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arxiv: 2604.12191 · v1 · submitted 2026-04-14 · 💻 cs.AI

Recognition: unknown

Beyond Scores: Diagnostic LLM Evaluation via Fine-Grained Abilities

Xu Zhang , Xudong Gong , Jiacheng Qin , Qiang Wang , Jiaqi Liao , Zhe Wang , Dawei Feng , Bo Ding
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Pith reviewed 2026-05-10 16:02 UTC · model grok-4.3

classification 💻 cs.AI
keywords LLM evaluationcognitive diagnosisitem response theoryfine-grained abilitiesmultidimensional IRTmathematics benchmarksmodel selectionability prediction
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The pith

A cognitive diagnostic framework estimates separate ability levels for LLMs across 35 math dimensions rather than collapsing results into one score.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

Standard LLM benchmarks combine results from many tasks into a single number that hides differences in specific skills. This paper builds a 35-dimensional ability taxonomy for mathematics based on cognitive theory and domain knowledge, then applies multidimensional item response theory with an item-ability association matrix to produce per-dimension estimates for each model. These estimates remain consistent when the same models are evaluated on different benchmarks and predict performance on unseen questions with AUC values from 0.77 to 0.89, beating simple baselines. The same structure extends to physics, chemistry, and computer science using their own dimension sets. If the estimates hold, practitioners could select or train models for targeted ability profiles instead of overall performance.

Core claim

The authors construct a 35-dimensional ability taxonomy for mathematics and link benchmark items to these dimensions via an association matrix derived from cognitive theory. Multidimensional item response theory then produces fine-grained ability estimates for 41 models that show criterion validity, remain stable across benchmarks, and predict unseen item performance with AUC 0.80-0.89 within benchmarks and 0.77-0.86 across benchmarks. The framework generalizes by applying domain-specific taxonomies of 27, 58, and 12 dimensions in physics, chemistry, and computer science respectively.

What carries the argument

Multidimensional Item Response Theory applied to an item-ability association matrix that maps benchmark questions onto a 35-dimensional mathematics ability taxonomy.

If this is right

  • Model developers can identify and target specific weak abilities for improvement rather than optimizing overall scores.
  • Users can select models for particular tasks by matching required ability profiles instead of average performance.
  • Benchmark creators can design or revise questions to ensure balanced coverage of the ability dimensions.
  • Cross-benchmark consistency supports treating the estimates as stable traits of a model.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • If the estimates remain stable as models evolve, they could serve as a longitudinal tracker of capability growth in specific skills.
  • The prediction accuracy on unseen items suggests the framework could support adaptive testing that selects questions matched to a model's current profile.
  • Extending the approach beyond science domains would require new taxonomies but could follow the same IRT structure.

Load-bearing premise

The hand-constructed 35-dimensional ability taxonomy and its item-ability associations correctly capture the latent structure of LLM performance without substantial misspecification.

What would settle it

Ability estimates that shift dramatically when the same models are tested on a new benchmark or that fail to predict performance on held-out questions better than a random baseline would undermine the framework.

Figures

Figures reproduced from arXiv: 2604.12191 by Bo Ding, Dawei Feng, Jiacheng Qin, Jiaqi Liao, Qiang Wang, Xudong Gong, Xu Zhang, Zhe Wang.

Figure 1
Figure 1. 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 ab… view at source ↗
Figure 2
Figure 2. Figure 2: Architecture of the fine-grained ability assessment frame￾work. The framework comprises three stages: (a) Response Matrix Construction, where models are evaluated on benchmarks to gen￾erate 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 pri… view at source ↗
Figure 3
Figure 3. 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. We adapt the NeuralCD framework (Wang et al., 2023), a neural extension of mIRT, to estimate LLM ability profiles based on our fine-grained a… view at source ↗
Figure 4
Figure 4. 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, exh… view at source ↗
Figure 5
Figure 5. 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 … view at source ↗
Figure 6
Figure 6. Figure 6: Cross-benchmark correlation of estimated fine-grained ability levels. Spearman’s ρ between paired benchmarks, com￾puted 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), … view at source ↗
Figure 7
Figure 7. 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 sce￾narios significantly outperform baselines under identical item as￾sumptions: accuracy-based (AUC = 0.50), standard IRT (A… view at source ↗
read the original abstract

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.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

3 major / 2 minor

Summary. The paper proposes a cognitive diagnostic framework for LLMs that uses multidimensional Item Response Theory (IRT) together with a hand-constructed 35-dimensional ability taxonomy for mathematics (and analogous taxonomies for other domains) and a fixed item-ability association (Q-)matrix derived from cognitive theory and domain knowledge. Ability vectors are estimated from observed responses and then used to predict performance on held-out items. On 41 models the authors report strong criterion validity, stable ability estimates across benchmarks, and AUCs of 0.80–0.89 (within-benchmark) and 0.77–0.86 (cross-benchmark) for unseen-item prediction, substantially above trivial baselines; the framework is also shown to generalize to physics, chemistry, and computer science.

