Explaining graph neural networks (GNNs) is a key approach to improve the trustworthiness of GNN in high-stakes applications, such as finance and healthcare. However, existing methods are vulnerable to perturbations, raising concerns about explanation reliability. Prior methods enhance explanation robustness using model retraining or explanation ensemble, with certain weaknesses. Retraining leads to models that are different from the original target model and misleading explanations, while ensemble can produce contradictory results due to different inputs or models. To improve explanation robustness without the above weaknesses, we take an unexplored route and exploit the two edge geometry properties curvature and resistance to enhance explanation robustness. We are the first to prove that these geometric notions can be used to bound explanation robustness. We design a general optimization algorithm to incorporate these geometric properties into a wide spectrum of base GNN explanation methods to enhance the robustness of base explanations. We empirically show that our method outperforms six base explanation methods in robustness across nine datasets spanning node classification, link prediction, and graph classification tasks, improving fidelity in 80% of the cases and achieving up to a 10% relative improvement in robust performance.

Through the introduction of a diffusion-convolution operation, we show how diffusion-based representations can be learned from graphstructured data and used as an effective basis for node classification. DCNNs have several attractive qualities, including a latent representation for graphical data that is invariant under isomorphism, as well as polynomial-time prediction and learning that can be represented as tensor operations and efficiently implemented on a GPU. Through several experiments with real structured datasets, we demonstrate that DCNNs are able to outperform probabilistic relational models and kernel-on-graph methods at relational node classification tasks.

Additionally,wepropose theGraphCroc, anewGAE thatsupports flexible encoder architectures tailored forvarious downstream tasksand ensures robust structural reconstruction, through a mirrored encoding-decoding process.

We thank all reviewers for the comments and the following response will be reflected in the final version. In fact, the convergence is exponential both in theory and in practice. Duchi et al. (2008) has proposed an Thus we focus on the comparison in the graph classification task. More experiments will be added. Global methods like Geom-GCN employ additional embedding approaches to capture global information.

Organization In Section A, we first introduce the baselines and our model and then describe the experimental details of graph classification and link prediction tasks but also our in-depth analyses. Then, in Section B, we provide the additional experimental results about analyses on datasets, ablation study for our proposed objectives, effects of our hyperparameters (λ1, α, λ2, and the perturbation magnitude), ablation study of attribute masking, and the comparison with augmentation-freeapproaches. In particular,thepre-training dataset consists of306K unlabeled protein ego-networksof50species,andthe fine-tuning dataset consists of 88K protein ego-networks of 8 species with the label given by the functionalityoftheegoprotein. For pre-training, the number of epochs is 100, the batch size is128, the learning rate is0.001, and the margin is10. For fine-tuning, we also follow the conventional setting from Hu et al.[3]. ForJOAOandGraphLoG, we use the publicsource codes4,toobtain the pre-trained models.

Recently, Graph Neural Networks (GNNs) have gained popularity in a variety of real-world scenarios. Despite the great success, the architecture design of GNNs heavily relies on manual labor. Thus, automated graph neural network (AutoGNN) has attracted interest and attention from the research community, which makes significant performance improvements in recent years.

SGD optimizer is set with momentum of 0.9. This is consistent with the choice of GA T where additive attention is used. Figure B.1: Ranking analysis for a new GNN design dimension Attention 14 B.2 Case Study: Link Prediction as a New Type of T asks Our GNN design framework is applicable to other graph learning tasks beyond node or graph classification tasks. Here we include additional results for link prediction tasks. The extended task space is shown in Figure B.2. Figure B.2: GNN task space for a new type of GNN tasks Link Prediction In Table C.1, we show the best GNN design that we discover for each task in the main manuscript.