【文献笔记】How powerful are graph neural networks?

Abstract

What do the author(s) want to know (motivation)?

• representational properties and limitations of GNN
• theoretical analysis of the expressibility of GNN
• Graph Isomorphism Network (GIN)
• validation

1 Introduction

Insight: GNN $\to$ WL-test if aggr is expressive and can model injective functions

2 Preliminaries

GNN

• GraphSAGE
  • W: learnable matrix
  • COMBINE: concatenation + linear mapping
• GCN
  

WL-test: whether two graphs are topologically identical

3 Theory framework: overview

A maximally powerful GNN would never map two different neighborhoods, i.e., multisets of feature vectors, to the same representation. This means its aggregation scheme must be injective. Thus, we abstract a GNN’s aggregation scheme as a class of different neighborhoods, i.e., multisets of feature vectors, to the same representation. This means its aggregation scheme must be injective.

4 Building powerful graph neural networks

GIN

5 Less powerful but still interesting GNNs

- 1-layer perceptrons are not sufficient

- structures that confuse mean and max-pooling

• permutation invariant but not injective

- mean learns distributions

The mean aggregator may perform well if, for the task, the statistical and distributional information in the graph is more important than the exact structure.

- max-pooling learns sets with distinct elements

7 Experiments

model parameters

• 5 GNN + 2 MLP
• batch normalization
• Adam, lr = 0.01, decay by 0.5 every 50 epochs

Results: GIN-0