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Graph Neural Networks (GNNs) are currently dominating in modelinggraph-structure data, while their high reliance on graph structure forinference significantly impedes them from widespread applications. By contrast,Graph-regularized MLPs (GR-MLPs) implicitly inject the graph structureinformation into model weights, while their performance can hardly match thatof GNNs in most tasks. This motivates us to study the causes of the limitedperformance of GR-MLPs. In this paper, we first demonstrate that nodeembeddings learned from conventional GR-MLPs suffer from dimensional collapse,a phenomenon in which the largest a few eigenvalues dominate the embeddingspace, through empirical observations and theoretical analysis. As a result,the expressive power of the learned node representations is constrained. Wefurther propose OrthoReg, a novel GR-MLP model to mitigate the dimensionalcollapse issue. Through a soft regularization loss on the correlation matrix ofnode embeddings, OrthoReg explicitly encourages orthogonal node representationsand thus can naturally avoid dimensionally collapsed representations.Experiments on traditional transductive semi-supervised classification tasksand inductive node classification for cold-start scenarios demonstrate itseffectiveness and superiority.

OrthoReg: Improving Graph-regularized MLPs via Orthogonality Regularization