Sparsity is Combinatorial Depth: Quantifying MoE Expressivity via Tropical Geometry

ArXi:2602.03204v2 Announce Type: replace While Mixture-of-Experts (MoE) architectures define the state-of-the-art, their theoretical success is often attributed to heuristic efficiency rather than geometric expressivity. In this work, we present the first analysis of MoE through the lens of tropical geometry, establishing that the Top-$k$ routing mechanism is algebraically isomorphic to the $k$-th elementary symmetric tropical polynomial.