Polysemantic Experts, Monosemantic Paths: Routing as Control in MoEs

Mixture-of-Experts (MoE) architectures enable efficient model scaling, yet expert routing behavior across underrepresented languages remains poorly understood. We analyze routing dynamics in two architecturally distinct MoE models -- a pure Transformer (Qwen3-30B-A3B) and a hybrid Mamba-Transformer (Nemotron-3-Nano-30B-A3B) -- using Hebrew as a morphologically rich, low-resource testbed. Both pre-trained models exhibit \emph{deep-layer routing collapse}: usage entropy drops sharply in final layers and tokens concentrate on a narrow expert subset, a pattern largely absent for English. Continual pre-training (CPT) on balanced bilingual data substantially corrects this imbalance, increasing entropy and shifting routing toward shared, language-agnostic experts; supervised fine-tuning (SFT) alone achieves less complete correction. Extending the analysis to Japanese reveals quantitatively consistent collapse signatures, providing cross-linguistic evidence that the phenomenon is a systematic consequence of pre-training underrepresentation rather than any language-intrinsic property. Routing improvements correlate with consistent downstream benchmark gains, positioning routing entropy and expert specialization as principled diagnostics for multilingual capacity in MoE systems.

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.

Sparse Mixture-of-Experts (MoE) architectures enable scaling LLM parameters under a fixed inference budget by activating only a small subset of experts via top-$k$ routing. While this preserves causality and suits autoregressive language models, the discrete top-$k$ operator is not differentiable, forcing a fixed number of active experts per input and resulting in inefficient use of computation. We propose SoftMoE, which replaces discrete routing with a truncated soft top-$k$ LapSum relaxation, allowing gradient-based optimization of expert routing. We further parameterize the mean number of active experts per layer and impose a global budget constraint, enabling the model to learn how to allocate expert capacity across layers. SoftMoE remains fully compatible with autoregressive modeling and achieves performance comparable to or better than sparse MoE on language modeling and downstream tasks, while activating significantly fewer experts. Notably, the learned allocation is highly non-uniform, with later layers activating more experts. The source code is publicly available$^\dagger$.