Message Passing Neural Networks (MPNNs) have demonstrated remarkable success in node classification on homophilic graphs. It has been shown that they do not solely rely on homophily but on neighborhood distributions of nodes, i.e., consistency of the neighborhood label distribution within the same class. MLP-based models do not use message passing, \eg Graph-MLP incorporates the neighborhood in a separate loss function. These models are faster and more robust to edge noise. Graph-MLP maps adjacent nodes closer in the embedding space but is unaware of the neighborhood pattern of the labels, i.e., relies solely on homophily. Edge Splitting GNN (ES-GNN) is a model specialized for heterophilic graphs and splits the edges into task-relevant and task-irrelevant, respectively. To mitigate the limitations of Graph-MLP on heterophilic graphs, we propose ES-MLP that combines Graph-MLP with an edge-splitting mechanism from ES-GNN. It incorporates the edge splitting into the loss of Graph-MLP to learn two separate adjacency matrices based on relevant and irrelevant feature pairs. Our experiments on seven datasets with six baselines show that ES-MLP is on par with homophilic and heterophilic models on all datasets without using edges during inference. We show that ES-MLP is robust to multiple types of edge noise during inference and that its inference time is two to five times faster than that of commonly used MPNNs. The source code is available at https://github.com/MatthiasKohn/ES-MLP.

Graph Neural Networks (GNNs) have achieved great success in learning graph representations and thus facilitating various graph-related tasks. However, most GNN methods adopt a supervised learning setting, which is not always feasible in real-world applications due to the difficulty to obtain labeled data. Hence, graph self-supervised learning has been attracting increasing attention. Graph contrastive learning (GCL) is a representative framework for self-supervised learning. In general, GCL learns node representations by contrasting semantically similar nodes (positive samples) and dissimilar nodes (negative samples) with anchor nodes. Without access to labels, positive samples are typically generated by data augmentation, and negative samples are uniformly sampled from the entire graph, which leads to a sub-optimal objective. Specifically, data augmentation naturally limits the number of positive samples that involve in the process (typically only one positive sample is adopted). On the other hand, the random sampling process would inevitably select false-negative samples (samples sharing the same semantics with the anchor). These issues limit the learning capability of GCL. In this work, we propose an enhanced objective that addresses the aforementioned issues. We first introduce an unachievable ideal objective that contains all positive samples and no false-negative samples. This ideal objective is then transformed into a probabilistic form based on the distributions for sampling positive and negative samples. We then model these distributions with node similarity and derive the enhanced objective. Comprehensive experiments on various datasets demonstrate the effectiveness of the proposed enhanced objective under different settings.

Graph Neural Network (GNN) has been demonstrated its effectiveness in dealing with non-Euclidean structural data. Both spatial-based and spectral-based GNNs are relying on adjacency matrix to guide message passing among neighbors during feature aggregation. Recent works have mainly focused on powerful message passing modules, however, in this paper, we show that none of the message passing modules is necessary. Instead, we propose a pure multilayer-perceptron-based framework, Graph-MLP with the supervision signal leveraging graph structure, which is sufficient for learning discriminative node representation. In model-level, Graph-MLP only includes multi-layer perceptrons, activation function, and layer normalization. In the loss level, we design a neighboring contrastive (NContrast) loss to bridge the gap between GNNs and MLPs by utilizing the adjacency information implicitly. This design allows our model to be lighter and more robust when facing large-scale graph data and corrupted adjacency information. Extensive experiments prove that even without adjacency information in testing phase, our framework can still reach comparable and even superior performance against the state-of-the-art models in the graph node classification task.