Submodular and strongly submodular functions and diversities

What the math gives to ML

The paper supplies a set-function viewpoint for modeling collections of neural representations, rather than only individual examples or pairs. Its strongest transferable asset is the hierarchy of monotonicity, subadditivity, submodularity, and strong submodularity constraints, which mathematically encode diminishing returns when additional elements are added to a set. This can be used to train token-pruning, patch-selection, retrieval, or mixture-routing modules whose selected elements become complementary instead of redundant. The most practical first transfer is a sampled strong-submodularity regularizer on a learned set utility, combined with greedy selection at inference.