  Many machine learning problems require the prediction of multi-dimensional
labels. Such structured prediction models can benefit from modeling
dependencies between labels. Recently, several deep learning approaches to
structured prediction have been proposed. Here we focus on capturing
cardinality constraints in such models. Namely, constraining the number of
non-zero labels that the model outputs. Such constraints have proven very
useful in previous structured prediction approaches, but it is a challenge to
introduce them into a deep learning framework. Here we show how to do this via
a novel deep architecture. Our approach outperforms strong baselines, achieving
state-of-the-art results on multi-label classification benchmarks.
