Organizations: University of Sydney · Zhejiang University · Google Research
Abstract
Mixture-of-experts (MoE) layers enable the scaling of transformer models while keeping the inference compute fixed. While task-expert specialization has been observed in empirical studies of frontier MoE transformer models, existing theoretical work analyzes this using continuous mixture models that cannot be used to model natural language effectively. An important open question is to \textit{theoretically explain task-expert specialization in transformer MoE models using discrete models of language}. To address this, we represent structured knowledge via syntactic templates and finite key-value dictionaries, and prove formally that a single-layer MoE transformer can encode knowledge by using experts that specialize in the corresponding tasks. Our construction shows how queries are routed to unique, task-specific experts whose size depends solely on the intrinsic complexity of the given task (i.e. the combined size of its syntactic templates and factual dictionary). Our construction provides a theoretical support for empirical results on localized knowledge circuits in MoE models. We support our theoretical findings with experiments evaluating model performance under varying MoE loss functions.
Mixture-of-Experts (MoE) enables efficient scaling of Transformer models by routing tokens to a small subset of experts. However, existing routers typically condition expert selection on shallow or isolated token representations, which often produce unstable and semantically inconsistent routing decisions across layers. In this work, we revisit expert selection from a representation perspective and identify context incompleteness as a key bottleneck limiting effective expert specialization. To address this issue, we propose Multi-level Context Fusion MOE (MCF-MOE), a framework that constructs context-aware representations by integrating complementary signals from cross-layer semantic aggregation and local token-level interactions, enabling more informative and consistent expert selection. Experiments on language modeling and understanding benchmarks demonstrate that MCF-MOE consistently improves routing consistency and downstream performance over strong MoE baselines, highlighting the importance of contextual completeness in expert routing. The code is available at https://anonymous.4open.science/r/MCFMOE.
Mixture-of-experts (MoE) models enable scalable transformer architectures by activating only a subset of experts per token. Recent evidence suggests that performance improves with increasingly granular experts, i.e., many small experts instead of a few large ones. However, this regime substantially increases routing cost, which can dominate computation. We introduce adaptive inverted-index routing for MoE (AIR-MoE), an inverted-index-inspired routing architecture based on vector quantization (VQ). In a first stage, AIR-MoE performs coarse shortlisting by assigning tokens to VQ codewords to construct a candidate set of experts. In a second stage, fine scoring computes exact routing scores restricted to this shortlist. This two-stage procedure approximates true top-k routing while avoiding full expert scoring and, in contrast to prior work, imposing no structural constraints on expert parameters. AIR-MoE serves as a drop-in replacement for standard routers and requires no modifications to the model architecture or loss function. We further provide a lower bound on the mass recall achieved by AIR-MoE that yields insights into its inner workings. Empirically, we demonstrate that AIR-MoE achieves improved performance compared to existing routing approaches in granular MoE settings.
Klaus-Rudolf Kladny, Maximilian Mordig, Bernhard Schölkopf +1
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.