SkillEval: Learning Interpretable Ability Profiles of LLMs via Cognitive Diagnosis Models
Organizations: Department of Computer Science ETH Zurich · Machine Learning and Optimization Lab EPFL · ETH AI Center ETH Zurich
Abstract
Current evaluation of LLMs on benchmarks typically aggregates performance over individual examples into a single scalar score. This approach is overly coarse and ignores the diverse scope of skills covered by benchmark datasets. To address this limitation and better exploit benchmark data, we propose SkillEval, a new evaluation framework that performs cross-model, skill-level analysis. The framework integrates advances from two areas: (1) it leverages the meta-cognitive capabilities of LLMs to automatically discover interpretable skills from questions, and (2) it applies cognitive diagnosis models (CDMs) from psychometrics to estimate per-skill abilities of LLMs. We conduct experiments on 3,811 LLMs evaluated on 9,523 items across five benchmarks spanning diverse domains (MATH, BBH, GPQA, MuSR, IFEval). Compared to the traditional average-based evaluation paradigm, SkillEval produces reliable, more calibrated and informative yet concise model profiles that more accurately predict model behavior on unseen items. We also demonstrate the utility of SkillEval in two downstream tasks: (1) LLM routing, which dynamically assigns each query to a capable but efficient model, reducing inference cost by over 60% while achieving improved performance, and (2) Computerized Adaptive Testing (CAT), where an unseen model can be efficiently evaluated using a trained CDM. Furthermore, we show that these skill profiles provide useful insights, for example, how benchmarks share skills and how instruction-tuned models differ from their base models.
Figures & tables
| Model | Flat | Per-LLM | Per-dim | ||
|---|---|---|---|---|---|
| Raw | Orthogonal | Full | |||
| IRTNet ( ) | 0.02 ( 0.06) | 0.02 ( 0.06) | 0.00 ( 0.01) | 0.43 ( 0.22) | 0.43 ( 0.21) |
| IRTNet ( ) | 0.00 ( 0.04) | 0.00 ( 0.04) | 0.00 ( 0.00) | 0.17 ( 0.02) | 0.17 ( 0.01) |
| IRTNet ( ) | 0.01 ( 0.00) | 0.01 ( 0.00) | 0.00 ( 0.00) | 0.10 ( 0.02) | 0.10 ( 0.02) |
| SkillEval ( ) | 0.99 ( 0.00) | 0.99 ( 0.01) | 0.96 ( 0.00) | 0.96 ( 0.00) | 0.96 ( 0.00) |
| Model | AUC | Acc | ||
|---|---|---|---|---|
| ID | OOD | ID | OOD | |
| IRT (2PL) | 86.16 | – | 78.76 | – |
| IRTNet ( ) | 81.38 | 75.04 | 74.21 | 69.05 |
| IRTNet ( ) | 81.36 | 75.14 | 74.21 | 69.07 |
| IRTNet ( ) | 81.74 | 75.35 | 74.68 | 69.38 |
| SkillEval ( ) | 81.73 | 72.15 | 75.57 | 67.62 |
| Method | Acc@1 | Acc@3 | Acc@5 | Acc@10 |
|---|---|---|---|---|
| Random | 40.47 | – | – | – |
| Strongest single LLM | 61.57 | – | – | – |
| IRT 2PL | 61.10 | 77.74 | 81.94 | 85.93 |
| KNN | 62.05 | 78.01 | 83.10 | 88.98 |
| IRTNet, 3 seeds | 63.08 | 77.31 | 81.21 | 86.44 |
| ( 0.98) | ( 0.55) | ( 1.60) | ( 0.76) |
Appendix figures & tables11 assets
Supplementary material from the paper’s appendix.
Appendix
| Symbol | Meaning |
|---|---|
| Number of LLMs ( ) | |
| Number of items ( ); also the number of answers used to profile a new LLM | |
| Number of skill clusters ( default) | |
| LLM index | |
| Item index | |
| Skill index |
| Skill cluster | Items | Example items |
|---|---|---|
| Quadratic Formula (MATH-primary, 429/451) | 451 | “Find the domain of ” “If and , find the greatest value of ” |
| Truthfulness of Nested Statements (BBH-primary, 1836/1880) | 1,880 | “Then he tells Billy: ‘Be sure that you do not come in at all tomorrow morning’ ” (causal judgement) “Teressa lies. Willian says Teressa lies. Jamey says Willian lies. Ryan says Jamey lies. Kandi says Ryan lies. Does Kandi tell the truth?” (web of lies) |
| Structural Isomers in Organic Compounds (GPQA-primary, 442/488) | 488 | “Identify product D [from NMR spectrum]: (A) 2-bromonaphthalene (B) 2-bromo-1,2,3,4-tetrahydronaphthalene…” |
| Word Count Constraints (IFEval-primary, 414/418) | 418 | “Write a social media post about the hajj pilgrimage. Use all lowercase and include the word ‘story’ at least twice” |
| Both | Skill 1 | Skill 2 | Neither | |
|---|---|---|---|---|
| BBH (conjunctive) | 0.74 | 0.33 | 0.22 | 0.10 |
| IFEval (compensatory) | 0.93 | 0.97 | 0.42 | 0.12 |
| Test AUC | Acc@1 | Acc@3 | Acc@5 | Acc@10 | |
|---|---|---|---|---|---|
| 50 | 0.720 | 0.640 | 0.783 | 0.829 | 0.877 |
| 100 | 0.717 | 0.657 | 0.780 | 0.829 | 0.875 |
| 150 | 0.719 | 0.654 | 0.778 | 0.831 | 0.887 |
| 200 | 0.716 | 0.661 | 0.797 | 0.846 | 0.885 |
| 300 | 0.719 | 0.672 | 0.794 | 0.843 | 0.882 |
| 400 | 0.721 | 0.669 | 0.802 | 0.841 | 0.887 |
| Error | Agreement | AUC | |||||
|---|---|---|---|---|---|---|---|
| Random | Adaptive | Count | Random | Adaptive | Random | Adaptive | |
| 0 | 0.095 | 0.095 | 0.095 | 0.000 | 0.000 | 0.682 | 0.682 |
| 5 | 0.087 | 0.079 | 0.202 | 0.207 | 0.301 | 0.682 | 0.684 |
| 10 | 0.082 | 0.068 | 0.218 | 0.252 | 0.351 | 0.682 | 0.686 |
| 20 | 0.075 | 0.061 | 0.217 | 0.329 | 0.417 | 0.682 | 0.687 |
| 50 | 0.068 | 0.056 | 0.154 | 0.396 | 0.470 | 0.684 | 0.688 |
| Benchmark | Random | Strongest | IRT 2PL | SkillEval | |
|---|---|---|---|---|---|
| MATH | 264 | 0.152 | 0.375 | 0.530 | 0.542 |
| BBH | 1159 | 0.471 | 0.716 | 0.690 | 0.735 |
| GPQA | 246 | 0.280 | 0.370 | 0.402 | 0.407 |
| MuSR | 136 | 0.301 | 0.529 | 0.419 | 0.544 |
| IFEval | 100 | 0.450 | 0.810 | 0.680 | 0.820 |
| Overall | 1905 | 0.405 | 0.616 | 0.611 | 0.657 |
| Held-out | Random | Strongest | SkillEval (transfer) | Reference | |
|---|---|---|---|---|---|
| MuSR | 756 | 0.415 | 0.467 | 0.470 | 0.544 |
| IFEval | 536 | 0.437 | 0.731 | 0.410 | 0.820 |
| Combined | 1292 | 0.400 | 0.577 | 0.445 | — |
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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