Are Benchmarks Reliable? Toward Structural Diagnosis via Item-Level Capability Boundaries
Organizations: Beijing Normal University
Abstract
Evaluating large language models (LLMs) relies heavily on benchmark scores, yet aggregate metrics can obscure whether individual items serve their intended measurement purpose. BSDProbe provides an item-level framework for benchmark structural diagnosis that jointly characterizes correctness transitions and their supporting response evidence. Repeated responses along an empirically ordered model axis yield complementary correctness and normalized entropy trajectories, from which four-dimensional profiles of boundary position, boundary width, boundary-signal validity, and order consistency are constructed for benchmark-level aggregation. Experiments on six benchmarks identify varying proportions of potentially anomalous items. With Qwen3 as both the selection and reference axis, BSDProbe achieves a 17.9% mean relative improvement in normalized discrimination ratio over the best baseline per benchmark and matches or exceeds all baselines in ranking agreement with the full benchmark.
Figures & tables
| Benchmark | Qwen3 | Qwen2.5 | Cross-model |
| MMLU | 31.80 | 26.78 | 31.04 |
| GPQA | 56.25 | 48.21 | 57.59 |
| GSM8K | 8.87 | 3.79 | 28.13 |
| MATH | 8.18 | 4.25 | 7.27 |
| PopQA | 20.04 | 20.34 | 27.48 |
| TriviaQA | 25.28 | 25.82 | 36.96 |
| Benchmark | Random | Tiny Benchmarks | Anchor Points | Bayesian | PSN-IRT | BSDProbe (Qwen3) | BSDProbe (Qwen2.5) | BSDProbe (Cross-model) |
| MMLU | ||||||||
| GPQA | ||||||||
| GSM8K | ||||||||
| MATH | ||||||||
| PopQA | ||||||||
| TriviaQA |
| Benchmark | Random | Tiny Benchmarks | Anchor Points | Bayesian | PSN-IRT | BSDProbe (Qwen3) | BSDProbe (Qwen2.5) | BSDProbe (Cross-model) |
| MMLU | ||||||||
| GPQA | ||||||||
| GSM8K | ||||||||
| MATH | ||||||||
| PopQA | ||||||||
| TriviaQA |
Appendix figures & tables11 assets
Supplementary material from the paper’s appendix.
Appendix
| Qwen3 axis | Qwen2.5 axis | Cross-model axis |
| Qwen3-0.6B | Qwen2.5-0.5B-Instruct | Llama-3.2-1B-Instruct |
| Qwen3-1.7B | Qwen2.5-1.5B-Instruct | Llama-3.2-3B-Instruct |
| Qwen3-4B | Qwen2.5-3B-Instruct | Llama-3.1-8B-Instruct |
| Qwen3-8B | Qwen2.5-7B-Instruct | GLM-4-9B-0414 |
| Qwen3-14B | Qwen2.5-14B-Instruct | DeepSeek-R1-Distill-Qwen-14B |
| Qwen3-32B | Qwen2.5-32B-Instruct | GLM-4-32B-0414 |
| Axis | Model | MMLU | GPQA | GSM8K | MATH | PopQA | TriviaQA |
| Qwen3 Axis | Qwen3-0.6B | 41.20% | 29.02% | 68.16% | 56.22% | 12.94% | 18.98% |
| Qwen3-1.7B | 61.15% | 29.69% | 85.29% | 76.87% | 15.08% | 35.38% | |
| Qwen3-4B | 74.69% | 37.28% | 93.56% | 86.00% | 18.17% | 52.20% | |
| Qwen3-8B | 78.97% | 45.54% | 94.39% | 85.86% | 23.38% | 66.43% | |
| Qwen3-14B | 81.95% | 50.89% | 95.98% | 88.12% | 26.29% | 71.95% | |
| Qwen3-32B | 85.22% | 57.81% | 95.98% | 88.10% | 28.31% | 76.54% |
| Task type | Benchmarks | Ordered cross-model axis |
| MCQ | MMLU, GPQA | Llama-3.2-1B-Instruct Llama-3.2-3B-Instruct Llama-3.1-8B-Instruct GLM-4-9B-0414 DeepSeek-R1-Distill-Qwen-14B GLM-4-32B-0414 |
| Math | GSM8K, MATH | Llama-3.2-1B-Instruct Llama-3.2-3B-Instruct Llama-3.1-8B-Instruct GLM-4-9B-0414 DeepSeek-R1-Distill-Qwen-14B GLM-4-32B-0414 |
