Linear Turán Numbers of Uniform Hypertrees

What the math gives to ML

The paper gives exact edge-count constraints for linear uniform hypergraphs, where each pair of vertices can co-occur in at most one hyperedge. The transferable asset is a principled way to build sparse, balanced interaction patterns: regular linear hypergraphs maximize the number of groups under a local overlap constraint, while degree-sensitive inequalities identify which vertices create structural congestion. In neural networks, this suggests replacing unconstrained sparse attention or expert-group connectivity with learned or fixed hypergraphs whose groups have bounded pairwise overlap and nearly uniform token degree. The results are most useful as architecture and regularization constraints for reducing quadratic interaction cost while preserving repeated multi-token coverage.