ACE: Adaptive Calibration-Free Expert Skipping for MoE-based LLMs
Abstract
Mixture-of-Experts (MoE) architectures provide an efficient paradigm for scaling large language models (LLMs), yet fixed top-k routing activates the same number of expert slots for every token, causing substantial redundant computation. Existing expert-skipping methods often rely on router confidence, calibration data, or additional training, and therefore cannot reliably estimate the actual contribution of routed experts. To this end, we propose ACE, a training-free, calibration-free, and checkpoint-preserving framework for token-adaptive expert skipping in MoE-based LLMs. ACE contains two complementary components: 1) Global Spectral Proxy (GSP), which estimates global transformation capacity from the coupled gate, up, and down projections together with RMSNorm scaling; and 2) Router-Conditioned Refinement (RCR), which constructs expert-specific direction prototypes from centered router weights and evaluates expert responses along routing-preferred directions. During inference, ACE combines both estimates with runtime router gates and skips an expert slot only when both views identify it as low-contribution, while always retaining the top-1 expert. All expert statistics are computed offline, leaving only table lookups and lightweight scalar operations online. Extensive experiments across three MoE-based LLMs and eight benchmarks demonstrate that ACE consistently outperforms existing static and dynamic baselines, with increasingly pronounced advantages under aggressive expert skipping. For instance, at a 50% skipping ratio on Qwen3.6-35B-A3B, ACE reduces WikiText-2 perplexity by 7.96% and improves average downstream accuracy by 4.15 percentage points over the strongest competing method.
Figures & tables
| Method | 10% | 20% | 30% | 40% | 50% | 60% | ||||||
| W2 | Acc. | W2 | Acc. | W2 | Acc. | W2 | Acc. | W2 | Acc. | W2 | Acc. | |
| BF16 | 7.52 | 80.67 | 7.52 | 80.67 | 7.52 | 80.67 | 7.52 | 80.67 | 7.52 | 80.67 | 7.52 | 80.67 |
| Score | 7.70 | 79.69 | 8.09 | 77.85 | 8.65 | 77.97 | 9.63 | 75.39 | 12.03 | 66.69 | 18.76 | 37.64 |
| NAEE | 7.70 | 80.39 | 8.07 | 79.34 | 8.68 | 77.77 | 9.82 | 72.93 | 12.48 | 64.40 | 19.56 | 43.44 |
| MoDES | 7.57 | 79.79 | 7.84 | 78.80 | 8.33 | 77.99 | 9.28 | 76.03 | 12.25 | 56.61 | 17.80 | 39.15 |
| DiEP | 10.09 | 76.58 | 16.00 | 64.36 | 28.42 | 47.05 | 65.87 | 27.44 | 136.92 | 3.96 | 459.88 | 3.62 |
| Method | 10% | 20% | 30% | 40% | 50% | 60% | ||||||
| W2 | Acc. | W2 | Acc. | W2 | Acc. | W2 | Acc. | W2 | Acc. | W2 | Acc. | |
| BF16 | 7.01 | 81.17 | 7.01 | 81.17 | 7.01 | 81.17 | 7.01 | 81.17 | 7.01 | 81.17 | 7.01 | 81.17 |
| Score | 7.38 | 81.66 | 7.79 | 80.51 | 8.36 | 78.41 | 9.21 | 74.61 | 10.58 | 67.45 | 13.38 | 54.66 |
| NAEE | 7.37 | 81.27 | 7.80 | 80.99 | 8.40 | 79.01 | 9.30 | 74.84 | 10.89 | 67.50 | 14.17 | 53.42 |
| MoDES | 7.38 | 80.86 | 7.41 | 80.59 | 7.72 | 78.19 | 8.10 | 75.74 | 9.42 | 71.42 | 10.87 | 69.04 |
| DiEP | 8.83 | 79.18 | 12.09 | 76.91 | 17.62 | 72.73 | 28.45 | 66.16 | 45.43 | 56.42 | 85.12 | 32.27 |
Appendix figures & tables19 assets
Supplementary material from the paper’s appendix.
