  Attention networks such as transformers have achieved state-of-the-art
performance in many domains. These networks rely heavily on the dot product
attention operator, which computes the similarity between two points by taking
their inner product. However, the inner product does not explicitly model the
complex structural properties of real world datasets, such as hierarchies
between data points. To remedy this, we introduce cone attention, a drop-in
replacement for dot product attention based on hyperbolic entailment cones.
Cone attention associates two points by the depth of their lowest common
ancestor in a hierarchy defined by hyperbolic cones, which intuitively measures
the divergence of two points and gives a hierarchy aware similarity score. We
test cone attention on a wide variety of models and tasks and show that it
improves task-level performance over dot product attention and other baselines,
and is able to match dot-product attention with significantly fewer parameters.
Our results suggest that cone attention is an effective way to capture
hierarchical relationships when calculating attention.
