Recent progress in Graph Neural Networks has resulted in wide adoption by many applications, including recommendation systems. The reason for Graph Neural Networks' superiority over other approaches is that many problems in recommendation systems can be naturally modeled as graphs, where nodes can be either users or items and edges represent preference relationships. In current Graph Neural Network approaches, nodes are represented with a static vector learned at training time. This static vector might only be suitable to capture some of the nuances of users or items they define. To overcome this limitation, we propose using a recently proposed model inspired by category theory: Sheaf Neural Networks. Sheaf Neural Networks, and its connected Laplacian, can address the previous problem by associating every node (and edge) with a vector space instead than a single vector. The vector space representation is richer and allows picking the proper representation at inference time. This approach can be generalized for different related tasks on graphs and achieves state-of-the-art performance in terms of F1-Score@N in collaborative filtering and Hits@20 in link prediction. For collaborative filtering, the approach is evaluated on the MovieLens 100K with a 5.1% improvement, on MovieLens 1M with a 5.4% improvement and on Book-Crossing with a 2.8% improvement, while for link prediction on the ogbl-ddi dataset with a 1.6% refinement with respect to the respective baselines.

翻译：图神经网络的最新进展使其在众多应用中得到了广泛采纳，包括推荐系统。图神经网络优于其他方法的原因在于，推荐系统中的许多问题可以自然地建模为图结构，其中节点代表用户或物品，边表示偏好关系。当前图神经网络方法中，节点通过训练时学习得到的静态向量表示。这种静态向量可能仅适用于捕捉所定义用户或物品的部分细微特征。为克服这一局限，我们提出采用一种受范畴论启发的最新模型：层状神经网络（Sheaf Neural Networks）。层状神经网络及其关联的拉普拉斯算子通过将每个节点（和边）与向量空间而非单个向量关联，能够解决前述问题。向量空间表示更为丰富，允许在推理时选择合适的表征。该方法可推广至图上的不同相关任务，并在协同过滤的F1-Score@N指标和链接预测的Hits@20指标上取得了最先进性能。在协同过滤任务中，该方法在MovieLens 100K数据集上提升5.1%，在MovieLens 1M数据集上提升5.4%，在Book-Crossing数据集上提升2.8%；在链接预测任务中，相较于基线方法，该方法在ogbl-ddi数据集上实现1.6%的改进。