Layer-wise MoE Routing Locality under Shared-Prefix Code Generation: Token-Identity Decomposition and Compile-Equivalent Fork Redundancy

Mixture-of-Experts (MoE) language models route each token to a small subset of experts, but whether the routes selected by a trained top-$k$ router are good ones is rarely evaluated directly. Holding the model fixed, we compare each standard route against sampled equal-compute alternatives for the same token and score each by the next-token probability it assigns to the realized token in a verified reasoning trajectory. The result is sharply token-conditional: the standard router is well-aligned with route utility on confident tokens but uninformative on the fragile tokens that drive hard reasoning, where lower-loss equal-compute routes consistently exist inside the frozen model but are not selected. The same pattern holds across Qwen3-30B-A3B, GPT-OSS-20B, DeepSeek-V2-Lite, and OLMoE-1B-7B, and follows structurally from how standard top-$k$ training evaluates routing decisions: the language modeling loss scores only the executed route, and load balancing depends only on aggregate routing statistics. A minimal router-only update to the final-layer router, leaving every expert and every other router frozen, is sufficient to shift pass@K on AIME 2024+2025 and HMMT 2025 for both Qwen3-30B-A3B and GPT-OSS-20B, suggesting that at least part of the failure reflects router-reachable misallocation rather than expert capacity alone.

Sparse mixture-of-experts (MoE) language models route each token to multiple experts, suggesting a geometric account of their benefit: co-selected experts should contribute distinct representation directions. Existing evidence often conflates route coherence, candidate quality, and candidate-by-context interaction. We distinguish these quantities using an Expert Subspace Separation Index (ESSI), matched-route residuals, and a prefix-controlled $2\times2$ factorial; frozen-route interventions and a controlled Top-$k$ study assess functional value. Three paired contrasts organize the findings. First, across six MoE architectures, expert subspaces overlap substantially, yet actual routes explain token representations better than matched alternatives. Second, across the 39 factorial cells in OLMoE, Mixtral, and DeepSeek, the selected candidate explains more of the residual representation than the strongest unselected rival in every cell, yet the actual prefix narrows this advantage throughout: all interactions are negative, and every 95% confidence interval lies below zero. Third, this geometric narrowing does not imply functional redundancy: adding later experts improves next-token prediction in 24 of 39 frozen-route comparisons, while the other 15 estimates are inconclusive; a controlled training study also favors Top-2 over Top-1 in all three seeds. We call this joint pattern coherent overlap: routing selects token-relevant experts from a shared geometric neighborhood, while useful multi-expert computation persists without disjoint linear coverage. Separating these quantities clarifies why geometric similarity alone cannot determine redundancy or pruning value.

In sparse Mixture-of-Experts language models, does the same token id imply the same router state and the same experts producing it? Holding the emitted token id fixed at repeated anchors, we find it does not: the experts that produce it still separate task context, trajectory history, and reasoning-effort mode. This residual structure supports test-time control: near \emph{boundary} anchors (the final-response transition) and \emph{delimiter} anchors (which open the answer, e.g.\ \texttt{\textbackslash boxed{} or code fences), routing neighborhoods already align with final-answer basins at a marker-only readout and strongest when the routing is read at the answer opening. We operationalize this as \textbf{RAD} (Routing Agreement Decoding), an answer-string-free multi-rollout selector: it locates a fixed anchor, represents each rollout by its anchor-window MoE routing states, and returns the densest Weighted-Jaccard $K$-NN route-basin center, without parsing, normalizing, executing, or voting over answer strings. Across 10 sparse-MoE configurations (gpt-oss, Qwen3-MoE) and 6 datasets spanning math, GPQA, and code, RAD is on par with Majority where string voting is well-posed, with small positive paired deltas (RAD $73.9$ / RAD+DC $74.2$ vs.\ Majority $73.6$). Like majority voting, RAD is not a verifier: a dense \emph{wrong} basin can still win. Its value is the interface: the same selector gives direct pass@1 on code, where exact-string voting is ill-defined, and the same routing-density principle, re-anchored to the agentic boundary, improves best-of-16 patch selection on SWE-bench Verified over random, where patches have no answer string to vote on.