MoRE: Scaling mixture of experts with hardware-aware low-rank routing

Mixture-of-Experts (MoE) layers are central to frontier language models, and recent architectures push toward more and smaller experts. In this regime, the standard linear router becomes a bottleneck: with M experts and hidden dimension h, its per-token cost Theta(Mh) dominates the MoE layer once M is large. We introduce MoRE (Mixture of Rank-reduced-routed Experts), which factorizes the router weight matrix at rank r and reduces the routing cost to O((h + M)r). We prove that rank logarithmic in M suffices for routing expressivity when the number of active experts is fixed, and is necessary up to precision factors. We also prove that logarithmic rank preserves load balance in a Gaussian memorization model, and training on a synthetic phonebook task shows that low rank does not hurt memorization. At matched active FLOPs, the factorization allows a factor of Theta(h/r) more experts. To realize this gain in wall-clock time, we design a fused Triton kernel at inference that avoids expensive memory operations on HBM. Empirically, MoRE improves memorization on the phonebook task and performance on knowledge-intensive Q&A benchmarks after pretraining, while matching reasoning ability. Code available at https://github.com/Matheart/MoREcode.