Recommendation Systems (RS) are often plagued by popularity bias. Specifically,when recommendation models are trained on long-tailed datasets, they not only inherit this bias but often exacerbate it. This effect undermines both the precision and fairness of RS and catalyzes the so-called Matthew Effect. Despite the widely recognition of this issue, the fundamental causes remain largely elusive. In our research, we delve deeply into popularity bias amplification. Our comprehensive theoretical and empirical investigations lead to two core insights: 1) Item popularity is memorized in the principal singular vector of the score matrix predicted by the recommendation model; 2) The dimension collapse phenomenon amplifies the impact of principal singular vector on model predictions, intensifying the popularity bias. Based on these insights, we propose a novel method to mitigate this bias by imposing penalties on the magnitude of the principal singular value. Considering the heavy computational burden in directly evaluating the gradient of the principal singular value, we develop an efficient algorithm that harnesses the inherent properties of the singular vector. Extensive experiments across seven real-world datasets and three testing scenarios have been conducted to validate the superiority of our method.

翻译：推荐系统（RS）常受流行度偏差困扰。具体而言，当推荐模型在长尾数据集上训练时，不仅会继承这种偏差，还会经常将其放大。这一效应损害了推荐系统的准确性与公平性，并催化了所谓的马太效应。尽管该问题已被广泛认知，但其根本原因仍不甚明了。本研究深入探究了流行度偏差放大现象。通过全面的理论与实证分析，我们得出两点核心见解：1）项目流行度被记录在推荐模型预测的得分矩阵的主奇异向量中；2）维度坍塌现象放大了主奇异向量对模型预测的影响，从而加剧了流行度偏差。基于这些见解，我们提出一种新颖方法，通过对主奇异值的幅度施加惩罚来缓解该偏差。考虑到直接评估主奇异值梯度的计算负担沉重，我们利用奇异向量的固有特性开发了一种高效算法。通过在七个真实世界数据集和三种测试场景下的大量实验，验证了我们方法的优越性。