Label Propagation Algorithm (LPA) and Graph Convolutional Neural Networks (GCN) are both message passing algorithms on graphs. Both solve the task of node classification, but LPA propagates node label information across the edges of the graph, while GCN propagates and transforms node feature information. However, while conceptually similar, theoretical relationship between LPA and GCN has not yet been systematically investigated. Moreover, it is unclear how LPA and GCN can be combined under a unified framework to improve the performance. Here we study the relationship between LPA and GCN in terms of
, in which we characterize how much the initial feature/label of one node influences the final feature/label of another node in GCN/LPA. Based on our theoretical analysis, we propose an end-to-end model that combines GCN and LPA. In our unified model, edge weights are learnable, and the LPA serves as regularization to assist the GCN in learning proper edge weights that lead to improved performance. Our model can also be seen as learning the weights of edges based on node labels, which is more direct and efficient than existing feature-based attention models or topology-based diffusion models. In a number of experiments for semi-supervised node classification and knowledge-graph-aware recommendation, our model shows superiority over state-of-the-art baselines.
Message passing algorithms, whose iterative nature captures well complicated interactions among interconnected variables in complex systems and extracts information from the fixed point of iterated messages, provide a powerful toolkit in tackling hard computational tasks in optimization, inference, and learning problems. In the context of constraint satisfaction problems (CSPs), when a control parameter (such as constraint density) is tuned, multiple threshold phenomena emerge, signaling fundamental structural transitions in their solution space. Finding solutions around these transition points is exceedingly challenging for algorithm design, where message passing algorithms suffer from a large message fluctuation far from convergence. Here we introduce a residual-based updating step into message passing algorithms, in which messages varying large between consecutive steps are given a high priority in updating process. For the specific example of model RB, a typical prototype of random CSPs with growing domains, we show that our algorithm improves the convergence of message updating and increases the success probability in finding solutions around the satisfiability threshold with a low computational cost. Our approach to message passing algorithms should be of value for exploring their power in developing algorithms to find ground-state solutions and understand the detailed structure of solution space of hard optimization problems.
Graph neural network (GNN) and label propagation algorithm (LPA) are both message passing algorithms, which have achieved superior performance in semi-supervised classification. GNN performs feature propagation by a neural network to make predictions, while LPA uses label propagation across graph adjacency matrix to get results. However, there is still no effective way to directly combine these two kinds of algorithms. To address this issue, we propose a novel Unified Message Passaging Model (UniMP) that can incorporate feature and label propagation at both training and inference time. First, UniMP adopts a Graph Transformer network, taking feature embedding and label embedding as input information for propagation. Second, to train the network without overfitting in self-loop input label information, UniMP introduces a masked label prediction strategy, in which some percentage of input label information are masked at random, and then predicted. UniMP conceptually unifies feature propagation and label propagation and is empirically powerful. It obtains new state-of-the-art semi-supervised classification results in Open Graph Benchmark (OGB).