Appendix
| Model | Workload | 10% | 20% | 30% | 40% | 50% | 60% |
| Qwen3-30B-A3B | WikiText-2 | 0.066076 | 0.078141 | 0.088436 | 0.098972 | 0.110965 | 0.125460 |
| ARC-C | 0.058638 | 0.071791 | 0.082505 | 0.093486 | 0.105523 | 0.121092 | |
| ARC-E | 0.058372 | 0.071509 | 0.082139 | 0.093135 | 0.105159 | 0.120699 | |
| PIQA | 0.059348 | 0.073267 | 0.084159 | 0.095478 | 0.106510 | 0.121876 | |
| MATH-500 | 0.064817 | 0.077139 | 0.087528 | 0.097363 | 0.108013 | 0.120972 | |
| GPQA-Diamond | 0.062387 | 0.074762 | 0.085411 | 0.095339 | 0.106186 | 0.120229 |
| Method | PPL | ARC-C | ARC-E | GPQA | HumanEval | LiveCodeBench | MATH-500 | PIQA | Avg. |
| BF16 | 7.52 | 93.17 | 94.23 | 56.57 | 93.90 | 55.26 | 80.00 | 91.57 | 80.67 |
| Score | 7.70 | 93.00 | 94.36 | 53.03 | 93.29 | 52.17 | 80.00 | 91.95 | 79.69 |
| NAEE | 7.70 | 93.33 | 94.27 | 57.57 | 92.94 | 53.37 | 80.00 | 91.22 | 80.39 |
| MoDES | 7.57 | 93.10 | 94.29 | 55.78 | 94.10 | 50.23 | 79.80 | 91.20 | 79.79 |
| DiEP | 10.09 | 90.78 | 93.98 | 48.48 | 86.59 | 48.72 | 78.60 | 88.90 | 76.58 |
| AIMER | 7.55 | 93.09 | 94.32 | 55.97 | 94.10 | 53.11 | 78.60 | 91.35 | 80.08 |
| Method | PPL | ARC-C | ARC-E | GPQA | HumanEval | LiveCodeBench | MATH-500 | PIQA | Avg. |
| BF16 | 7.52 | 93.17 | 94.23 | 56.57 | 93.90 | 55.26 | 80.00 | 91.57 | 80.67 |
| Score | 8.09 | 93.00 | 94.23 | 48.99 | 91.46 | 48.18 | 78.20 | 90.86 | 77.85 |
| NAEE | 8.07 | 92.83 | 94.36 | 52.02 | 92.34 | 52.89 | 80.00 | 90.96 | 79.34 |
| MoDES | 7.84 | 93.19 | 94.23 | 54.11 | 91.48 | 50.10 | 78.40 | 90.10 | 78.80 |
| DiEP | 16.00 | 87.29 | 91.41 | 19.19 | 60.98 | 47.39 | 59.80 | 84.44 | 64.36 |
| AIMER | 7.65 | 93.09 | 94.23 | 57.10 | 91.46 | 54.17 | 78.80 | 90.70 | 79.94 |
| Method | PPL | ARC-C | ARC-E | GPQA | HumanEval | LiveCodeBench | MATH-500 | PIQA | Avg. |
| BF16 | 7.52 | 93.17 | 94.23 | 56.57 | 93.90 | 55.26 | 80.00 | 91.57 | 80.67 |
| Score | 8.65 | 92.58 | 94.28 | 50.51 | 92.68 | 48.01 | 78.20 | 89.55 | 77.97 |
| NAEE | 8.68 | 91.89 | 94.11 | 50.00 | 91.29 | 47.20 | 79.00 | 90.91 | 77.77 |
| MoDES | 8.33 | 91.19 | 94.89 | 51.98 | 93.01 | 49.88 | 75.40 | 89.60 | 77.99 |
| DiEP | 28.42 | 78.41 | 86.78 | 4.55 | 47.56 | 37.86 | 3.80 | 70.40 | 47.05 |
