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This paper addresses a question difficulty estimation of which goal is to estimate the difficulty level of a given question in question-answering (QA) tasks. Since a question in the tasks is composed of a questionary sentence and a set of information components such as a description and candidate answers, it is important to model the relationship among the information components to estimate the difficulty level of the question. However, existing approaches to this task modeled a simple relationship such as a relationship between a questionary sentence and a description, but such simple relationships are insufficient to predict the difficulty level accurately. Therefore, this paper proposes an attention-based model to consider the complicated relationship among the information components. The proposed model first represents bi-directional relationships between a questionary sentence and each information component using a dual multi-head co-attention, since the questionary sentence is a key factor in the QA questions and it affects and is affected by information components. Then, the proposed model considers inter-information relationship over the bi-directional representations through a self-attention model. The inter-information relationship helps predict the difficulty of the questions accurately which require reasoning over multiple kinds of information components. The experimental results from three well-known and real-world QA data sets prove that the proposed model outperforms the previous state-of-the-art and pre-trained language model baselines. It is also shown that the proposed model is robust against the increase of the number of information components.

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