Proposes a router redesign for Mixture-of-Experts (MoE) that aligns each router row with its expert's principal singular direction using Manifold Power Iteration (MPI), improving token–expert affinity. MPI applies a 'power‑then‑retract' step to push router rows toward principal singular vectors while enforcing norm constraints; the paper gives convergence theory and pretraining results on 1B–11B MoE models.
