| QA systems often fail on ambiguous questions because they assume a single correct answer. We propose CenterDistill, a weakly supervised framework that learns semantic center distributions from clustered question embeddings to guide inference-time behaviour: answer, clarify, or present alternatives. Unlike prior work, it requires no manual interpretation labels and derives supervision directly from data. The model jointly predicts center distributions and answer spans, using the predicted distribution to select behaviour at inference. In English–Spanish cross-lingual QA, CenterDistill achieves 90.1% behaviour accuracy, 92.6% center assignment accuracy, and 8.8 worst-cluster F1, outperforming confidence-based and multi-task baselines. Results on English–German further show that the behaviour policy generalizes across language pairs. The code is publicly available at: https://github.com/hacky1997/Centerdistill |
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