Question Under Discussion (QUD) is a discourse framework that uses implicit questions to reveal discourse relationships between sentences. In QUD parsing, each sentence is viewed as an answer to a question triggered by an anchor sentence in prior context. The resulting QUD structure is required to conform to several theoretical criteria like answer compatibility (how well the question is answered), making QUD parsing a challenging task. Previous works construct QUD parsers in a pipelined manner (i.e. detect the trigger sentence in context and then generate the question). However, these parsers lack a holistic view of the task and can hardly satisfy all the criteria. In this work, we introduce QUDSELECT, a joint-training framework that selectively decodes the QUD dependency structures considering the QUD criteria. Using instruction-tuning, we train models to simultaneously predict the anchor sentence and generate the associated question. To explicitly incorporate the criteria, we adopt a selective decoding strategy of sampling multiple QUD candidates during inference, followed by selecting the best one with criteria scorers. Our method outperforms the state-of-the-art baseline models by 9% in human evaluation and 4% in automatic evaluation, demonstrating the effectiveness of our framework.

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