The need to compactly and robustly represent item-attribute relations arises in many important tasks, such as faceted browsing and recommendation systems. A popular machine learning approach for this task denotes that an item has an attribute by a high dot-product between vectors for the item and attribute -- a representation that is not only dense, but also tends to correct noisy and incomplete data. While this method works well for queries retrieving items by a single attribute (such as \emph{movies that are comedies}), we find that vector embeddings do not so accurately support compositional queries (such as movies that are comedies and British but not romances). To address these set-theoretic compositions, this paper proposes to replace vectors with box embeddings, a region-based representation that can be thought of as learnable Venn diagrams. We introduce a new benchmark dataset for compositional queries, and present experiments and analysis providing insights into the behavior of both. We find that, while vector and box embeddings are equally suited to single attribute queries, for compositional queries box embeddings provide substantial advantages over vectors, particularly at the moderate and larger retrieval set sizes that are most useful for users' search and browsing.

翻译：在许多重要任务（如分面浏览与推荐系统）中，需要紧凑且鲁棒地表示物品-属性关联。一种流行的机器学习方法通过物品向量与属性向量之间的高内积来表征物品具有某属性——这种表示不仅密集，还能自动校正含噪与不完整数据。尽管该方法在通过单一属性检索物品的查询（如"喜剧电影"）中表现良好，但研究发现向量嵌入无法精确支持组合查询（如"既是喜剧又是英国片且非爱情片的电影"）。为解决这类基于集合论的组合问题，本文提出用盒状嵌入替代向量嵌入，这是一种可视为可学习文氏图的区域化表示方法。我们构建了面向组合查询的新型基准数据集，通过实验与分析揭示两类表示的行为特征。研究发现：尽管向量嵌入与盒状嵌入在单一属性查询中性能相当，但在组合查询中（尤其是对用户搜索与浏览最具实用价值的中大规模检索集），盒状嵌入相较向量嵌入展现出显著优势。