Theoretical Analysis Shows Late-Interaction Retrieval Models Can Outperform Standard Vector Inner Products

[Submitted on 7 Jul 2026]

5h ago· 2 min readenInsight

Summary

This paper provides a theoretical analysis of late-interaction retrieval models using the MaxSim similarity function. The authors prove that MaxSim can exactly replicate inner products between non-negative k-sparse vectors with O(k) representation space, and that there exist similarities MaxSim can express that standard vector inner products cannot. They introduce Signed MaxSim, an extension that can replicate any real-valued inner product. The paper also shows MaxSim can act as an aggregation of soft-OR operations and evaluate logical expressions in positive Conjunctive Normal Form. Empirical results on a retrieval task with negation queries show Signed MaxSim significantly improves performance over standard ColBERT/MaxSim baselines.

Source

Twitter / XTheoretical Analysis Shows Late-Interaction Retrieval Models Can Outperform Standard Vector Inner Productsarxiv.org

Key quotes

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This paper shows by construction that MaxSim similarity can exactly replicate the inner product between any two non-negative k-sparse vectors with possibly infinite dimension, requiring only O(k) representation space.

There exist similarities that MaxSim can express while standard vector inner products with the same representation space cannot.

Our findings show that MaxSim is at least as capable as standard vector inner products for any non-negative vectors and our extension, Signed MaxSim, is as capable for any vectors.

On a retrieval task featuring queries with negations, Signed MaxSim improves out-of-domain performance significantly over a standard ColBERT/MaxSim baseline with nDCG@10 increasing from 0.597 to 1.000 under a vocabulary shift and from 0.008 to 0.788 on negation-only queries.

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Late-interaction retrieval models that use the MaxSim similarity function have shown strong empirical performance, often outperforming single-vector dense and sparse retrieval models. Despite these empirical findings, little is known about the theoretical

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