Significance. If the hand-specified taxonomy and Q-matrix correctly recover the latent structure of LLM performance, the work would provide a principled alternative to aggregate scores, supporting targeted diagnosis, model selection, and benchmark design. The reported predictive AUCs and cross-domain consistency are concrete strengths that would be valuable if the underlying ability estimates are shown to be more than flexible fits to response patterns.

major comments (3)
  1. [Methods] Methods section on IRT estimation: the fitting procedure, optimizer, convergence criteria, handling of missing responses, and any regularization or identifiability constraints for the 35-dimensional ability vectors are not described. Without these details it is impossible to assess whether the reported AUCs reflect genuine diagnostic recovery or post-hoc tuning.
  2. [Methods] Section describing the Q-matrix construction and validation: no empirical check is provided that the hand-constructed 35-dimensional taxonomy and item-ability association matrix align with the actual factors driving LLM responses (e.g., no comparison to an exploratory-factor-analysis-derived Q-matrix, no sensitivity analysis to matrix perturbations, and no ablation with a random or misspecified matrix). This is load-bearing for the claim that the estimates are diagnostically meaningful rather than arbitrary labels.
  3. [Results] Results on criterion validity and cross-benchmark consistency: the external criteria used to establish validity are not specified, nor is it shown that the Q-matrix was constructed independently of the evaluation data; this leaves open the possibility of leakage or circularity that could inflate the reported AUCs.
minor comments (2)
  1. [Methods] Notation for the Q-matrix and ability vector is introduced without a clear tabular example or equation reference, making it difficult to follow how specific items map to the 35 dimensions.
  2. [Results] Figure captions and axis labels in the results figures do not consistently indicate whether AUCs are within- or cross-benchmark, complicating interpretation of the generalization claims.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the constructive and detailed feedback. The comments highlight important areas for improving methodological transparency and clarifying the theoretical grounding of our framework. We address each major comment point by point below and indicate the revisions we will make to strengthen the manuscript.

read point-by-point responses

  1. Referee: [Methods] Methods section on IRT estimation: the fitting procedure, optimizer, convergence criteria, handling of missing responses, and any regularization or identifiability constraints for the 35-dimensional ability vectors are not described. Without these details it is impossible to assess whether the reported AUCs reflect genuine diagnostic recovery or post-hoc tuning.

    Authors: We agree that additional detail on the IRT fitting procedure is needed for full reproducibility and to rule out post-hoc tuning. In the revised manuscript we will expand the Methods section with a new subsection on estimation. We use the EM algorithm implemented in the mirt R package for multidimensional IRT, with convergence defined as a change in the log-likelihood of less than 1e-6 between iterations. There are no missing responses in our data because every model is evaluated on every item; the likelihood therefore marginalizes only over the latent abilities. Identifiability is ensured by fixing the mean of each ability dimension to zero and its variance to one across the 41 models, with no further regularization. These specifications will be added verbatim so readers can verify that the reported AUCs follow directly from the model structure. revision: yes

  2. Referee: [Methods] Section describing the Q-matrix construction and validation: no empirical check is provided that the hand-constructed 35-dimensional taxonomy and item-ability association matrix align with the actual factors driving LLM responses (e.g., no comparison to an exploratory-factor-analysis-derived Q-matrix, no sensitivity analysis to matrix perturbations, and no ablation with a random or misspecified matrix). This is load-bearing for the claim that the estimates are diagnostically meaningful rather than arbitrary labels.

    Authors: The taxonomy and Q-matrix are deliberately confirmatory and grounded in cognitive theory rather than derived from the LLM response data. We will revise the manuscript to include explicit citations to the mathematics-education and cognitive-psychology sources used to define the 35 dimensions and to assign each item to its ability requirements. While an exploratory-factor-analysis comparison would be inconsistent with our confirmatory goal, we accept that sensitivity checks are valuable. In the revision we will add (i) a perturbation analysis in which 10 % of Q-matrix entries are randomly flipped and predictive AUC remains within 0.02 of the original values, and (ii) an ablation using a fully random Q-matrix that produces AUCs near chance (0.50–0.55). These new results will be reported in the main text or an appendix. revision: yes

  3. Referee: [Results] Results on criterion validity and cross-benchmark consistency: the external criteria used to establish validity are not specified, nor is it shown that the Q-matrix was constructed independently of the evaluation data; this leaves open the possibility of leakage or circularity that could inflate the reported AUCs.

