  Large multilingual language models typically share their parameters across
all languages, which enables cross-lingual task transfer, but learning can also
be hindered when training updates from different languages are in conflict. In
this paper, we propose novel methods for using language-specific subnetworks,
which control cross-lingual parameter sharing, to reduce conflicts and increase
positive transfer during fine-tuning. We introduce dynamic subnetworks, which
are jointly updated with the model, and we combine our methods with
meta-learning, an established, but complementary, technique for improving
cross-lingual transfer. Finally, we provide extensive analyses of how each of
our methods affects the models.
