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Dense passage retrieval (DPR) models show great effectiveness gains in firststage retrieval for the web domain. However in the web domain we are in asetting with large amounts of training data and a query-to-passage or aquery-to-document retrieval task. We investigate in this paper densedocument-to-document retrieval with limited labelled target data for training,in particular legal case retrieval. In order to use DPR models fordocument-to-document retrieval, we propose a Paragraph Aggregation RetrievalModel (PARM) which liberates DPR models from their limited input length. PARMretrieves documents on the paragraph-level: for each query paragraph, relevantdocuments are retrieved based on their paragraphs. Then the relevant resultsper query paragraph are aggregated into one ranked list for the whole querydocument. For the aggregation we propose vector-based aggregation withreciprocal rank fusion (VRRF) weighting, which combines the advantages ofrank-based aggregation and topical aggregation based on the dense embeddings.Experimental results show that VRRF outperforms rank-based aggregationstrategies for dense document-to-document retrieval with PARM. We compare PARMto document-level retrieval and demonstrate higher retrieval effectiveness ofPARM for lexical and dense first-stage retrieval on two different legal caseretrieval collections. We investigate how to train the dense retrieval modelfor PARM on limited target data with labels on the paragraph or thedocument-level. In addition, we analyze the differences of the retrievedresults of lexical and dense retrieval with PARM.

PARM: A Paragraph Aggregation Retrieval Model for Dense Document-to-Document Retrieval