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 higher-order 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.
Highlights
Many interesting structures found in scientific and industrial applications can be expressed as graphs
Along with automatic differentiation capabilities of neural network software and the availability of predefined layers such as convolution or pooling, this implementation trick allows to implement Graph neural networks (GNNs)-Layer-wise Relevance Propagation (LRP) for complex GNN architectures without much code overhead. This implementation trick is used in a GNN-LRP demo code that we provide at https://git.tu-berlin.de/thomas schnake/demo gnn lrp
The graph isomorphism network (GIN) receives as input the connectivity matrix Λ = A/2 where A is the adjacency matrix augmented with self-connections
Summary
Many interesting structures found in scientific and industrial applications can be expressed as graphs. The conceptual starting point of our method is the observation that the function implemented by the GNN is locally polynomial with the input graph. This function can be analyzed using a higher-order Taylor expansion to arrive at an attribution of the GNN prediction on collections of edges, e.g. walks into the input graph. We find that the higher-order expansion can be expressed as a nesting of multiple first-order expansions, starting at the top layer of the GNN and moving towards the input layer This theoretical insight enables a principled adaptation of the Layer-wise Relevance Propagation (LRP) [16] explanation technique to GNN models, where the propagation procedure is guided along individual walks in the input graph. The code for this paper can be found at https://git. tu-berlin.de/thomas schnake/paper gnn lrp
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