  To process novel sentences, language models (LMs) must generalize
compositionally -- combine familiar elements in new ways. What aspects of a
model's structure promote compositional generalization? Focusing on
transformers, we test the hypothesis, motivated by theoretical and empirical
work, that deeper transformers generalize more compositionally. Simply adding
layers increases the total number of parameters; to address this confound
between depth and size, we construct three classes of models which trade off
depth for width such that the total number of parameters is kept constant (41M,
134M and 374M parameters). We pretrain all models as LMs and fine-tune them on
tasks that test for compositional generalization. We report three main
conclusions: (1) after fine-tuning, deeper models generalize more
compositionally than shallower models do, but the benefit of additional layers
diminishes rapidly; (2) within each family, deeper models show better language
modeling performance, but returns are similarly diminishing; (3) the benefits
of depth for compositional generalization cannot be attributed solely to better
performance on language modeling. Because model latency is approximately linear
in the number of layers, these results lead us to the recommendation that, with
a given total parameter budget, transformers can be made shallower than is
typical without sacrificing performance.
