Organizations: College of Computer Science and Technology, National University of Defense Technology, Changsha, Hunan, China · State Key Laboratory of Complex & Critical Software Environment, Changsha, Hunan, China · School of Humanities and Social Sciences, School of Public Administration, Beihang University, Beijing, China · National Key Laboratory of Parallel and Distributed Computing, Changsha, Hunan, China
Current evaluations of large language models aggregate performance across diverse tasks into single scores. This obscures fine-grained ability variation, limiting targeted model improvement and ability-guided selection for specific tasks. Motivated by this gap, we propose a cognitive diagnostic framework that estimates model abilities across multiple fine-grained dimensions. For mathematics, we construct a 35-dimensional ability taxonomy grounded in cognitive theory and domain knowledge. The framework employs multidimensional Item Response Theory with an item-ability association matrix to estimate fine-grained ability levels, which in turn enable prediction of performance on unseen items (questions of benchmark). Evaluated on 41 models, our approach demonstrates strong criterion validity, consistent ability estimates across benchmarks, and accurate prediction of unseen items with AUC ranging from 0.80 to 0.89 within benchmarks and from 0.77 to 0.86 across benchmarks, substantially exceeding trivial baselines. The framework generalizes across scientific domains, producing consistent diagnostic performance in physics (27 dimensions), chemistry (58 dimensions), and computer science (12 dimensions). This work establishes a principled framework for fine-grained assessment of abilities, with potential applications in targeted training, ability-guided model selection, and ability-aware benchmark design.
Figures & tables
Figure 1: A diagnostic framework for evaluating LLMs via fine-grained mathematical abilities. Centered on Bloom’s taxonomy, we decompose Mathematical Abilities into two core dimensions: Knowledge (e.g., Algebra, Calculus) and Cognitive (e.g., Multi-step Problem Solving, Critical Reasoning). Each is further subdivided into interpretable sub-skills. The framework links benchmark questions (left) to their underlying abilities and maps them to real-world problem domains (right), enabling granular diagnosis beyond aggregate scores and bridging the gap between evaluation benchmarks and practical task demands.
Figure 2: Architecture of the fine-grained ability assessment framework. The framework comprises three stages: (a) Response Matrix Construction, where models are evaluated on benchmarks to generate a binary model-item response matrix; (b) Association Matrix Construction, in which each item of benchmark is mapped to fine-grained abilities (e.g., domain knowledge or cognitive processes) via expert annotation and prior knowledge, forming a Q-matrix; and (c) Fine-Grain Ability Evaluation, where a cognitive diagnostic model estimates latent ability profiles by jointly analyzing the response and association matrices.
Figure 3: Structure of the IRT-based fine-grained ability evaluation model. Based on the IRT method, a simple fully connected neural network is implemented on the Interaction Layer to fit model performance in downstream tasks, thereby achieving fine-grained ability evaluation.
Figure 4: Distribution of item coverage across 35 fine-grained abilities in three mathematical benchmarks. The distributions are inconsistent across knowledge-oriented and cognition-oriented dimensions, with pronounced differences among individual dimensions. Left : benchmark-knowledge ability associations, indicating distinct assessment emphases across benchmarks. Right : benchmark-cognition ability associations, exhibiting greater overlap in assessment tendencies while retaining benchmark-specific emphases.
Figure 5: Correlation between estimated fine-grained abilities and model performance on associated benchmark items. Spearman’s rank correlation coefficient ( ρ ) measures the association between each ability dimension (columns) and model accuracy on its linked items across three benchmarks (rows). Color coding : Blue indicates ρ>0.7 (strong), yellow indicates 0.5<ρ≤0.7 (moderate), and red indicates 0.3<ρ≤0.5 (weak). Significance markers : ** denotes p<0.01 , * denotes p<0.05 . N/A indicates that no items in the benchmark are associated with that dimension (i.e., invalid for evaluation). Dimensions with consistent strong correlation across benchmarks reflect stable diagnostic signals; weak correlations often arise from low item coverage (<10 items).