| AIMER | 7.82 | 92.66 | 94.23 | 56.09 | 93.14 | 51.77 | 79.00 | 88.66 | 79.36 |
| Method | PPL | ARC-C | ARC-E | GPQA | HumanEval | LiveCodeBench | MATH-500 | PIQA | Avg. |
| BF16 | 7.52 | 93.17 | 94.23 | 56.57 | 93.90 | 55.26 | 80.00 | 91.57 | 80.67 |
| Score | 9.63 | 89.27 | 93.64 | 49.49 | 83.93 | 46.92 | 76.60 | 87.87 | 75.39 |
| NAEE | 9.82 | 89.51 | 93.35 | 38.89 | 83.15 | 37.82 | 79.00 | 88.82 | 72.93 |
| MoDES | 9.28 | 89.17 | 93.30 | 48.99 | 85.95 | 49.91 | 76.40 | 88.48 | 76.03 |
| DiEP | 65.87 | 54.52 | 61.11 | 5.56 | 0.00 | 22.17 | 3.80 | 44.89 | 27.44 |
| AIMER | 8.24 | 91.66 | 93.56 | 52.17 | 87.47 | 48.98 | 78.20 | 88.12 | 77.17 |
| Method | PPL | ARC-C | ARC-E | GPQA | HumanEval | LiveCodeBench | MATH-500 | PIQA | Avg. |
| BF16 | 7.52 | 93.17 | 94.23 | 56.57 | 93.90 | 55.26 | 80.00 | 91.57 | 80.67 |
| Score | 12.03 | 88.48 | 91.92 | 30.30 | 70.18 | 37.02 | 65.00 | 83.90 | 66.69 |
| NAEE | 12.48 | 86.43 | 92.05 | 26.77 | 67.68 | 23.89 | 73.20 | 80.75 | 64.40 |
| MoDES | 12.25 | 86.19 | 90.47 | 27.19 | 60.98 | 25.79 | 26.40 | 79.28 | 56.61 |
| DiEP | 136.92 | 5.03 | 5.39 | 3.54 | 0.00 | 5.02 | 1.80 | 6.96 | 3.96 |
| AIMER | 8.86 | 88.99 | 88.89 | 52.18 | 85.23 | 44.89 | 74.20 | 79.43 | 73.40 |
| Method | PPL | ARC-C | ARC-E | GPQA | HumanEval | LiveCodeBench | MATH-500 | PIQA | Avg. |
| BF16 | 7.52 | 93.17 | 94.23 | 56.57 | 93.90 | 55.26 | 80.00 | 91.57 | 80.67 |
| Score | 18.76 | 75.34 | 81.86 | 10.10 | 10.50 | 5.95 | 13.20 | 66.54 | 37.64 |
| NAEE | 19.56 | 56.25 | 56.25 | 17.68 | 27.44 | 5.88 | 60.40 | 80.21 | 43.44 |
| MoDES | 17.80 | 68.81 | 79.96 | 10.39 | 10.29 | 13.82 | 19.80 | 70.98 | 39.15 |
| DiEP | 459.88 | 4.44 | 6.40 | 4.04 | 0.00 | 0.00 | 2.60 | 7.89 | 3.62 |
| AIMER | 10.89 | 79.82 | 82.87 | 25.29 | 70.29 | 31.17 | 57.10 | 79.64 | 60.88 |
| Method | PPL | ARC-C | ARC-E | GPQA | HumanEval | LiveCodeBench | MATH-500 | PIQA | Avg. |
| BF16 | 7.01 | 95.14 | 94.82 | 47.47 | 95.12 | 57.35 | 84.60 | 93.69 | 81.17 |
| Score | 7.38 | 95.31 | 94.78 | 45.45 | 97.56 | 59.72 | 84.80 | 94.02 | 81.66 |
| NAEE | 7.37 | 94.97 | 94.87 | 45.45 | 96.95 | 58.39 | 84.00 | 94.23 | 81.27 |
| MoDES | 7.38 | 95.22 | 94.39 | 47.89 | 95.31 | 56.21 | 83.20 | 93.80 | 80.86 |
