Graph neural network (GNN) has shown superior performance in dealing with graphs, which has attracted considerable research attention recently. However, most of the existing GNN models are primarily designed for graphs in Euclidean spaces. Recent research has proven that the graph data exhibits non-Euclidean latent anatomy. Unfortunately, there was rarely study of GNN in non-Euclidean settings so far. To bridge this gap, in this paper, we study the GNN with attention mechanism in hyperbolic spaces at the first attempt. The research of hyperbolic GNN has some unique challenges: since the hyperbolic spaces are not vector spaces, the vector operations (e.g., vector addition, subtraction, and scalar multiplication) cannot be carried. To tackle this problem, we employ the gyrovector spaces, which provide an elegant algebraic formalism for hyperbolic geometry, to transform the features in a graph; and then we propose the hyperbolic proximity based attention mechanism to aggregate the features. Moreover, as mathematical operations in hyperbolic spaces could be more complicated than those in Euclidean spaces, we further devise a novel acceleration strategy using logarithmic and exponential mappings to improve the efficiency of our proposed model. The comprehensive experimental results on four real-world datasets demonstrate the performance of our proposed hyperbolic graph attention network model, by comparisons with other state-of-the-art baseline methods.

Graph-level representation learning is to learn low-dimensional representation for the entire graph, which has shown a large impact on real-world applications. Recently, limited by expensive labeled data, contrastive learning based graph-level representation learning attracts considerable attention. However, these methods mainly focus on graph augmentation for positive samples, while the effect of negative samples is less explored. In this paper, we study the impact of negative samples on learning graph-level representations, and a novel curriculum contrastive learning framework for self-supervised graph-level representation, called CuCo, is proposed. Specifically, we introduce four graph augmentation techniques to obtain the positive and negative samples, and utilize graph neural networks to learn their representations. Then a scoring function is proposed to sort negative samples from easy to hard and a pacing function is to automatically select the negative samples in each training procedure. Extensive experiments on fifteen graph classification real-world datasets, as well as the parameter analysis, well demonstrate that our proposed CuCo yields truly encouraging results in terms of performance on classification and convergence.

Graph neural networks (GNNs) have become the defacto standard for representation learning on graphs, which derive effective node representations by recursively aggregating information from graph neighborhoods. While GNNs can be trained from scratch, pre-training GNNs to learn transferable knowledge for downstream tasks has recently been demonstrated to improve the state of the art. However, conventional GNN pre-training methods follow a two-step paradigm: 1) pre-training on abundant unlabeled data and 2) fine-tuning on downstream labeled data, between which there exists a significant gap due to the divergence of optimization objectives in the two steps. In this paper, we conduct an analysis to show the divergence between pre-training and fine-tuning, and to alleviate such divergence, we propose L2P-GNN, a self-supervised pre-training strategy for GNNs. The key insight is that L2P-GNN attempts to learn how to fine-tune during the pre-training process in the form of transferable prior knowledge. To encode both local and global information into the prior, L2P-GNN is further designed with a dual adaptation mechanism at both node and graph levels. Finally, we conduct a systematic empirical study on the pre-training of various GNN models, using both a public collection of protein graphs and a new compilation of bibliographic graphs for pre-training. Experimental results show that L2P-GNN is capable of learning effective and transferable prior knowledge that yields powerful representations for downstream tasks. (Code and datasets are available at https://github.com/rootlu/L2P-GNN.)

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