  Generative retrieval generates identifiers of relevant documents in an
end-to-end manner using a sequence-to-sequence architecture for a given query.
The relation between generative retrieval and other retrieval methods,
especially those based on matching within dense retrieval models, is not yet
fully comprehended. Prior work has demonstrated that generative retrieval with
atomic identifiers is equivalent to single-vector dense retrieval. Accordingly,
generative retrieval exhibits behavior analogous to hierarchical search within
a tree index in dense retrieval when using hierarchical semantic identifiers.
However, prior work focuses solely on the retrieval stage without considering
the deep interactions within the decoder of generative retrieval.
  In this paper, we fill this gap by demonstrating that generative retrieval
and multi-vector dense retrieval share the same framework for measuring the
relevance to a query of a document. Specifically, we examine the attention
layer and prediction head of generative retrieval, revealing that generative
retrieval can be understood as a special case of multi-vector dense retrieval.
Both methods compute relevance as a sum of products of query and document
vectors and an alignment matrix. We then explore how generative retrieval
applies this framework, employing distinct strategies for computing document
token vectors and the alignment matrix. We have conducted experiments to verify
our conclusions and show that both paradigms exhibit commonalities of term
matching in their alignment matrix.
