Graph Neural Networks Use Graphs When They Shouldn't

Predictions over graphs play a crucial role in various domains, including social networks, molecular biology, medicine, and more. Graph Neural Networks (GNNs) have emerged as the dominant approach for learning on graph data. Instances of graph labeling problems consist of the graph-structure (i.e., the adjacency matrix), along with node-specific feature vectors. In some cases, this graph-structure is non-informative for the predictive task. For instance, molecular properties such as molar mass depend solely on the constituent atoms (node features), and not on the molecular structure. While GNNs have the ability to ignore the graph-structure in such cases, it is not clear that they will. In this work, we show that GNNs actually tend to overfit the graph-structure in the sense that they use it even when a better solution can be obtained by ignoring it. We examine this phenomenon with respect to different graph distributions and find that regular graphs are more robust to this overfitting. We then provide a theoretical explanation for this phenomenon, via analyzing the implicit bias of gradient-descent-based learning of GNNs in this setting. Finally, based on our empirical and theoretical findings, we propose a graph-editing method to mitigate the tendency of GNNs to overfit graph-structures that should be ignored. We show that this method indeed improves the accuracy of GNNs across multiple benchmarks.

Graph Trees with Attention

When dealing with tabular data, models based on regression and decision trees are a popular choice due to the high accuracy they provide on such tasks and their ease of application as compared to other model classes. Yet, when it comes to graph-structure data, current tree learning algorithms do not provide tools to manage the structure of the data other than relying on feature engineering. In this work we address the above gap, and introduce Graph Trees with Attention (GTA), a new family of tree-based learning algorithms that are designed to operate on graphs. GTA leverages both the graph structure and the features at the vertices and employs an attention mechanism that allows decisions to concentrate on sub-structures of the graph. We analyze GTA models and show that they are strictly more expressive than plain decision trees. We also demonstrate the benefits of GTA empirically on multiple graph and node prediction benchmarks. In these experiments, GTA always outperformed other tree-based models and often outperformed other types of graph-learning algorithms such as Graph Neural Networks (GNNs) and Graph Kernels. Finally, we also provide an explainability mechanism for GTA, and demonstrate it can provide intuitive explanations.