Adapter layers are lightweight, learnable units inserted between transformer layers. Recent work explores using such layers for neural machine translation (NMT), to adapt pre-trained models to new domains or language pairs, training only a small set of parameters for each new setting (language pair or domain). In this work we study the compositionality of language and domain adapters in the context of Machine Translation. We aim to study, 1) parameter-efficient adaptation to multiple domains and languages simultaneously (full-resource scenario) and 2) cross-lingual transfer in domains where parallel data is unavailable for certain language pairs (partial-resource scenario). We find that in the partial resource scenario a naive combination of domain-specific and language-specific adapters often results in `catastrophic forgetting' of the missing languages. We study other ways to combine the adapters to alleviate this issue and maximize cross-lingual transfer. With our best adapter combinations, we obtain improvements of 3-4 BLEU on average for source languages that do not have in-domain data. For target languages without in-domain data, we achieve a similar improvement by combining adapters with back-translation. Supplementary material is available at https://tinyurl.com/r66stbxj
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