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Certain Head, Uncertain Tail: Expert-Sample for Test-Time Scaling in Fine-Grained MoE

ICML 2026 · Large language models › Reasoning and chain of thought · approach: Test-time compute scaling · 0 citations (OpenAlex)

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Proposes Expert-Sample, a training-free routing-level sampling method that keeps the top-ranked experts in fine-grained MoE and samples the remaining experts from a wider rank range to boost pass@n and best-of-N accuracy.

Problem

Test-time scaling with token-level sampling faces a diversity-stability trade-off controlled by temperature; the inference-time routing space of fine-grained MoE models is unexplored as a source of diversity.

Approach

Router scores in fine-grained MoE show a high-confidence head of experts followed by a flat uncertain tail; Expert-Sample deterministically keeps the head (top floor(k/2)+1 experts) and Gumbel-top-k samples the remaining slots from ranks k_keep+1 to 4k with temperature-scaled logits, keeping original gating weights for aggregation.

Key results

• On Qwen3-30B-A3B-Instruct with GPQA-Diamond at 32 samples, pass@32 rises from 85.4% to 91.9% and BoN accuracy from 59.1% to 62.6%.
• Across 20 model-dataset combinations, Expert-Sample yields average accuracy gains of 4.28% on top of BoN and 3.15% on top of WMV.
• Expert-Sample adds about 4.32% average pass@64 improvement over normal-temperature token sampling across 12 model-benchmark combinations; throughput change within about ±1%.

Surprising findings

• Reducing activated experts to about half of default top-k leaves greedy accuracy almost unchanged, yet substantially degrades multi-sample pass@n.
• High-temperature token sampling is inconsistent, sometimes underperforming normal-temperature sampling in pass@n.

Limitations

• Evaluated only on fine-grained MoE models; not applicable to dense models.
• Diversity scores rely on LLM judges (DeepSeek-R1, GPT-4o, Claude) whose absolute scores vary across judges.
• Hyperparameters were tuned on AIME-120 testbeds and may not transfer perfectly to all tasks.

Experimental setup

Datasets: AIME-120 GPQA-Diamond LiveCodeBench-V6-Lite AIME 2024 AIME 2025 HMMT 2025 MATH-500-Hard WikiText-2

Benchmarks: AIME-120 GPQA-Diamond LiveCodeBench-V6-Lite AIME 2024 AIME 2025 HMMT 2025 MATH-500-Hard

Metrics: pass@n accuracy with Best-of-N accuracy with weighted majority voting pass rate reasoning diversity score throughput

Baselines: token sampling (T=0.7) high-temperature token sampling (T=1.3) Entropy-based Dynamic Temperature sampling Best-of-N weighted majority voting

Builds on: Mixture-of-Experts Gumbel-top-k sampling entropy-based dynamic temperature sampling

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