| QA | PopQA, TriviaQA | Llama-3.2-1B-Instruct GLM-4-9B-0414 Llama-3.2-3B-Instruct DeepSeek-R1-Distill-Qwen-14B Llama-3.1-8B-Instruct GLM-4-32B-0414 |
| Benchmark | |||||
| GPQA | 0.0921 | 0.0504 | 0.0345 | 0.0261 | 0.0216 |
| GSM8K | 0.0182 | 0.0119 | 0.0101 | 0.0084 | 0.0073 |
| MATH | 0.0680 | 0.0513 | 0.0440 | 0.0394 | 0.0363 |
| MMLU | 0.0245 | 0.0145 | 0.0102 | 0.0080 | 0.0066 |
| PopQA | 0.1998 | 0.1442 | 0.1169 | 0.0998 | 0.0880 |
| TriviaQA | 0.0593 | 0.0389 | 0.0299 | 0.0246 | 0.0214 |
| Benchmark | Items | Self-JSD | Cross-JSD | 95% CI for | |
| GPQA | 448 | 0.0113 | 0.1878 | 0.1766 | [0.1631, 0.1893] |
| GSM8K | 1317 | 0.0025 | 0.0673 | 0.0648 | [0.0534, 0.0768] |
| MATH | 5000 | 0.0060 | 0.1521 | 0.1461 | [0.1394, 0.1529] |
| MMLU | 14042 | 0.0046 | 0.1909 | 0.1863 | [0.1822, 0.1904] |
| PopQA | 14267 | 0.0019 | 0.2184 | 0.2165 | [0.2115, 0.2212] |
| TriviaQA | 7993 | 0.0024 | 0.2877 | 0.2853 | [0.2812, 0.2893] |
| Benchmark | Agree. (%) | MAE | MAE | Agree. (%) | MAE | MAE | Agree. (%) | MAE | MAE |
| GPQA | 64.8 | 0.080 | 0.096 | 80.7 | 0.049 | 0.066 | 89.8 | 0.029 | 0.041 |
| GSM8K | 94.0 | 0.028 | 0.033 | 96.7 | 0.016 | 0.021 | 98.3 | 0.009 | 0.012 |
| MATH | 93.6 | 0.051 | 0.064 | 95.8 | 0.031 | 0.043 | 97.6 | 0.018 | 0.026 |
| MMLU | 82.2 | 0.032 | 0.041 | 91.3 | 0.019 | 0.026 | 95.9 | 0.011 | 0.016 |
| PopQA | 91.0 | 0.027 | 0.032 | 95.9 | 0.016 | 0.021 | 98.2 | 0.009 | 0.013 |
| Benchmark | Agree. (%) | MAE | MAE | Agree. (%) | MAE | MAE | Agree. (%) | MAE | MAE |
| GPQA | 65.6–75.7 | 0.166 | 0.187 | 75.0–86.4 | 0.114 | 0.133 | 83.5–93.3 | 0.066 | 0.080 |
| GSM8K | 93.9–94.8 | 0.142 | 0.161 | 95.5–96.8 | 0.073 | 0.084 | 97.3–98.2 | 0.033 | 0.038 |
| MATH | 93.4–93.8 | 0.147 | 0.164 | 95.1–95.5 | 0.080 | 0.095 | 97.0–97.6 | 0.038 | 0.049 |
| MMLU | 79.2–84.2 | 0.158 | 0.179 | 85.1–90.5 | 0.095 | 0.109 | 90.8–95.5 | 0.049 | 0.058 |
| PopQA | 88.4–90.3 | 0.161 | 0.185 | 92.1–94.5 | 0.102 | 0.112 | 95.5–97.4 | 0.053 | 0.058 |
| Benchmark | Random | Tiny Benchmarks | Anchor Points | Bayesian | PSN-IRT | BSDProbe (Qwen3) | BSDProbe (Qwen2.5) | BSDProbe (Cross-model) |
| MMLU | ||||||||
| GPQA | ||||||||
| GSM8K | ||||||||
| MATH | ||||||||
| PopQA | ||||||||
| TriviaQA |
| Benchmark | Random | Tiny Benchmarks | Anchor Points | Bayesian | PSN-IRT | BSDProbe (Qwen3) | BSDProbe (Qwen2.5) | BSDProbe (Cross-model) |
| MMLU | ||||||||
| GPQA | ||||||||
| GSM8K | ||||||||
| MATH | ||||||||
| PopQA | ||||||||
| TriviaQA |
| Benchmark | Random | Tiny Benchmarks | Anchor Points | Bayesian | PSN-IRT | BSDProbe (Qwen3) | BSDProbe (Qwen2.5) | BSDProbe (Cross-model) |
| MMLU | ||||||||
| GPQA | ||||||||
| GSM8K | ||||||||
| MATH | ||||||||
| PopQA | ||||||||
| TriviaQA |
| Benchmark | Random | Tiny Benchmarks | Anchor Points | Bayesian | PSN-IRT | BSDProbe (Qwen3) | BSDProbe (Qwen2.5) | BSDProbe (Cross-model) |
| MMLU | ||||||||
| GPQA | ||||||||
| GSM8K | ||||||||
| MATH | ||||||||
| PopQA | ||||||||
| TriviaQA |
LLM Evaluation
Large language model evaluation measures what models can do, how reliably they do it, and whether benchmark scores predict real-world performance.
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