| DiEP | 8.83 | 93.28 | 94.19 | 45.48 | 95.10 | 52.87 | 80.20 | 93.11 | 79.18 |
| GSP | 7.18 | 95.05 | 94.82 | 46.46 | 96.34 | 56.30 | 84.40 | 94.45 | 81.12 |
| Method | PPL | ARC-C | ARC-E | GPQA | HumanEval | LiveCodeBench | MATH-500 | PIQA | Avg. |
| BF16 | 7.01 | 95.14 | 94.82 | 47.47 | 95.12 | 57.35 | 84.60 | 93.69 | 81.17 |
| Score | 7.79 | 94.71 | 94.82 | 46.46 | 93.90 | 54.88 | 85.60 | 93.20 | 80.51 |
| NAEE | 7.80 | 94.88 | 94.99 | 49.49 | 96.34 | 52.89 | 84.40 | 93.96 | 80.99 |
| MoDES | 7.41 | 94.11 | 94.20 | 46.66 | 95.29 | 56.19 | 84.60 | 93.08 | 80.59 |
| DiEP | 12.09 | 91.22 | 91.17 | 42.09 | 93.67 | 49.34 | 79.80 | 91.11 | 76.91 |
| GSP | 7.38 | 93.86 | 94.82 | 47.98 | 95.73 | 51.85 | 84.80 | 94.45 | 80.50 |
| Method | PPL | ARC-C | ARC-E | GPQA | HumanEval | LiveCodeBench | MATH-500 | PIQA | Avg. |
| BF16 | 7.01 | 95.14 | 94.82 | 47.47 | 95.12 | 57.35 | 84.60 | 93.69 | 81.17 |
| Score | 8.36 | 95.14 | 94.78 | 46.97 | 89.02 | 47.20 | 83.40 | 92.34 | 78.41 |
| NAEE | 8.40 | 95.14 | 94.70 | 44.44 | 93.29 | 47.20 | 84.40 | 93.91 | 79.01 |
| MoDES | 7.72 | 94.77 | 94.65 | 44.79 | 89.80 | 48.19 | 84.00 | 91.11 | 78.19 |
| DiEP | 17.62 | 88.49 | 87.48 | 40.11 | 89.71 | 42.88 | 75.20 | 85.24 | 72.73 |
| GSP | 7.66 | 94.97 | 94.70 | 46.97 | 94.51 | 48.34 | 83.40 | 93.31 | 79.46 |
| Method | PPL | ARC-C | ARC-E | GPQA | HumanEval | LiveCodeBench | MATH-500 | PIQA | Avg. |
| BF16 | 7.01 | 95.14 | 94.82 | 47.47 | 95.12 | 57.35 | 84.60 | 93.69 | 81.17 |
| Score | 9.21 | 94.88 | 94.44 | 34.34 | 84.15 | 39.05 | 82.00 | 93.42 | 74.61 |
| NAEE | 9.30 | 94.62 | 94.40 | 38.89 | 84.15 | 37.82 | 81.20 | 92.82 | 74.84 |
| MoDES | 8.10 | 94.22 | 94.12 | 38.67 | 89.38 | 44.28 | 79.40 | 90.11 | 75.74 |
| DiEP | 28.45 | 80.84 | 82.07 | 35.75 | 80.11 | 32.98 | 71.20 | 80.16 | 66.16 |
| GSP | 8.08 | 95.05 | 94.61 | 41.41 | 95.73 | 45.21 | 82.40 | 93.36 | 78.25 |
| Method | PPL | ARC-C | ARC-E | GPQA | HumanEval | LiveCodeBench | MATH-500 | PIQA | Avg. |
| BF16 | 7.01 | 95.14 | 94.82 | 47.47 | 95.12 | 57.35 | 84.60 | 93.69 | 81.17 |
| Score | 10.58 | 93.77 | 94.15 | 30.81 | 60.98 | 25.21 | 75.80 | 91.46 | 67.45 |
