  Lattices are an efficient and effective method to encode ambiguity of
upstream systems in natural language processing tasks, for example to compactly
capture multiple speech recognition hypotheses, or to represent multiple
linguistic analyses. Previous work has extended recurrent neural networks to
model lattice inputs and achieved improvements in various tasks, but these
models suffer from very slow computation speeds. This paper extends the
recently proposed paradigm of self-attention to handle lattice inputs.
Self-attention is a sequence modeling technique that relates inputs to one
another by computing pairwise similarities and has gained popularity for both
its strong results and its computational efficiency. To extend such models to
handle lattices, we introduce probabilistic reachability masks that incorporate
lattice structure into the model and support lattice scores if available. We
also propose a method for adapting positional embeddings to lattice structures.
We apply the proposed model to a speech translation task and find that it
outperforms all examined baselines while being much faster to compute than
previous neural lattice models during both training and inference.
