MoE Routing Testbed: Studying Expert Specialization and Routing Behavior at Small Scale

Mixture of Experts (MoEs) are now ubiquitous in large language models, yet the mechanisms behind their "expert specialization" remain poorly understood. We show that, since MoE routers are linear maps, hidden state similarity is both necessary and sufficient to explain expert usage similarity, and specialization is therefore an emergent property of the representation space, not of the routing architecture itself. We confirm this at both token and sequence level across five pre-trained models. We additionally prove that load-balancing loss suppresses shared hidden state directions to maintain routing diversity, which might provide a theoretical explanation for specialization collapse under less diverse data, e.g. small batch. Despite this clean mechanistic account, we find that specialization patterns in pre-trained MoEs resist human interpretation: expert overlap between different models answering the same question is no higher than between entirely different questions ($\sim$60%); prompt-level routing does not predict rollout-level routing; and deeper layers exhibit near-identical expert activation across semantically unrelated inputs, especially in reasoning models. We conclude that, while the efficiency perspective of MoEs is well understood, understanding expert specialization is at least as hard as understanding LLM hidden state geometry, a long-standing open problem in the literature.

Sparse Mixture-of-Experts (MoE) architectures employ increasingly sophisticated routing mechanisms -- learned routers, multi-hop trajectories, token-dependent gating. We ask: does routing topology actually determine language modeling quality? We build a geometric MoE (ST-MoE) using cosine-similarity routing against learned centroids in a low-dimensional space ($d_{space} = 64$), requiring 80% fewer routing parameters than standard linear routers. Through 62 controlled experiments on WikiText-103 at 76--84M parameters trained to convergence (50K steps, 1.64B tokens), we find that routing topology does not determine asymptotic perplexity (PPL): five cosine-routing variants are statistically equivalent within a 1-PPL margin (Two One-Sided Tests [TOST], $p < 0.05$ for all 10 pairwise comparisons; 15 runs across 3 seeds, observed range 33.93--34.72). The finding extends to hash, random-fixed, and top-1 routing (single-seed; graceful 1.1--2.2 PPL degradation) and replicates on OpenWebText (0.03 PPL gap, 6 runs, 3 seeds each). A standard linear router with 5.3$\times$ more routing parameters reaches PPL 32.76, but iso-parameter cosine routing closes 67% of this gap -- the true mechanism advantage is $\sim$1.2%. The mechanistic explanation is convergent redundancy: multi-hop updates are collinear ($\cos(Δh_0, Δh_1) = 0.805$), implementing magnitude amplification rather than compositional reasoning; a single learnable scalar replicates multi-hop performance. As a practical payoff, zero-shot relative-norm halting saves 25% of MoE FLOPs at +0.12% PPL. Expert-level specialization and causal controllability -- which coexist with topology-level equifinality -- are explored in a companion paper.

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 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.