| NAEE | 10.89 | 94.20 | 93.98 | 26.77 | 67.68 | 23.89 | 75.20 | 90.75 | 67.50 |
| MoDES | 9.42 | 93.18 | 92.65 | 33.01 | 80.49 | 34.42 | 76.00 | 90.20 | 71.42 |
| DiEP | 45.43 | 73.87 | 77.98 | 20.76 | 56.91 | 20.88 | 68.40 | 76.11 | 56.42 |
| GSP | 8.87 | 94.28 | 94.49 | 34.34 | 90.85 | 39.72 | 79.60 | 91.78 | 75.01 |
| Method | PPL | ARC-C | ARC-E | GPQA | HumanEval | LiveCodeBench | MATH-500 | PIQA | Avg. |
| BF16 | 7.01 | 95.14 | 94.82 | 47.47 | 95.12 | 57.35 | 84.60 | 93.69 | 81.17 |
| Score | 13.38 | 89.68 | 91.04 | 21.72 | 29.27 | 6.26 | 59.00 | 85.64 | 54.66 |
| NAEE | 14.17 | 88.31 | 91.04 | 17.68 | 27.44 | 5.88 | 61.40 | 82.21 | 53.42 |
| MoDES | 10.87 | 91.87 | 94.11 | 28.40 | 82.29 | 27.44 | 70.70 | 88.45 | 69.04 |
| DiEP | 85.12 | 70.37 | 70.11 | 11.28 | 0.00 | 0.00 | 10.20 | 63.91 | 32.27 |
| GSP | 10.48 | 93.86 | 94.28 | 30.81 | 83.54 | 27.96 | 73.20 | 90.15 | 70.54 |
| Method | PPL | ARC-C | ARC-E | GPQA | HumanEval | LiveCodeBench | MATH-500 | PIQA | Avg. |
| BF16 | – | 95.82 | 94.91 | 51.52 | 95.73 | 59.81 | 86.60 | 87.05 | 81.63 |
| Score | – | 94.11 | 94.28 | 52.02 | 92.68 | 58.10 | 85.60 | 87.32 | 80.59 |
| NAEE | – | 94.45 | 94.40 | 50.00 | 93.90 | 56.21 | 88.20 | 87.54 | 80.67 |
| MoDES | – | 94.07 | 93.88 | 53.29 | 93.90 | 57.34 | 86.20 | 87.05 | 80.82 |
| DiEP | – | 94.10 | 93.19 | 50.33 | 92.45 | 55.98 | 84.20 | 87.05 | 79.61 |
| GSP | – | 94.11 | 93.90 | 53.48 | 93.90 | 57.91 | 87.40 | 87.27 | 81.14 |
| Method | PPL | ARC-C | ARC-E | GPQA | HumanEval | LiveCodeBench | MATH-500 | PIQA | Avg. |
| BF16 | – | 95.82 | 94.91 | 51.52 | 95.73 | 59.81 | 86.60 | 87.05 | 81.63 |
| Score | – | 94.28 | 94.11 | 52.02 | 92.68 | 55.26 | 85.60 | 87.05 | 80.14 |
| NAEE | – | 94.45 | 94.23 | 54.04 | 93.90 | 55.83 | 85.60 | 87.05 | 80.73 |
| MoDES | – | 93.78 | 94.02 | 53.97 | 93.90 | 56.27 | 85.60 | 86.84 | 80.63 |
| DiEP | – | 92.98 | 92.46 | 50.98 | 92.17 | 53.91 | 84.00 | 84.10 | 78.66 |
| GSP | – | 94.11 | 94.15 | 53.54 | 95.73 | 56.94 | 86.40 | 87.27 | 81.16 |
| Method | PPL | ARC-C | ARC-E | GPQA | HumanEval | LiveCodeBench | MATH-500 | PIQA | Avg. |
| BF16 | – | 95.82 | 94.91 | 51.52 | 95.73 | 59.81 | 86.60 | 87.05 | 81.63 |
| Score | – | 94.28 | 94.15 | 50.51 | 90.24 | 49.19 | 82.20 | 86.78 | 78.19 |
