What Can Transformer Learn with Varying Depth? Case Studies on Sequence
  Learning Tasks
Xingwu Chen Difan Zou
We study the capabilities of the transformer architecture with varying depth.
Specifically, we designed a novel set of sequence learning tasks to
systematically evaluate and comprehend how the depth of transformer affects its
ability to perform memorization, reasoning, generalization, and contextual
generalization. We show a transformer with only one attention layer can excel
in memorization but falls short in other tasks. Then, we show that exhibiting
reasoning and generalization ability requires the transformer to have at least
two attention layers, while context generalization ability may necessitate
three attention layers. Additionally, we identify a class of simple operations
that a single attention layer can execute, and show that the complex tasks can
be approached as the combinations of these simple operations and thus can be
resolved by stacking multiple attention layers. This sheds light on studying
more practical and complex tasks beyond our design. Numerical experiments
corroborate our theoretical findings.