Signed MaxSim from UMass Researchers Achieves Perfect Retrieval on Negation Queries

Researchers from UMass Amherst (Killingback, Ingale, Zamani, Musco) published a theoretical and empirical paper proving that late-interaction retrieval models using MaxSim similarity possess greater representation power than standard single-vector dense or sparse retrieval models. They show by construction that MaxSim can exactly replicate the inner product between any two non-negative k-sparse vectors using only O(k) representation space, and that there exist similarities MaxSim can express that standard inner products cannot. To handle real-valued vectors (including negative weights), they introduce Signed MaxSim, which can exactly replicate any real-valued inner product—something standard MaxSim cannot do. The paper also demonstrates that MaxSim acts as an aggregation of soft-OR operations and can evaluate logical expressions in positive Conjunctive Normal Form, providing the first theoretical justification for late-interaction methods' empirical success.

Empirically, the team tested Signed MaxSim on retrieval tasks with negations (e.g., queries requiring exclusion of terms). Under a vocabulary shift, Signed MaxSim boosted nDCG@10 from 0.597 to 1.000—perfect ranking. On queries containing only negation terms, the improvement was even more dramatic: nDCG@10 jumped from 0.008 to 0.788. This shows that late-interaction models with Signed MaxSim can handle complex logical queries that stymie standard vector search. The work has immediate implications for search engines, recommendation systems, and any application needing precise, negation-aware retrieval. By extending the theoretical capacity of late-interaction models, the researchers open the door to more expressive and accurate information retrieval systems without sacrificing efficiency.