MoE Reuse:A delayed-one-layer routing-reuse architecture

Sparse Mixture-of-Experts (MoE) decouples parameter count from compute, yet every routed expert must still reside in device memory as weights. This paper answers two questions. (1) Given N experts, how should the K resident experts be selected so that the routing damage caused by eviction is minimised? (2) Without updating a single backbone parameter, can reuse recover the capability that was lost? For (1) we formalise RCES (Route-Coverage Resident Expert Selection). Because each token's top-k occupies exactly k mutually distinct slots, the per-layer hit rates sum identically to k (measured on Qwen1.5-MoE-A2.7B: sum_e r_e = 4.0000, no approximation). Coverage and blood-loss rate are therefore exact quantities rather than estimates, and the blood-loss rate is a linear functional of the resident-set choice -- hence selecting the top-K experts by r_e element-wise is its exact minimiser. This is an algebraic identity, not an experimental result. We further define the coverage ceiling C_max(K), the bound that no selection rule can exceed. For (2) we propose delayed-one-layer routing reuse. The routing distribution probs_l computed at layer l is ordinarily used only for that layer's top-k selection and then discarded; reuse passes it through a 60x60 linear map phi_l and adds it to the routing logits of layer l+1, thereby changing which experts the next layer selects. The per-layer compute is exactly identical to that of a 1-pass forward. On Qwen1.5-MoE-A2.7B (24 layers / 60 experts / top-4), with the entire backbone frozen and only 84,180 parameters trained (0.00059% of the model), perplexity on the WikiText test set falls from 9.485 to 9.101 (-4.04%) at K=60 (no eviction). The result is reproduced bit-for-bit across four independent runs and passes a four-fold verification: the trainable count is exactly 84,180; with phi zero-initialised the new structure is bit-identical to the original model; switching reuse off is the original backbone forward pass; and our rewritten forward pass matches the official HuggingFace implementation with zero difference across 9,723,904 logits. The eviction dose-response on the real model (K=60/36/25/12, blood loss 0% to 60.23%) shows damage that accelerates super-linearly, from which we derive the model's routing survival threshold. We also report a metric validity check: over the K sequence on which backbone capability decreases monotonically, only the generation hit rate is monotone among five candidate metrics; every fixed reference-string likelihood metric fails, and such metrics mistake degradation for improvement.