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Context: Using E_{q} and E_{d}, ColBERT computes the relevance score between q and d via late interaction, which we define as a summation of maximum similarity (MaxSim) operators. In particular, we find the maximum cosine similarity of each v\in E_{q} with vectors in E_{d}, and combine the outputs via summation. Besides cosine, we also evaluate squared L2 distance as a measure of vector similarity. Intuitively, this interaction mechanism softly searches for each query term t_{q}—in a manner that reflects its context in the query—against the document’s embeddings, quantifying the strength of the “match” via the largest similarity score between t_{q} and a document term t_{d}. Given these term scores, it then estimates the document relevance by summing the matching evidence across all query terms. Given the representation of a query q and a document d, the relevance score of d to q, denoted as S_{q,d}, is estimated via late interaction between their bags of contextualized embeddings. As mentioned before, this is conducted as a sum of maximum similarity computations, namely cosine similarity (implemented as dot-products due to the embedding normalization) or squared L2 distance.

Question: What if a query term can be matched to multiple document terms? Does MaxSim suffice for capturing query-document relevance, for this case too?
if a query term can be matched to multiple document terms, MaxSim suffice for capturing query-document relevance.  ColBERT computes the relevance score between q and d via late interaction, which we define as a summation of maximum similarity (MaxSim) operators. In particular, we find the maximum cosine similarity of each v\in E_{q} with vectors in E_{d}, and combine the outputs via summation.