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.

Graph motifs capture crucial structural patterns within user–item interaction graphs and offer meaningful semantics that are typically underutilised in conventional graph-based collaborative filtering. Existing contrastive learning methods in recommender systems rely primarily on simple perturbations, which limits their ability to leverage deeper motif-based structural information. To address this gap, we propose a novel motif-guided contrastive learning framework for recommender systems. To exploit complementary structural biases inherent to user–item interactions, our approach explicitly incorporates three distinct motifs into the construction of the contrastive view. By contrasting views that capture the structural differences among different motifs, our model learns meaningful group-level relationships and potentially suppresses noise arising from sparse or isolated interactions. Extensive experiments on four real-world recommendation datasets validate that our motif-based contrastive approach achieves the best overall performance, outperforming state-of-the-art baselines on three of the four benchmarks with statistically significant margins on the more skewed datasets, while remaining competitive on the fourth, which demonstrates notable robustness and improved accuracy.