Figure 6: Cross-benchmark correlation of estimated fine-grained ability levels. Spearman’s ρ between paired benchmarks, computed over 19 of 35 ability dimensions with >10 items in all benchmarks. Color: purple = MMLU-MATH vs MATH500, blue = MMLU-MATH vs MMLU-Pro-MATH, red = MMLU-Pro-MATH vs MATH500. Shape: squares ( p<0.01 ), triangles ( p<0.05 ), diamonds ( p>0.05 ). Dashed lines mark thresholds: ρ=0.3 (weak), 0.5 (moderate), 0.7 (strong). 14 of these 19 dimensions show ρ>0.5 across all pairwise comparisons.
Figure 7: AUC distribution across 41 LLMs for nine prediction scenarios. Boxplots show median, IQR, and outliers (whiskers = 1.5 × IQR). First three: within-benchmark prediction on MMLU-MATH, MATH500, MMLU-Pro-MATH; remaining six: cross-benchmark prediction over all ordered benchmark pairs. All scenarios significantly outperform baselines under identical item assumptions: accuracy-based (AUC = 0.50), standard IRT (AUC = 0.50), and random prediction (mean AUC = 0.49).
Appendix figures & tables5 assets
Supplementary material from the paper’s appendix.
Appendix
ID
Category
Series
Model
Parameter Size
1
Online Model
DeepSeek
deepseek-v3.2
N/A
2
deepseek-v3
N/A
3
GPT
gpt-4o
N/A
4
gpt-5.1
N/A
5
gpt-o1
N/A
6
gpt-o3
N/A
Appendix
Table 1: List of evaluated language models with unique identifiers.
ID
Subject
Name
# Items
Source
Answer Format
1
Math
MMLU-MATH
748
cais/mmlu
Multiple-choice
2
MMLU-Pro-MATH
1351
TIGER-Lab/MMLU-Pro
Multiple-choice
3
MATH500
500
HuggingFaceH4/MATH-500
Free-response
4
Chemistry
MMLU-Pro-Chemistry
1132
TIGER-Lab/MMLU-Pro
Multiple-choice
5
Physics
MMLU-Pro-Physics
1299
TIGER-Lab/MMLU-Pro
Multiple-choice
6
Computer science
MMLU-Pro-CS
410
TIGER-Lab/MMLU-Pro
Multiple-choice
Appendix
Table 2: List of evaluated benchmarks with detailed metadata.
Dimension
MMLU-MATH
MMLU-Pro-MATH
MATH500
Count
Ratio
Count
Ratio
Count
Ratio
ability_0
61
0.0816
55
0.0407
20
0.0400
ability_1
340
0.4545
300
0.2221
125
0.2500
ability_2
77
0.1029
112
0.0829
84
0.1680
ability_3
183
0.2447
189
0.1399
167
0.3340
ability_4
23
0.0307
57
0.0422
64
0.1280
Appendix
Table 3: Item coverage of per ability dimension across mathematical benchmarks.
Model
MMLU-MATH
MATH500
MMLU-Pro-MATH
0
0.8711 ± 0.0489
0.8732 ± 0.0401
0.8522 ± 0.0303
1
0.8672 ± 0.0356
0.8434 ± 0.0863
0.8683 ± 0.0288
2
0.8548 ± 0.0338
0.8049 ± 0.0681
0.8584 ± 0.0222
3
0.8560 ± 0.0593
0.8557 ± 0.0405
0.8573 ± 0.0398
4
0.8583 ± 0.0607
0.8634 ± 0.0654
0.8547 ± 0.0316
5
0.8474 ± 0.0331
0.8586 ± 0.0552
0.8517 ± 0.0480
Appendix
Table 4: Within-benchmark unseen item prediction performance per model (AUC ± std over 10 random splits with different seeds).
