  A "bigger is better" explosion in the number of parameters in deep neural
networks has made it increasingly challenging to make state-of-the-art networks
accessible in compute-restricted environments. Compression techniques have
taken on renewed importance as a way to bridge the gap. However, evaluation of
the trade-offs incurred by popular compression techniques has been centered on
high-resource datasets. In this work, we instead consider the impact of
compression in a data-limited regime. We introduce the term low-resource double
bind to refer to the co-occurrence of data limitations and compute resource
constraints. This is a common setting for NLP for low-resource languages, yet
the trade-offs in performance are poorly studied. Our work offers surprising
insights into the relationship between capacity and generalization in
data-limited regimes for the task of machine translation. Our experiments on
magnitude pruning for translations from English into Yoruba, Hausa, Igbo and
German show that in low-resource regimes, sparsity preserves performance on
frequent sentences but has a disparate impact on infrequent ones. However, it
improves robustness to out-of-distribution shifts, especially for datasets that
are very distinct from the training distribution. Our findings suggest that
sparsity can play a beneficial role at curbing memorization of low frequency
attributes, and therefore offers a promising solution to the low-resource
double bind.
