Title: GraphLog: A Benchmark for Measuring Logical Generalization in Graph Neural Networks. Abstract: Relational inductive biases have a key role in building learning agents that can generalize and reason in a compositional manner. While relational learning algorithms such as graph neural networks (GNNs) show promise, we do not understand their effectiveness to adapt to new tasks. In this work, we study the logical generalization capabilities of GNNs by designing a benchmark suite grounded in first-order logic. Our benchmark suite, GraphLog, requires that learning algorithms perform rule induction in different synthetic logics, represented as knowledge graphs. 
GraphLog consists of relation prediction tasks on 57 distinct procedurally generated logical worlds. We use GraphLog to evaluate GNNs in three different setups: single-task supervised learning, multi-task (with pretraining), and continual learning. Unlike previous benchmarks, GraphLog enables us to precisely control the logical relationship between the different worlds by controlling the underlying first-order logic rules. We find that models' ability to generalize and adapt strongly correlates to the availability of diverse sets of logical rules during multi-task training. We also find the severe catastrophic forgetting effect in continual learning scenarios, and GraphLog provides a precise mechanism to control the distribution shift. Overall, our results highlight new challenges for the design of GNN models, opening up an exciting area of research in generalization using graph-structured data.