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Recently, there has been a growing interest in designing text generationsystems from a discourse coherence perspective, e.g., modeling theinterdependence between sentences. Still, recent BERT-based evaluation metricsare weak in recognizing coherence, and thus are not reliable in a way to spotthe discourse-level improvements of those text generation systems. In thiswork, we introduce DiscoScore, a parametrized discourse metric, which uses BERTto model discourse coherence from different perspectives, driven by Centeringtheory. Our experiments encompass 16 non-discourse and discourse metrics,including DiscoScore and popular coherence models, evaluated on summarizationand document-level machine translation (MT). We find that (i) the majority ofBERT-based metrics correlate much worse with human rated coherence than earlydiscourse metrics, invented a decade ago; (ii) the recent state-of-the-artBARTScore is weak when operated at system level -- which is particularlyproblematic as systems are typically compared in this manner. DiscoScore, incontrast, achieves strong system-level correlation with human ratings, not onlyin coherence but also in factual consistency and other aspects, and surpassesBARTScore by over 10 correlation points on average. Further, aiming tounderstand DiscoScore, we provide justifications to the importance of discoursecoherence for evaluation metrics, and explain the superiority of one variantover another. Our code is available at\url{https://github.com/AIPHES/DiscoScore}.

DiscoScore: Evaluating Text Generation with BERT and Discourse Coherence