Revisit Orthogonality in Graph-Regularized MLPs

This paper introduces OrthoReg, a simple yet effective Graph-regularized MLP model for semi-supervised node representation learning. We first demonstrate, through empirical observations and theoretical analysis, that node embeddings learned from conventional GR-MLPs suffer from the over-correlation issue. This issue arises when a few dominant singular values overwhelm the embedding space, leading to the limited expressive power of the learned node representations. To mitigate this problem, we propose a novel GR-MLP model called OrthoReg. By incorporating a soft regularization loss on the correlation matrix of node embeddings, OrthoReg explicitly encourages orthogonal node representations, effectively avoiding over-correlated representations. Compared to the currently popular GNN models, our OrthoReg possesses two distinct advantages: 1) Much faster inference speed, particularly for large-scale graphs. 2) Significantly superior performance in inductive cold-start settings. Experiments on semi-supervised node classification tasks, together with the extensive ablation studies, have demonstrated the effectiveness of the proposed designs.