Revealing Combinatorial Reasoning of GNNs via Graph Concept Bottleneck Layer

Abstract: Despite their success in various domains, the growing dependence on GNNs raises a critical concern about the nature of the combinatorial reasoning underlying their predictions, which is often hidden within their black-box architectures. Addressing this challenge requires understanding how GNNs translate topological patterns into logical rules. However, current works only uncover the hard logical rules over graph concepts, which cannot quantify the contribution of each concept to prediction. Moreover, they are post-hoc interpretable methods that generate explanations after model training and may not accurately reflect the true combinatorial reasoning of GNNs, since they approximate it with a surrogate. In this work, we develop a graph concept bottleneck layer that can be integrated into any GNN architectures to guide them to predict the selected discriminative global graph concepts. The predicted concept scores are further projected to class labels by a sparse linear layer. It enforces the combinatorial reasoning of GNNs' predictions to fit the soft logical rule over graph concepts and thus can quantify the contribution of each concept. To further improve the quality of the concept bottleneck, we treat concepts as "graph words" and graphs as "graph sentences", and leverage LLMs to learn graph concept embeddings. Extensive experiments on multiple datasets show that our method GCBMs achieve state-of-the-art performance both in classification and interpretability.