Graph Information Vanishing Phenomenon in Implicit Graph Neural Networks

Graph neural networks (GNNs) have been highly successful in graph representation learning. The goal of GNNs is to enrich node representations by aggregating information from neighboring nodes. Much work has attempted to improve the quality of aggregation by introducing a variety of graph information with representational capabilities. The class of GNNs that improves the quality of aggregation by encoding graph information with representational capabilities into the weights of neighboring nodes through different learnable transformation structures (LTSs) are referred to as implicit GNNs. However, we argue that LTSs only transform graph information into the weights of neighboring nodes in the direction that minimizes the loss function during the learning process and does not actually utilize the effective properties of graph information, a phenomenon that we refer to as graph information vanishing (GIV). To validate this point, we perform thousands of experiments on seven node classification benchmark datasets. We first replace the graph information utilized by five implicit GNNs with random values and surprisingly observe that the variation range of accuracies is less than +/- 0.3%. Then, we quantitatively characterize the similarity of the weights generated from graph information and random values by cosine similarity, and the cosine similarities are greater than 0.99. The empirical experiments show that graph information is equivalent to initializing the input of LTSs. We believe that graph information as an additional supervised signal to constrain the training of GNNs can effectively solve GIV. Here, we propose GinfoNN, which utilizes both labels and discrete graph curvature as supervised signals to jointly constrain the training of the model. The experimental results show that the classification accuracies of GinfoNN improve by two percentage points over baselines on large and dense datasets.