  Hallucinations pose a significant challenge to the reliability of neural
models for abstractive summarisation. While automatically generated summaries
may be fluent, they often lack faithfulness to the original document. This
issue becomes even more pronounced in low-resource settings, such as
cross-lingual transfer. With the existing faithful metrics focusing on English,
even measuring the extent of this phenomenon in cross-lingual settings is hard.
To address this, we first develop a novel metric, mFACT, evaluating the
faithfulness of non-English summaries, leveraging translation-based transfer
from multiple English faithfulness metrics. We then propose a simple but
effective method to reduce hallucinations with a cross-lingual transfer, which
weighs the loss of each training example by its faithfulness score. Through
extensive experiments in multiple languages, we demonstrate that mFACT is the
metric that is most suited to detect hallucinations. Moreover, we find that our
proposed loss weighting method drastically increases both performance and
faithfulness according to both automatic and human evaluation when compared to
strong baselines for cross-lingual transfer such as MAD-X. Our code and dataset
are available at https://github.com/yfqiu-nlp/mfact-summ.
