Legal case retrieval is a specialized IR task that involves retrieving supporting cases given a query case. Compared with traditional ad-hoc text retrieval, the legal case retrieval task is more challenging since the query case is much longer and more complex than common keyword queries. Besides that, the definition of relevance between a query case and a supporting case is beyond general topical relevance and it is therefore difficult to construct a large-scale case retrieval dataset, especially one with accurate relevance judgments. To address these challenges, we propose BERT-PLI, a novel model that utilizes BERT to capture the semantic relationships at the paragraph-level and then infers the relevance between two cases by aggregating paragraph-level interactions. We fine-tune the BERT model with a relatively small-scale case law entailment dataset to adapt it to the legal scenario and employ a cascade framework to reduce the computational cost. We conduct extensive experiments on the benchmark of the relevant case retrieval task in COLIEE 2019. Experimental results demonstrate that our proposed method outperforms existing solutions.

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Compared to general web search engines, web image search engines display results in a di erent way. In web image search, results are typically placed in a grid-based manner rather than a sequential result list. In this scenario, users can view results not only in a vertical direction but also in a horizontal direction. Moreover, pagination is usually not (explicitly) supported on image search search engine result pages (SERPs), and users can view results by scrolling down without having to click a "next page" button. These di erences lead to di erent interaction mechanisms and user behavior patterns, which, in turn, create challenges to evaluation metrics that have originally been developed for general web search. While considerable e ort has been invested in developing evaluation metrics for general web search, there has been relatively little e ort to construct grid-based evaluation metrics. To inform the development of grid-based evaluation metrics for web image search, we conduct a comprehensive analysis of user behavior so as to uncover how users allocate their attention in a grid-based web image search result interface. We obtain three ndings: (1) "Middle bias": Con rming previous studies, we nd that image results in the horizontal middle positions may receive more attention from users than those in the leftmost or rightmost positions. (2) "Slower decay": Unlike web search, users' attention does not decrease monotonically or dramatically with the rank position in image search, especially within a row. (3) "Row skipping": Users may ignore particular rows and directly jump to results at some distance. Motivated by these observations, we propose corresponding user behavior assumptions to capture users' search interaction processes and evaluate their search performance. We show how to derive new metrics from these assumptions and demonstrate * Corresponding author This paper is published under the Creative Commons Attribution 4.0 International (CC-BY 4.0) license. Authors reserve their rights to disseminate the work on their personal and corporate Web sites with the appropriate attribution.

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