Reviews: Deep Submodular Functions: Definitions and Learning

Problem definition - The paper proposes a new family of submodular functions called deep submodular functions. They are defined similar to a neural network where there are many nodes in each level. At each node you take a positive linear combination of previous layer and then apply a concave function. Contributions - The main important contribution of the paper is proposing the family of DSF and showing applications to text summarization. They show that DSF's generalize all of them except cycle matroid rank.