Graph neural nets

1 Tutorials

Pantelis Elinas wrote a good tutorial. One of his motivating examples is nifty: He argues graph learning is powerful because it includes the fundamental problem of discovering knowledge graphs and thus research discovery. He recommends the following summaries: M. M. Bronstein et al. (2017);M. M. Bronstein et al. (2021);Hamilton (2020);Hamilton, Ying, and Leskovec (2018);Xia et al. (2021).

• Beyond Message Passing, a Physics-Inspired Paradigm for Graph Neural Networks; this is possibly the broadest overview of the field I have seen.
• Thomas Kipf’s summary of the field
• Xavier Besson’s implementation of one graph convnet.
• Chaitanya Joshi’s overviews of spatial graph convnets and his attempt to link them to attention mechanisms.

Chami et al. (2022):

There has been a surge of recent interest in graph representation learning (GRL). GRL methods have generally fallen into three main categories, based on the availability of labelled data. The first, network embedding, focuses on learning unsupervised representations of relational structure. The second, graph regularised neural networks, leverages graphs to augment neural network losses with a regularisation objective for semi-supervised learning. The third, graph neural networks, aims to learn differentiable functions over discrete topologies with arbitrary structure. However, despite the popularity of these areas there has been surprisingly little work on unifying the three paradigms. Here, we aim to bridge the gap between network embedding, graph regularisation and graph neural networks. We propose a comprehensive taxonomy of GRL methods, aiming to unify several disparate bodies of work. Specifically, we propose the GraphEDM framework, which generalises popular algorithms for semi-supervised learning (e.g. GraphSage, GCN, GAT), and unsupervised learning (e.g. DeepWalk, node2vec) of graph representations into a single consistent approach. To illustrate the generality of GraphEDM, we fit over thirty existing methods into this framework. We believe that this unifying view both provides a solid foundation for understanding the intuition behind these methods, and enables future research in the area.

2 Fun tweaks

Distance encoding:

Distance Encoding is a general class of graph-structure-related features that can be utilized by graph neural networks to improve the structural representation power. Given a node set whose structural representation is to be learnt, DE for a node over the graph is defined as a mapping of a set of landing probabilities of random walks from each node of the node set of interest to this node. Distance encoding generally includes measures such as shortest-path-distances and generalised PageRank scores. Distance encoding can be merged into the design of graph neural networks in simple but effective ways: First, we propose DEGNN that utilizes distance encoding as extra node features. We further enhance DEGNN by allowing distance encoding to control the aggregation procedure of traditional GNNs, which yields another model DEAGNN. Since distance encoding purely depends on the graph structure and is independent from node identifiers, it has inductive and generalisation ability.

3 Background: Graph filtering

Some of the field seems to be based upon more classic linear systems theory applied to networks in the form of spectral graph theory. See signal processing on graphs.

4 Connection to physics

Bronstein again, Beyond Message Passing, a Physics-Inspired Paradigm for Graph Neural Networks.

5 Relationship to graphical models

We can understand graphical models as learning causal models, e.g. Yu et al. (2019), Zečević et al. (2021).

6 Tooling

7 References