Higher-Order Explanations of Graph Neural Networks via Relevant Walks

Thomas Schnake, Oliver Eberle, Jonas Lederer, Shinichi Nakajima, Kristof T. Schütt, Klaus-Robert Müller, Grégoire Montavon

Abstract: Graph Neural Networks (GNNs) are a popular approach for predicting graph structured data. As GNNs tightly entangle the input graph into the neural network structure, common explainable AI approaches are not applicable. To a large extent, GNNs have remained black-boxes for the user so far. In this paper, we show that GNNs can in fact be naturally explained using <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">higher-order</i> expansions, i.e., by identifying groups of edges that jointly contribute to the prediction. Practically, we find that such explanations can be extracted using a nested attribution scheme, where existing techniques such as layer-wise relevance propagation (LRP) can be applied at each step. The output is a collection of walks into the input graph that are relevant for the prediction. Our novel explanation method, which we denote by GNN-LRP, is applicable to a broad range of graph neural networks and lets us extract practically relevant insights on sentiment analysis of text data, structure-property relationships in quantum chemistry, and image classification.