Model
MMLU → MATH500
MMLU → MMLU-Pro
MATH500 → MMLU
MATH500 → MMLU-Pro
MMLU-Pro → MMLU
MMLU-Pro → MATH500
0
0.7686 ± 0.0070
0.8345 ± 0.0035
0.8254 ± 0.0027
0.8305 ± 0.0023
0.8448 ± 0.0057
0.7870 ± 0.0022
1
0.7942 ± 0.0031
0.8329 ± 0.0032
0.8132 ± 0.0017
0.8106 ± 0.0022
0.8330 ± 0.0030
0.8287 ± 0.0045
2
0.7766 ± 0.0033
0.8385 ± 0.0035
0.8498 ± 0.0032
0.8203 ± 0.0017
0.8521 ± 0.0038
0.7953 ± 0.0028
3
0.7784 ± 0.0041
0.8425 ± 0.0046
0.8390 ± 0.0017
0.8268 ± 0.0019
0.8636 ± 0.0046
0.7917 ± 0.0052
4
0.8085 ± 0.0052
0.8288 ± 0.0041
0.8299 ± 0.0019
0.8110 ± 0.0018
0.8309 ± 0.0047
0.8201 ± 0.0028
5
0.7774 ± 0.0036
0.8457 ± 0.0045
0.8158 ± 0.0049
0.8172 ± 0.0020
0.8145 ± 0.0042
0.8197 ± 0.0024
Appendix
Table 5: Cross-benchmark unseen item prediction performance per model (AUC ± std over repeat for 10 times).
Thousands of diverse benchmarks have been developed to measure the quality of large language models (LLMs). Yet prior work has demonstrated that LLM performance is often sufficiently explained by a small set of latent factors, or abilities. This suggests the potential for more efficient and principled benchmarking, but it remains difficult to compare the quality of different methods. Motivated by predictive validity, we argue that the quality of a benchmarking framework should be grounded in how efficiently it enables the prediction of model performance on unseen tasks. To analyze this objective, we collect the "Wide-scale Item Level Dataset" (WILD), a dataset of item-model response pairs, comprising evaluations of 65 models on 109,564 unique items spanning 163 tasks drawn from 27 datasets. This dataset enables the first analysis of how different techniques can predict a model's performance on a large, diverse collection of unseen tasks under different budget constraints. We demonstrate that combining a modified multidimensional item response theory (IRT) model with adaptive item selection driven by optimal experimental design can predict performance on 112 held-out benchmark tasks with a mean absolute error (MAE) of less than 7%, and can do so after observing only 16 items. We further demonstrate that incorporating cost-aware discount factors into our selection criteria can reduce the total tokens needed to reach 7% MAE from 141,000 tokens to only 22,000, an 85% reduction in evaluation cost.
Evaluating large language models (LLMs) typically requires thousands of benchmark items, making the process expensive, slow, and increasingly impractical at scale. Existing evaluation protocols rely on average accuracy over fixed item sets, treating all items as equally informative despite substantial variation in difficulty and discrimination. We introduce ATLAS, an adaptive testing framework based on Item Response Theory (IRT) that estimates model ability using Fisher information-guided item selection. ATLAS reduces the number of required items by up to 90% while maintaining measurement precision. For instance, it matches whole-bank ability estimates using only 41 items (0.157 MAE) on HellaSwag (5,600 items). We further reconstruct accuracy from ATLAS's ability estimates and find that reconstructed accuracies closely match raw accuracies across all five benchmarks, indicating that ability θ preserves the global performance structure. At the same time, θ provides finer discrimination within accuracy-equivalent models: among more than 3,000 evaluated models, 23-31% shift by more than 10 rank positions, and models with identical accuracies receive meaningfully different ability estimates. Code and calibrated item banks are available at https://github.com/Peiyu-Georgia-Li/ATLAS.git.
Evaluation of large language models (LLMs) increasingly requires predicting how a model will perform on new questions or tasks before collecting large amounts of new annotations. This problem is challenging because question difficulty, scenario, and underlying capability demands can vary substantially. Simple retrospective averages may confound model ability with item characteristics. In this paper, we study a model-based evaluation framework that combines multidimensional item response theory model with question contexts to predict LLM performance on unseen questions. The framework represents LLMs through latent capability profiles while using question content to inform item characteristics, allowing information to transfer beyond previously observed items. Empirically, we find that for within-scenario evaluation, incorporating question embeddings improves prediction relative to model-free baselines, and that multidimensional latent structure provides a richer description of capability variation than unidimensional alternatives. At the same time, our results reveal an important limitation that the generalizability does not necessarily translate into reliable prediction under cross-scenario shift. These findings suggest that context-aware psychometric modeling is a promising direction for efficient and interpretable LLM evaluation, while also highlighting cross-scenario generalization as a central open challenge.
Ergan Shang, Weijing Tang, Yinqiu He
Department of Statistics and Data Science, Carnegie Mellon University · Department of Statistics, University of Madison