Routing-Calibrated Expert Selection for MoE Reuse: Mechanism And Empirical Validation

Mixture-of-Experts (MoE) efficiency research has followed three routes: improving the routing algorithm, pruning or compressing expert weights, and distilling expert knowledge into KV banks. All three share one property -- each introduces new content or a new selection criterion. This paper studies the opposite question: if an intermediate quantity has already been computed and is about to be discarded, can giving it a second consumer yield a capability gain? We call the mechanism reuse, and we give its criterion, its formalisation, measured effectiveness, and an analysis of why it works and when it fails. CRITERION. A quantity that has already been computed is used where it would not otherwise have been used. Operationally: it acquires a second consumer. In layer l, the routing distribution probs_l must be computed anyway; it serves only that layer's top-k selection and is then discarded, with no second consumer. FORMALISM. Because each token's top-k occupies exactly k mutually distinct slots, the per-layer hit rates r_e satisfy the exact identity sum_e r_e = k (measured: 4.0000, no approximation). Coverage and blood-loss are therefore exact quantities, and blood-loss is a linear functional of the resident set, so selecting the top-K experts by r_e is its exact minimiser. We name this rule RCES (Routing-Calibrated Expert Selection). We further define the coverage ceiling C_max(K) that no rule can exceed. TWO REUSE CHANNELS, BOTH WITH THE BACKBONE FROZEN. On Qwen1.5-MoE-A2.7B (24 layers / 60 experts / top-4), with every backbone parameter frozen: (a) phi channel. Pass probs_l through a 60x60 linear map phi_l and add it to the routing logits of layer l+1, changing which experts the next layer selects. Trainable parameters: 84,180 (0.00059% of the model). WikiText test perplexity falls from 9.485 to 9.094 (-4.13%). (b) SR channel (second routing), zero parameters, zero training. The first routing is the native top-4 and is left bit-for-bit untouched. The second routing appends, per token and per layer, the highest-ranked RCES experts that are not already active, weighted by their own native gate probability. Measured firing rate: 98.4% of tokens receive an append, averaging 1.84 of 2 slots, injecting 6.6% of the native routing weight. Cost: 0 new parameters, 0 training steps. MAIN RESULT (2044-question bank, paired McNemar). phi + SR improves task accuracy by +3.2 pp over the frozen backbone (61.8% vs 58.6%, p = 4.08e-4, 95% CI [+1.47, +4.99]) while holding the perplexity gain (-4.13%). On the non-numeric subset (1343 questions) the gain is also +3.2 pp (p = 7.17e-3). The SR channel alone -- zero parameters, zero training -- gives +1.8 pp (p = 8.88e-4). The two channels are additive: phi +1.4 pp, SR +1.8 pp, both +3.2 pp. A REFUTED EXPLANATION. A natural hypothesis is that reuse damages the native routing and the downstream layers can no longer read it. Against that: phi and phi+SR produce almost identical routing drift (0.2971 vs 0.2977; the native top-4 is unchanged for 36.0% vs 36.1% of token-layer pairs) while differing by 3.7 pp in task accuracy (p = 0.019). The SR channel structurally cannot alter the first routing, since it acts only on the dispatch output. What determines the task outcome is not how much the routing moved, but whether the information was put back. THE PLACEMENT LAW. These results, together with the earlier experiments in this line of work, condense into one statement in which the mechanism and the RCES criterion are held fixed and the only variable is where the mechanism is placed: any mechanism that intervenes in the FIRST routing -- that changes who is selected -- yields no task gain or active harm, while the same mechanism placed on the SECOND routing -- that appends one more computation -- yields a task gain. Hard masking (-38.3 pp), a large phi bias (-11.0 pp), and SR substitution all fall on the intervention side; SR appending (+1.8 pp) falls on the append side. The generative capability of the model is locked to the native routing distribution, and appending does not touch it. A MEASUREMENT WARNING. The 300-question bank reports the opposite sign for phi alone (-2.0 pp) and fails to resolve the phi+SR effect (+1.7 pp, p = 0.56). At 2044 questions all three comparisons become significant. Task-side claims in this area require the larger bank. A METHODOLOGICAL TRAP. "Zero weight is a no-op" is false on the evaluated hardware. The legacy expert dispatch padded the slot array with a zero-weight placeholder index, which left a duplicate token row inside an expert's input batch; the forward pass then diverged from the backbone (first divergence at layer 1, max routing-logit gap 1.0) and flipped 6 of 300 question verdicts, even though the platform itself reproduces bit-for-bit. Merging per-token weights and dropping zero-weight rows before the expert GEMM restores bit-identical output. ARTIFACTS. Source scripts, dependency modules, raw result files, the two phi checkpoints, and the exact cluster launch scripts are collected for reproduction.