  Transformers trained on natural language data have been shown to learn its
hierarchical structure and generalize to sentences with unseen syntactic
structures without explicitly encoding any structural bias. In this work, we
investigate sources of inductive bias in transformer models and their training
that could cause such generalization behavior to emerge. We extensively
experiment with transformer models trained on multiple synthetic datasets and
with different training objectives and show that while other objectives e.g.
sequence-to-sequence modeling, prefix language modeling, often failed to lead
to hierarchical generalization, models trained with the language modeling
objective consistently learned to generalize hierarchically. We then conduct
pruning experiments to study how transformers trained with the language
modeling objective encode hierarchical structure. When pruned, we find joint
existence of subnetworks within the model with different generalization
behaviors (subnetworks corresponding to hierarchical structure and linear
order). Finally, we take a Bayesian perspective to further uncover
transformers' preference for hierarchical generalization: We establish a
correlation between whether transformers generalize hierarchically on a dataset
and whether the simplest explanation of that dataset is provided by a
hierarchical grammar compared to regular grammars exhibiting linear
generalization.
