Learning Where to Look: Geometric Multi-Interest Retrieval for Recommender Systems

The retrieval stage of recommender systems must efficiently identify a small set of items relevant to a given user from a large item corpus. Despite their differences, many existing retrieval methods share a common structure: query-based nearest-neighbor retrieval in an item embedding space. From this perspective, retrieval involves two fundamental questions: where to place the query vectors and how far to search. In this work, we develop a geometric framework for multi-interest retrieval. We show that cosine-similarity retrieval corresponds to searching spherical caps on the embedding sphere, and formulate efficient retrieval as a geometric covering problem. Our theoretical analysis shows that multiple retrieval regions can substantially reduce the retrieval cost for users with diverse interests. We further identify two sources of query placement error: sampling error, caused by estimating interests from limited historical interactions, and drift error, caused by changes in user interests over time. To address these errors, we learn multiple retrieval regions directly from user histories, with each region parameterized by a query center and an angular radius. The model is trained to cover future target items while minimizing the total retrieval region. Experiments on four recommendation datasets show that our approach consistently improves top-ranked retrieval quality over strong single-interest and multi-interest baselines, while maintaining compact retrieval regions.