  Massively multilingual models subsuming tens or even hundreds of languages
pose great challenges to multi-task optimization. While it is a common practice
to apply a language-agnostic procedure optimizing a joint multilingual task
objective, how to properly characterize and take advantage of its underlying
problem structure for improving optimization efficiency remains under-explored.
In this paper, we attempt to peek into the black-box of multilingual
optimization through the lens of loss function geometry. We find that gradient
similarity measured along the optimization trajectory is an important signal,
which correlates well with not only language proximity but also the overall
model performance. Such observation helps us to identify a critical limitation
of existing gradient-based multi-task learning methods, and thus we derive a
simple and scalable optimization procedure, named Gradient Vaccine, which
encourages more geometrically aligned parameter updates for close tasks.
Empirically, our method obtains significant model performance gains on
multilingual machine translation and XTREME benchmark tasks for multilingual
language models. Our work reveals the importance of properly measuring and
utilizing language proximity in multilingual optimization, and has broader
implications for multi-task learning beyond multilingual modeling.
