Searching for Actions on the Hyperbole

In this paper, we introduce hierarchical action search. Starting from the observation that hierarchies are mostly ignored in the action literature, we retrieve not only individual actions but also relevant and related actions, given an action name or video example as input. We propose a hyperbolic action network, which is centered around a hyperbolic space shared by action hierarchies and videos. Our discriminative hyperbolic embedding projects actions on the shared space while jointly optimizing hypernymhyponym relations between action pairs and a large margin separation between all actions. The projected actions serve as hyperbolic prototypes that we match with projected video representations. The result is a learned space where videos are positioned in entailment cones formed by different subtrees. To perform search in this space, we start from a query and increasingly enlarge its entailment cone to retrieve hierarchically relevant action videos. Experiments on three action datasets with new hierarchy annotations show the effectiveness of our approach for hierarchical action search by name and by video example, regardless of whether queried actions have been seen or not during training. Our implementation is available at https: //github.com/Tenglon/hyperbolic_action