We propose a new self-explainable Graph Neural Network (GNN) model: GraphChef. GraphChef integrates decision trees into the GNN message passing framework. Given a dataset, GraphChef returns a set of rules (a recipe) that explains each class in the dataset unlike existing GNNs and explanation methods that reason on individual graphs. Thanks to the decision trees, GraphChef recipes are human understandable. We also present a new pruning method to produce small and easy to digest trees. Experiments demonstrate that GraphChef reaches comparable accuracy to not self-explainable GNNs and produced decision trees are indeed small. We further validate the correctness of the discovered recipes on datasets where explanation ground truth is available: Reddit-Binary, MUTAG, BA-2Motifs, BA-Shapes, Tree-Cycle, and Tree-Grid.

We study the problem of learning comparisons between numbers with neural networks. Despite comparisons being a seemingly simple problem, we find that both general-purpose models such as multilayer perceptrons (MLPs) as well as arithmetic architectures such as the Neural Arithmetic Logic Unit (NALU) struggle with learning comparisons. Neither architecture can extrapolate to much larger numbers than those seen in the training set. We propose a novel differentiable architecture, the Neural Status Register (NSR) to solve this problem. We experimentally validate the NSR in various settings. We can combine the NSR with other neural models to solve interesting problems such as piecewise-defined arithmetic, comparison of digit images, recurrent problems, or finding shortest paths in graphs. The NSR outperforms all baseline architectures, especially when it comes to extrapolating to larger numbers.

We study the evaluation of graph explanation methods. The state of the art to evaluate explanation methods is to first train a GNN, then generate explanations, and finally compare those explanations with the ground truth. We show five pitfalls that sabotage this pipeline because the GNN does not use the ground-truth edges. Thus, the explanation method cannot detect the ground truth. We propose three novel benchmarks: (i) pattern detection, (ii) community detection, and (iii) handling negative evidence and gradient saturation. In a re-evaluation of state-of-the-art explanation methods, we show paths for improving existing methods and highlight further paths for GNN explanation research.

This paper studies Dropout Graph Neural Networks (DropGNNs), a new approach that aims to overcome the limitations of standard GNN frameworks. In DropGNNs, we execute multiple runs of a GNN on the input graph, with some of the nodes randomly and independently dropped in each of these runs. Then, we combine the results of these runs to obtain the final result. We prove that DropGNNs can distinguish various graph neighborhoods that cannot be separated by message passing GNNs. We derive theoretical bounds for the number of runs required to ensure a reliable distribution of dropouts, and we prove several properties regarding the expressive capabilities and limits of DropGNNs. We experimentally validate our theoretical findings on expressiveness. Furthermore, we show that DropGNNs perform competitively on established GNN benchmarks.

The increasing scale of encyclopedic knowledge graphs (KGs) calls for summarization as a way to help users efficiently access and distill world knowledge. Motivated by the disparity between individuals' limited information needs and the massive scale of KGs, in this paper we propose a new problem called personalized knowledge graph summarization. The goal is to construct compact "personal summaries" of KGs containing only the facts most relevant to individuals' interests. Such summaries can be stored and utilized on-device, allowing individuals private, anytime access to the information that interests them most. We formalize the problem as one of constructing a sparse graph, or summary, that maximizes a user's inferred "utility" over a given KG, subject to a user-and device-specific constraint on the summary's size. To solve it, we propose GLIMPSE, a summarization framework that provides theoretical guarantees on the summary's utility and is linear in the number of edges in the KG. In an evaluation with real user queries to open-source, encyclopedic KGs of up to one billion triples, we show that GLIMPSE efficiently creates summaries that outperform strong baselines by up to 19% in query answering F1 score.