A prevalent practice in recommender systems consists of averaging item embeddings to represent users or higher-level concepts in the same embedding space. This paper investigates the relevance of such a practice. For this purpose, we propose an expected precision score, designed to measure the consistency of an average embedding relative to the items used for its construction. We subsequently analyze the mathematical expression of this score in a theoretical setting with specific assumptions, as well as its empirical behavior on real-world data from music streaming services. Our results emphasize that real-world averages are less consistent for recommendation, which paves the way for future research to better align real-world embeddings with assumptions from our theoretical setting.

翻译：推荐系统中的常见做法是通过对物品嵌入进行平均，以在相同嵌入空间中表征用户或更高层次概念。本文研究了该做法的合理性。为此，我们提出了一种预期精确度指标，用于衡量平均嵌入相对于构建其的物品的一致性。随后，我们在特定假设的理论框架下分析该指标的数学表达式，并基于音乐流媒体服务的真实数据考察其经验行为。研究结果表明，真实世界中的平均嵌入在推荐任务中一致性较低，这为未来研究如何使真实世界嵌入更符合理论假设奠定了基础。