EPCF: An Equivariant Positional Propagation Enhanced Graph Neural Network for Collaborative Filtering

Graph neural networks (GNNs) have shown great advantages in collaborative filtering recommender systems due to their capacity to model user–item relationships through information propagation. However, traditional GNN-based recommenders often fail to distinguish nodes with the same local structure, leading to identical representations after propagation. Some studies address this issue by introducing positional encoding. However, most existing positional encoding approaches break the permutation and orthogonal symmetries of graph representations and degrade generalization ability. To address this limitation, we propose EPCF (equivariant positional collaborative filtering), a novel GNN model for collaborative filtering that introduces an equivariant propagation mechanism for Laplacian positional features. The proposed mechanism preserves equivariance of positional features under orthogonal transformations while maintaining the permutation equivariance inherent to graphs, which can improve generalization. The equivariant positional features are further leveraged to guide node embedding propagation. Our experiments on real-world datasets show that EPCF achieves better average performance than the evaluated baselines, achieving average improvements of 7.01% in Recall@20 and 1.17% in area under the curve (AUC) over the strongest baselines. Furthermore, integrating EPCF as a plug-in mechanism into five different GNN backbone models achieves improvements of 23.13% in Recall@20 and 2.14% in AUC across five datasets, demonstrating its generalization capability.