  We propose the Limited Multi-Label (LML) projection layer as a new primitive
operation for end-to-end learning systems. The LML layer provides a
probabilistic way of modeling multi-label predictions limited to having exactly
k labels. We derive efficient forward and backward passes for this layer and
show how the layer can be used to optimize the top-k recall for multi-label
tasks with incomplete label information. We evaluate LML layers on top-k
CIFAR-100 classification and scene graph generation. We show that LML layers
add a negligible amount of computational overhead, strictly improve the model's
representational capacity, and improve accuracy. We also revisit the truncated
top-k entropy method as a competitive baseline for top-k classification.
