Beyond Instance-Level Alignment and Uniformity: Semantic Factor Learning for Collaborative Filtering

Collaborative filtering (CF) is widely used in recommender systems (RecSys) due to its simplicity and efficiency. However, existing CF methods follow an instance-level learning paradigm. During the instance learning stage, a large number of uninteracted user-item instances, of which items are potential interested by the user, are incorrectly treated as true negative samples resulting in a severe limitation to the generalization and scalability of models. Moreover, mainstream graph convolutional networks (GCNs) inherently suffer from high computational cost and over-smoothing issues, which limit the ability in capturing higher-order connectivity and lead to a poor generalization under sparse supervision signals. To address the above limitations, we propose Semantic Factor enhanced Alignment and Uniformity (SaFeAU), a novel framework that augments interacted instances with semantic factors, thereby mitigating false negative labeling and enabling matrix factorization (MF) to capture high-order CF signals without graph neighborhood aggregation. Specifically, SaFeAU consists of three tightly coupled components. First, Semantic Factor Routing (SFR) disentangles item representations into independent and global semantic factors. Building on these factors, Semantic Factor Matching (SFM) identifies uninteracted items, which share the same semantic factors with interacted ones, as potential positive pairs for enriching sparse supervision signals. Finally, Semantic Pairs Alignment (SPA) aligns both observed and potential positive pairs while promoting uniformity of user and item representations. Extensive experiments on four sparse real-world datasets show that SaFeAU consistently outperforms GCN-based and MF-based state-of-the-art CF methods in both recommendation accuracy and computational efficiency, confirming the effectiveness of the proposed semantic enhanced learning paradigm.

Deep graph matching meets mixed-integer linear programming: Relax at your own risk ?

Graph matching is an important problem that has received widespread attention, especially in the field of computer vision. Recently, state-of-the-art methods seek to incorporate graph matching with deep learning. However, there is no research to explain what role the graph matching algorithm plays in the model. Therefore, we propose an approach integrating a MILP formulation of the graph matching problem. This formulation is solved to optimal and it provides inherent baseline. Meanwhile, similar approaches are derived by releasing the optimal guarantee of the graph matching solver and by introducing a quality level. This quality level controls the quality of the solutions provided by the graph matching solver. In addition, several relaxations of the graph matching problem are put to the test. Our experimental evaluation gives several theoretical insights and guides the direction of deep graph matching methods.