| NAEE | – | 93.94 | 93.98 | 45.96 | 93.68 | 50.62 | 81.40 | 86.24 | 77.97 |
| MoDES | – | 93.77 | 93.78 | 48.38 | 93.44 | 50.43 | 83.00 | 86.17 | 78.42 |
| DiEP | – | 90.38 | 92.06 | 46.70 | 90.45 | 50.38 | 81.20 | 80.14 | 75.90 |
| GSP | – | 94.54 | 93.98 | 52.02 | 93.34 | 54.28 | 82.80 | 87.00 | 79.71 |
| Method | PPL | ARC-C | ARC-E | GPQA | HumanEval | LiveCodeBench | MATH-500 | PIQA | Avg. |
| BF16 | – | 95.82 | 94.91 | 51.52 | 95.73 | 59.81 | 86.60 | 87.05 | 81.63 |
| Score | – | 92.32 | 93.73 | 49.49 | 87.20 | 43.13 | 81.00 | 85.80 | 76.10 |
| NAEE | – | 94.03 | 93.77 | 50.51 | 78.66 | 42.37 | 72.40 | 85.15 | 73.84 |
| MoDES | – | 93.45 | 93.84 | 49.05 | 93.05 | 47.92 | 81.80 | 85.78 | 77.84 |
| DiEP | – | 88.58 | 91.39 | 42.09 | 88.20 | 44.84 | 75.80 | 74.11 | 72.14 |
| GSP | – | 94.45 | 94.15 | 51.01 | 93.90 | 48.98 | 81.80 | 86.29 | 78.65 |
| Method | PPL | ARC-C | ARC-E | GPQA | HumanEval | LiveCodeBench | MATH-500 | PIQA | Avg. |
| BF16 | – | 95.82 | 94.91 | 51.52 | 95.73 | 59.81 | 86.60 | 87.05 | 81.63 |
| Score | – | 90.78 | 92.89 | 39.90 | 85.98 | 35.07 | 70.60 | 82.75 | 71.14 |
| NAEE | – | 92.32 | 93.60 | 42.42 | 76.83 | 29.95 | 60.00 | 82.86 | 68.28 |
| MoDES | – | 69.84 | 59.28 | 27.89 | 22.56 | 0.00 | 20.80 | 70.81 | 38.74 |
| DiEP | – | 50.76 | 50.92 | 20.08 | 15.98 | 0.00 | 10.60 | 67.47 | 30.83 |
| GSP | – | 93.69 | 94.19 | 46.97 | 90.85 | 41.29 | 77.40 | 85.69 | 75.73 |
| Method | PPL | ARC-C | ARC-E | GPQA | HumanEval | LiveCodeBench | MATH-500 | PIQA | Avg. |
| BF16 | – | 95.82 | 94.91 | 51.52 | 95.73 | 59.81 | 86.60 | 87.05 | 81.63 |
| Score | – | 85.07 | 90.53 | 32.83 | 73.78 | 26.07 | 59.40 | 80.69 | 64.05 |
| NAEE | – | 86.18 | 91.71 | 34.34 | 58.54 | 16.21 | 36.00 | 78.56 | 57.36 |
| MoDES | – | 50.01 | 48.18 | 28.01 | 6.10 | 0.00 | 6.80 | 48.92 | 26.86 |
| DiEP | – | 29.87 | 38.97 | 18.92 | 0.00 | 0.00 | 0.00 | 39.17 | 18.13 |
| GSP | – | 90.53 | 93.35 | 40.40 | 87.80 | 30.98 | 61.60 | 82.86 | 69.65 |
Mixture-of-Experts Inference
Mixture-of-experts inference studies how to run sparsely activated expert models efficiently while preserving their quality.
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