In this paper, we first mathematically formulate thetwochallenging problems forgraph data andtake an initiative on tackling them under a unified probabilistic model.

To summarize, graph condensation task holds great promise and is expected to bring significant benefits to various graph learning tasks and applications.

With the explosive growth of information technology, multi-view graph data have become increasingly prevalent and valuable. Most existing multi-view clustering techniques either focus on the scenario of multiple graphs or multi-view attributes. In this paper, we propose a generic framework to cluster multi-view attributed graph data. Specifcally, inspired by the success of contrastive learning, we propose multi-view contrastive graph clustering (MCGC) method to learn a consensus graph since the original graph could be noisy or incomplete and is not directly applicable. Our method composes of two key steps: we frst flter out the undesirable highfrequency noise while preserving the graph geometric features via graph fltering and obtain a smooth representation of nodes; we then learn a consensus graph regularized by graph contrastive loss. Results on several benchmark datasets show the superiority of our method with respect to state-of-the-art approaches. In particular, our simple approach outperforms existing deep learning-based methods.

Pseudo labeling (PL) is a wide-applied strategy to enlarge the labeled dataset by self-annotating the potential samples during the training process. Several works have shown that it can improve the graph learning model performance in general. However, we notice that the incorrect labels can be fatal to the graph training process. Inappropriate PL may result in the performance degrading, especially on graph data where the noise can propagate. Surprisingly, the corresponding error is seldom theoretically analyzed in the literature.

Graph neural networks (GNNs) are recognized for their strong performance across various applications, with the backpropagation (BP) algorithm playing a central role in the development of most GNN models. However, despite its effectiveness, BP has limitations that challenge its biological plausibility and affect the efficiency, scalability and parallelism of training neural networks for graph-based tasks. While several non-backpropagation (non-BP) training algorithms, such as the direct feedback alignment (DFA), have been successfully applied to fully-connected and convolutional network components for handling Euclidean data, directly adapting these non-BP frameworks to manage non-Euclidean graph data in GNN models presents significant challenges. These challenges primarily arise from the violation of the independent and identically distributed (i.i.d.) assumption in graph data and the difficulty in accessing prediction errors for all samples (nodes) within the graph. To overcome these obstacles, in this paper we propose DFA-GNN, a novel forward learning framework tailored for GNNs with a case study of semi-supervised learning.

Semi-implicit graph variational auto-encoder (SIG-VAE) is proposed to expand the flexibility of variational graph auto-encoders (VGAE) to model graph data. SIG-VAE employs a hierarchical variational framework to enable neighboring node sharing for better generative modeling of graph dependency structure, together with a Bernoulli-Poisson link decoder. Not only does this hierarchical construction provide a more flexible generative graph model to better capture real-world graph properties, but also does SIG-VAE naturally lead to semi-implicit hierarchical variational inference that allows faithful modeling of implicit posteriors of given graph data, which may exhibit heavy tails, multiple modes, skewness, and rich dependency structures. SIG-VAE integrates a carefully designed generative model, well suited to model real-world sparse graphs, and a sophisticated variational inference network, which propagates the graph structural information and distribution uncertainty to capture complex posteriors. SIG-VAE clearly outperforms a simple combination of VGAE with variational inference, including semi-implicit variational inference~(SIVI) or normalizing flow (NF), which does not propagate uncertainty in its inference network, and provides more interpretable latent representations than VGAE does. Extensive experiments with a variety of graph data show that SIG-VAE significantly outperforms state-of-the-art methods on several different graph analytic tasks.

However, their performance often hinges on high-quality node labels, which are challenging to obtain in real-world scenarios due to unreliable sources or adversarial attacks. Consequently, label noise is common in real-world graph data, negatively impacting GNNs by propagating incorrect information during training. To address this issue, the study of Graph Neural Networks under Label Noise (GLN) has recently gained traction. However, due to variations in dataset selection, data splitting, and preprocessing techniques, the community currently lacks a comprehensive benchmark, which impedes deeper understanding and further development of GLN. To fill this gap, we introduce NoisyGL in this paper, the first comprehensive benchmark for graph neural networks under label noise. NoisyGL enables fair comparisons and detailed analyses of GLN methods on noisy labeled graph data across various datasets, with unified experimental settings and interface. Our benchmark has uncovered several important insights that were missed in previous research, and we believe these findings will be highly beneficial for future studies. We hope our open-source benchmark library will foster further advancements in this field.

Despite the remarkable success of graph neural networks (GNNs) for graph representation learning, they are generally built on the (unreliable) i.i.d.