Measurable Matroids: Foundations and Min--Max Theorems

What the math gives to ML

The paper develops measure-theoretic matroid intersection and union, preserving rank-based min–max formulas on atomless spaces. The transferable asset is a principled way to combine several global independence, capacity, and diversity constraints while producing an explicit Hall-type deficiency certificate when they cannot all be satisfied. A practical neural adaptation is a constrained mixture-of-experts router that projects token-expert assignments onto token, expert, and hierarchical group capacities. This is adjacent to existing flow-based routing, so the experiment should target multi-constraint routing and compare both quality and routing overhead against top-k plus load balancing.