Recent advancements in Graph Neural Networks (GNN) have facilitated their widespread adoption in various applications, including recommendation systems. GNNs have proven to be effective in addressing the challenges posed by recommendation systems by efficiently modeling graphs in which nodes represent users or items and edges denote preference relationships. However, current GNN techniques represent nodes by means of a single static vector, which may inadequately capture the intricate complexities of users and items. To overcome these limitations, we propose a solution integrating a cutting-edge model inspired by category theory: Sheaf4Rec. Unlike single vector representations, Sheaf Neural Networks and their corresponding Laplacians represent each node (and edge) using a vector space. Our approach takes advantage from this theory and results in a more comprehensive representation that can be effectively exploited during inference, providing a versatile method applicable to a wide range of graph-related tasks and demonstrating unparalleled performance. Our proposed model exhibits a noteworthy relative improvement of up to 8.53% on F1-Score@10 and an impressive increase of up to 11.29% on NDCG@10, outperforming existing state-of-the-art models such as Neural Graph Collaborative Filtering (NGCF), KGTORe and other recently developed GNN-based models. In addition to its superior predictive capabilities, Sheaf4Rec shows remarkable improvements in terms of efficiency: we observe substantial runtime improvements ranging from 2.5% up to 37% when compared to other GNN-based competitor models, indicating a more efficient way of handling information while achieving better performance. Code is available at https://github.com/antoniopurificato/Sheaf4Rec.

翻译：图神经网络（GNN）的最新进展推动了其在包括推荐系统在内的多种应用中的广泛采用。GNN通过高效建模节点代表用户或物品、边表示偏好关系的图，已被证明能有效应对推荐系统带来的挑战。然而，当前GNN技术通过单一静态向量表示节点，可能无法充分捕捉用户和物品的复杂特性。为克服这些局限，我们提出了一种融合范畴论启发的前沿模型——Sheaf4Rec。与单一向量表示不同，层状神经网络及其对应的拉普拉斯算子使用向量空间表示每个节点（和边）。我们的方法利用这一理论，在推理过程中实现了更全面的表示，可灵活应用于广泛的图相关任务，并展现出无与伦比的性能。所提模型在F1-Score@10上实现了最高8.53%的相对提升，在NDCG@10上实现了高达11.29%的显著提升，超越了现有最先进模型（如神经图协同过滤（NGCF）、KGTORe及其他近期基于GNN的模型）。除卓越的预测能力外，Sheaf4Rec在效率方面也展现出显著改进：与其他基于GNN的竞争模型相比，我们观察到运行时间大幅提升2.5%至37%，表明其能以更高效的方式处理信息同时获得更优性能。代码见https://github.com/antoniopurificato/Sheaf4Rec。