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A classical survey, which is outdated but still relevant as an introduction: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