Collaborative filtering (CF) is a pivotal technique in modern recommender systems. The learning process of CF models typically consists of three components: interaction encoder, loss function, and negative sampling. Although many existing studies have proposed various CF models to design sophisticated interaction encoders, recent work shows that simply reformulating the loss functions can achieve significant performance gains. This paper delves into analyzing the relationship among existing loss functions. Our mathematical analysis reveals that the previous loss functions can be interpreted as alignment and uniformity functions: (i) the alignment matches user and item representations, and (ii) the uniformity disperses user and item distributions. Inspired by this analysis, we propose a novel loss function that improves the design of alignment and uniformity considering the unique patterns of datasets called Margin-aware Alignment and Weighted Uniformity (MAWU). The key novelty of MAWU is two-fold: (i) margin-aware alignment (MA) mitigates user/item-specific popularity biases, and (ii) weighted uniformity (WU) adjusts the significance between user and item uniformities to reflect the inherent characteristics of datasets. Extensive experimental results show that MF and LightGCN equipped with MAWU are comparable or superior to state-of-the-art CF models with various loss functions on three public datasets.

翻译：协同过滤（CF）是现代推荐系统中的关键技术。CF模型的学习过程通常包含三个组成部分：交互编码器、损失函数和负采样。尽管现有研究已提出多种CF模型来设计复杂的交互编码器，但近期工作表明，仅通过重新构造损失函数即可实现显著的性能提升。本文深入分析了现有损失函数之间的关系。数学分析揭示，先前的损失函数可被解释为对齐与均匀性函数：(i) 对齐函数匹配用户与物品表示，(ii) 均匀性函数分散用户与物品的分布。受此分析启发，我们提出一种新型损失函数——边界感知对齐与加权均匀性（MAWU），该方法在考虑数据集独特模式的基础上改进了对齐与均匀性的设计。MAWU的关键创新体现在两方面：(i) 边界感知对齐（MA）缓解了用户/物品特定的流行度偏差，(ii) 加权均匀性（WU）通过调整用户均匀性与物品均匀性之间的重要性权重，反映数据集的内在特性。大量实验结果表明，在三个公开数据集上，配备MAWU的MF和LightGCN模型性能可媲美甚至超越采用各类损失函数的最先进CF模型。