# Graph Neural Networks

## Type

Master's thesis / guided research

## Prerequisites

- Basic knowledge of deep learning
- Either a background in (1) functional analysis (for more theoretical projects) and or (2) proficiency with PyTorch or Tensorflow (for more applied projects)
- An eagerness to learn more functional analysis and PyTorch/Tensorflow

## Description

In many applications in data science, like social networks, chemistry, recommendation systems, knowledge graphs, traffic networks, and functional brain networks, the data is represented by graphs. Graph neural networks (GNNs) extend classical deep learning methods to graph-structured data and have achieved resounding success in the past few years. By now, GNNs are ubiquitous both in the industry and the applied sciences. Since graphs are irregular objects, graph neural networks present challenging problems, such as how to define convolution on graphs, how to train a network on certain graphs and apply it to other graphs, how to define a convolutional network that is stable and robust to domain perturbations, and how to determine the expressive capacity of graph neural networks. Contemporary research focuses on such questions, which span the spectrum between theoretical analysis and application.

## References

#### General geometric deep learning surveys

A classical survey, which is outdated but still relevant as an introduction:

Geometric deep learning: going beyond Euclidean data

https://arxiv.org/abs/1611.08097

#### A more recent and comprehensive survey

A Comprehensive Survey on Graph Neural Networks

https://arxiv.org/abs/1901.00596

#### A more recent survey from a graph signal processing point of view

Graph signal processing for machine learning: A review and new perspectives

https://arxiv.org/abs/2007.16061

#### Two classical spectral and spatial methods

Convolutional Neural Networks on Graphs with Fast Localized Spectral Filtering

https://arxiv.org/abs/1606.09375

Neural Message Passing for Quantum Chemistry

https://arxiv.org/pdf/1704.01212.pdf

#### Papers about transferability, stability, and robustness

Transferability of Spectral Graph Convolutional Neural Networks

https://arxiv.org/abs/1907.12972

Certifiable Robustness and Robust Training for Graph Convolutional Networks

https://arxiv.org/pdf/1906.12269.pdf

#### Expressivity

How Powerful are Graph Neural Networks?

https://arxiv.org/pdf/1810.00826.pdf