  Transformer networks are the de facto standard architecture in natural
language processing. To date, there are no theoretical analyses of the
Transformer's ability to capture tree structures. We focus on the ability of
Transformer networks to learn tree structures that are important for tree
transduction problems. We first analyze the theoretical capability of the
standard Transformer architecture to learn tree structures given enumeration of
all possible tree backbones, which we define as trees without labels. We then
prove that two linear layers with ReLU activation function can recover any tree
backbone from any two nonzero, linearly independent starting backbones. This
implies that a Transformer can learn tree structures well in theory. We conduct
experiments with synthetic data and find that the standard Transformer achieves
similar accuracy compared to a Transformer where tree position information is
explicitly encoded, albeit with slower convergence. This confirms empirically
that Transformers can learn tree structures.
