  We propose methods that enable efficient hierarchical classification in
parallel. Our methods transform a batch of classification scores and labels,
corresponding to given nodes in a semantic tree, to scores and labels
corresponding to all nodes in the ancestral paths going down the tree to every
given node, relying only on tensor operations that execute efficiently on
hardware accelerators. We implement our methods and test them on current
hardware accelerators with a tree incorporating all English-language synsets in
WordNet 3.0, spanning 117,659 classes in 20 levels of depth. We transform
batches of scores and labels to their respective ancestral paths, incurring
negligible computation and consuming only a fixed 0.04GB of memory over the
footprint of data.
