Considering the complex graph structure, are some nodes consistently well-trained and following this principle even with different graph augmentations?

Graph Contrastive Learning (GCL) has emerged as a popular training approach for learning node embeddings from augmented graphs without labels. Despite the key principle that maximizing the similarity between positive node pairs while minimizing it between negative node pairs is well established, some fundamental problems are still unclear. Considering the complex graph structure, are some nodes consistently well-trained and following this principle even with different graph augmentations? Or are there some nodes more likely to be untrained across graph augmentations and violate the principle? How to distinguish these nodes and further guide the training of GCL?

Generalizable, transferrable, and robust representation learning on graph-structured data remains a challenge for current graph neural networks (GNNs). Unlike what has been developed for convolutional neural networks (CNNs) for image data, self-supervised learning and pre-training are less explored for GNNs. In this paper, we propose a graph contrastive learning (GraphCL) framework for learning unsupervised representations of graph data. We first design four types of graph augmentations to incorporate various priors. We then systematically study the impact of various combinations of graph augmentations on multiple datasets, in four different settings: semi-supervised, unsupervised, and transfer learning as well as adversarial attacks. The results show that, even without tuning augmentation extents nor using sophisticated GNN architectures, our GraphCL framework can produce graph representations of similar or better generalizability, transferrability, and robustness compared to state-of-the-art methods. We also investigate the impact of parameterized graph augmentation extents and patterns, and observe further performance gains in preliminary experiments.

Graph Contrastive Learning (GCL), learning the node representations by augmenting graphs, has attracted considerable attentions. Despite the proliferation of various graph augmentation strategies, there are still some fundamental questions unclear: what information is essentially learned by GCL? Are there some general augmentation rules behind different augmentations? If so, what are they and what insights can they bring? In this paper, we answer these questions by establishing the connection between GCL and graph spectrum. By an experimental investigation in spectral domain, we firstly find the General grAph augMEntation (GAME) rule for GCL, i.e., the difference of the high-frequency parts between two augmented graphs should be larger than that of low-frequency parts. This rule reveals the fundamental principle to revisit the current graph augmentations and design new effective graph augmentations. Then we theoretically prove that GCL is able to learn the invariance information by contrastive invariance theorem, together with our GAME rule, for the first time, we uncover that the learned representations by GCL essentially encode the low-frequency information, which explains why GCL works. Guided by this rule, we propose a spectral graph contrastive learning module (SpCo), which is a general and GCL-friendly plug-in. We combine it with different existing GCL models, and extensive experiments well demonstrate that it can further improve the performances of a wide variety of different GCL methods.

Considering the complex graph structure, are some nodes consistently well-trained and following this principle even with different graph augmentations?

Nevertheless, unlike images, it is much more difficult to design reasonable augmentations without changing the nature of graphs.

Although graph contrastive learning (GCL) has been widely investigated, it is still a challenge to generate effective and stable graph augmentations. Existing methods often apply heuristic augmentation like random edge dropping, which may disrupt important graph structures and result in unstable GCL performance. In this paper, we propose Positive-incentive Noise driven Graph Data Augmentation (PiNGDA), where positive-incentive noise (pi-noise) scientifically analyzes the beneficial effect of noise under the information theory. To bridge the standard GCL and pi-noise framework, we design a Gaussian auxiliary variable to convert the loss function to information entropy. We prove that the standard GCL with pre-defined augmentations is equivalent to estimate the beneficial noise via the point estimation. Following our analysis, PiNGDA is derived from learning the beneficial noise on both topology and attributes through a trainable noise generator for graph augmentations, instead of the simple estimation. Since the generator learns how to produce beneficial perturbations on graph topology and node attributes, PiNGDA is more reliable compared with the existing methods. Extensive experimental results validate the effectiveness and stability of PiNGDA.

Graph Neural Networks (GNNs) update node representations through message passing, which is primarily based on the homophily principle, assuming that adjacent nodes share similar features. However, in real-world graphs with long-tailed degree distributions, high-degree nodes dominate message passing, causing a degree bias where low-degree nodes remain under-represented due to inadequate messages. The main challenge in addressing degree bias is how to discover non-adjacent nodes to provide additional messages to low-degree nodes while reducing excessive messages for high-degree nodes. Nevertheless, exploiting non-adjacent nodes to provide valuable messages is challenging, as it could generate noisy information and disrupt the original graph structures. To solve it, we propose a novel Degree Fairness Graph Transformer, named DegFairGT, to mitigate degree bias by discovering structural similarities between non-adjacent nodes through learnable structural augmentation and structural self-attention. Our key idea is to exploit non-adjacent nodes with similar roles in the same community to generate informative edges under our augmentation, which could provide informative messages between nodes with similar roles while ensuring that the homophily principle is maintained within the community. To enable DegFairGT to learn such structural similarities, we then propose a structural self-attention to capture the similarities between node pairs. To preserve global graph structures and prevent graph augmentation from hindering graph structure, we propose a Self-Supervised Learning task to preserve p-step transition probability and regularize graph augmentation. Extensive experiments on six datasets showed that DegFairGT outperformed state-of-the-art baselines in degree fairness analysis, node classification, and node clustering tasks.