Joint Learning of Set Cardinality and State Distribution

We present a novel approach for learning to predict sets using deep learning. In recent years, deep neural networks have shown remarkable results in computer vision, natural language processing and other related problems. Despite their success, traditional architectures suffer from a serious limitation in that they are built to deal with structured input and output data, i.e. vectors or matrices. Many real-world problems, however, are naturally described as sets, rather than vectors. Existing techniques that allow for sequential data, such as recurrent neural networks, typically heavily depend on the input and output order and do not guarantee a valid solution. Here, we derive in a principled way, a mathematical formulation for set prediction where the output is permutation invariant. In particular, our approach jointly learns both the cardinality and the state distribution of the target set. We demonstrate the validity of our method on the task of multi-label image classification and achieve a new state of the art on the PASCAL VOC and MS COCO datasets.