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Natural language inference (NLI) is the task of detecting the existence of entailment or contradiction in a given sentence pair. Although NLI techniques could help numerous information retrieval tasks, most solutions for NLI are neural approaches whose lack of interpretability prohibits both straightforward integration and diagnosis for further improvement. We target the task of generating token-level explanations for NLI from a neural model. Many existing approaches for token-level explanation are either computationally costly or require additional annotations for training. In this article, we first introduce a novel method for training an explanation generator that does not require additional human labels. Instead, the explanation generator is trained with the objective of predicting how the model’s classification output will change when parts of the inputs are modified. Second, we propose to build an explanation generator in a multi-task learning setting along with the original NLI task so the explanation generator can utilize the model’s internal behavior. The experiment results suggest that the proposed explanation generator outperforms numerous strong baselines. In addition, our method does not require excessive additional computation at prediction time, which renders it an order of magnitude faster than the best-performing baseline.