Spend Experts Where You Are Unsure: Confidence-Adaptive Routing for Mixture-of-Experts LoRA

Mixture-of-Experts (MoE) models decouple total parameters from per-token compute, but deployment still requires storing every expert. Recent theory shows that pruning experts with the smallest router-norm changes during fine-tuning can preserve accuracy, but assumes full fine-tuning. We test whether lightweight adaptation can recover this signal. We briefly fine-tune with a parameter-efficient adapter, rank experts by the induced $\ell_2$ router change, and prune the least-changed experts in one shot. On Mixtral-8$\times$7B-Instruct (44.83% MMLU-Pro), router-only LoRA trains 0.002% of parameters and outperforms all-module LoRA at matched rank with half the experts removed (27.54% vs. 24.42%); signal quality declines as adaptation spreads to attention and expert weights. Accuracy improves monotonically with LoRA rank, reaching 28.76%. IA3, which leaves router weights frozen, matches direct router adaptation, whereas unconstrained additive adapters degrade the signal. Router-guided MMLU-Pro accuracy decays quasi-linearly rather than collapsing, remains nearly 1.8 times that of magnitude-based or random pruning at maximal compression, and reduces memory by 49% and per-token latency by 37%. At 25% compression, retention is competitive with methods using full activation statistics. The criterion also transfers to Qwen1.5-MoE fine-tuned for mathematics, retaining 49.7% mean accuracy over eleven benchmarks with half the experts removed while random pruning falls to single digits. Router sensitivity under lightweight fine-tuning therefore makes provably motivated expert pruning practical at scale.

Mixtures of low-rank adaptation experts increase parameter-efficient capacity by routing each input through a subset of adapters. Recent dynamic routers activate more experts when the router or prediction is uncertain. This rule silently equates uncertainty with useful additional computation: an uncertain example may contain complementary, unqueried expert evidence, but it may instead remain ambiguous after every expert agrees. We formulate routing as certified value-of-information allocation. VI-MoLE learns the counterfactual risk remaining after each expert prefix, converts these predictions into simultaneous upper-risk certificates on held-out calibration data, and spends a global adapter budget on the token--layer action with the largest certified marginal risk reduction per unit cost. A terminal certificate then decides whether to answer or abstain. Unlike an uncertainty gate, this procedure distinguishes present ambiguity from recoverable and residual risk. We prove simultaneous certificate validity, optimal greedy allocation under diminishing certified gains, and allocation regret under value-estimation error. The evaluation protocol tests matched-compute accuracy, certificate coverage, risk--coverage, distribution shift, and tail latency against fixed and dynamic MoE-LoRA routers.

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.