  Explainable multi-hop question answering (QA) not only predicts answers but
also identifies rationales, i. e. subsets of input sentences used to derive the
answers. This problem has been extensively studied under the supervised
setting, where both answer and rationale annotations are given. Because
rationale annotations are expensive to collect and not always available, recent
efforts have been devoted to developing methods that do not rely on supervision
for rationales. However, such methods have limited capacities in modeling
interactions between sentences, let alone reasoning across multiple documents.
This work proposes a principled, probabilistic approach for training
explainable multi-hop QA systems without rationale supervision. Our approach
performs multi-hop reasoning by explicitly modeling rationales as sets,
enabling the model to capture interactions between documents and sentences
within a document. Experimental results show that our approach is more accurate
at selecting rationales than the previous methods, while maintaining similar
accuracy in predicting answers.
