernels

## Summary

The paper titled "Graph Kernel Neural Networks" introduces a novel approach to extending the convolution operator, commonly used in neural architectures for image data, to work effectively on graphs. Graphs, with their irregular structure, pose a challenge when applying convolutional operations. To address this issue, the authors propose using graph kernels which are kernel functions that compute an inner product on graphs. By incorporating graph kernels into the standard convolution operator they develop a structural model that does not require computing the embedding of the input graph. One key advantage of this architecture is its flexibility in accommodating different types and numbers of graph kernels. Additionally, it offers interpretability through the learned structural masks during training similar to traditional convolutional neural networks' convolutional masks. The authors conduct an extensive ablation study to investigate the impact of model hyperparameters and demonstrate competitive performance on standard graph classification datasets. Overall, this paper presents a significant contribution by enabling the application of convolutional operations on graphs using graph kernels. The proposed architecture not only overcomes the challenges posed by irregular graph structures but also provides interpretability and achieves promising results in graph classification tasks.