Retrieval with extremely long queries and documents is a well-known and challenging task in information retrieval and is commonly known as Query-by-Document (QBD) retrieval. Specifically designed Transformer models that can handle long input sequences have not shown high effectiveness in QBD tasks in previous work. We propose a Re-Ranker based on the novel Proportional Relevance Score (RPRS) to compute the relevance score between a query and the top-k candidate documents. Our extensive evaluation shows RPRS obtains significantly better results than the state-of-the-art models on five different datasets. Furthermore, RPRS is highly efficient since all documents can be pre-processed, embedded, and indexed before query time which gives our re-ranker the advantage of having a complexity of O(N) where N is the total number of sentences in the query and candidate documents. Furthermore, our method solves the problem of the low-resource training in QBD retrieval tasks as it does not need large amounts of training data, and has only three parameters with a limited range that can be optimized with a grid search even if a small amount of labeled data is available. Our detailed analysis shows that RPRS benefits from covering the full length of candidate documents and queries.
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