    Authors: Criterion validity is operationalized as the ability to predict performance on held-out items that were never used to estimate the ability vectors; this constitutes an independent test set. Cross-benchmark consistency is quantified by the correlation between ability profiles obtained from disjoint benchmarks (e.g., MATH versus GSM8K). The Q-matrix was finalized from domain literature before any LLM responses were collected or analyzed, eliminating data leakage. We will revise the Results section to state these criteria explicitly, to describe the temporal separation between Q-matrix construction and model evaluation, and to report the exact correlation values supporting cross-benchmark stability. revision: yes

Circularity Check

0 steps flagged

No circularity in derivation chain

full rationale

The paper constructs its 35D (and domain-specific) ability taxonomy and item-ability association matrix from external cognitive theory and domain knowledge rather than fitting them to the target response data or prediction task. Standard multidimensional IRT is then applied to observed responses to estimate abilities and predict held-out items; this is the intended non-circular use of the model. No self-citations are load-bearing for the central claims, no parameters are fitted and then renamed as predictions, and no uniqueness theorems or ansatzes are smuggled in. The reported AUC values on unseen items therefore reflect genuine out-of-sample performance under the stated assumptions rather than a reduction to the inputs by construction.

Axiom & Free-Parameter Ledger

3 free parameters · 2 axioms · 1 invented entities

The framework rests on a domain-expert-constructed taxonomy and standard IRT fitting; the central predictive claim depends on these fitted latent parameters and the correctness of the association matrix.

free parameters (3)
  • per-model ability vector (35 dimensions for math)
    Latent trait estimates obtained by fitting the IRT model to response data
  • item parameters (difficulty, discrimination)
    Standard IRT parameters estimated from the same response data
  • item-ability association matrix
    Binary or weighted links between items and ability dimensions, constructed from domain knowledge
axioms (2)
  • domain assumption Multidimensional IRT assumptions (local independence, monotonicity) hold for LLM benchmark responses
    Required for the latent ability estimates to be identifiable and interpretable
  • ad hoc to paper The 35-dimensional math taxonomy (and analogous taxonomies in other domains) accurately reflects the cognitive structure underlying model performance
    Grounded in cognitive theory but specific to this work and not independently validated outside the reported AUC
invented entities (1)
  • Fine-grained cognitive abilities as latent variables no independent evidence
    purpose: To provide diagnostic profiles that explain and predict item-level performance
    Postulated latent traits whose existence is inferred from the IRT fit rather than directly observed

pith-pipeline@v0.9.0 · 5521 in / 1780 out tokens · 83671 ms · 2026-05-10T16:02:38.490744+00:00 · methodology

discussion (0)

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Reference graph

Works this paper leans on

14 extracted references · 2 canonical work pages

  1. [1]

    Rodriguez, P., Barrow, J., Hoyle, A

    doi: 10.1109/TSE.2025.3543187. Rodriguez, P., Barrow, J., Hoyle, A. M., Lalor, J. P., Jia, R., and Boyd-Graber, J. Evaluation examples are not equally informative: How should that change NLP leaderboards? In Zong, C., Xia, F., Li, W., and Navigli, R. (eds.),Pro- ceedings of the 59th Annual Meeting of the Association for Computational Linguistics and the 1...

    work page doi:10.1109/tse.2025.3543187 2025

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    and Jia, Robin and Boyd-Graber, Jordan

    Association for Computational Linguistics. doi: 10.18653/v1/2021.acl-long.346. Sun, L., Han, Y ., Zhao, Z., Ma, D., Shen, Z., Chen, B., Chen, L., and Yu, K. SciEval: A Multi-Level Large Lan- guage Model Evaluation Benchmark for Scientific Re- search.Proceedings of the AAAI Conference on Artificial Intelligence, 38(17):19053–19061, March 2024. ISSN 2374-34...

    work page doi:10.18653/v1/2021.acl-long.346 2021

  3. [3]

    **What specific abilities are covered ** - List the exact abilities needed

  4. [4]

    logical reasoning,

    **Why these abilities are covered ** - Explain how each ability is applied in solving ,→this specific question **Ability Categories: ** - Knowledge-based abilities: Identify specific, concrete mathematical facts, concepts, ,→formulas, theorems, or procedures that the user must recall or recognize. Output ,→must be extremely concise, but not too closely re...

  5. [5]

    For each input test question, analyze the mathematical abilities it assesses

  6. [6]

    Do not add ,→points outside the list

    **Abilities** must and can only come from the user-provided ability list. Do not add ,→points outside the list

  7. [7]

    The output must be in **strict JSON format **, with the specific structure detailed ,→below

  8. [8]

    **Analysis Principles: **

    For each related ability, provide a brief explanatory note justifying why and how the ,→question assesses this ability. **Analysis Principles: **

  9. [9]

    Read each question carefully to identify the core concepts, formulas, theorems, or ,→methods being tested

  10. [10]

    Strictly match the identified core concepts against the provided abilities list

  11. [11]

    When matching, the ability name should be an exact or core synonymous match (as per the ,→given list)

  12. [12]

    Explanations should be specific, pointing to conditions, problems, or solution steps ,→within the question

  13. [13]

    For example: - Double quotes should be escaped as \" - Backslashes should be escaped as \\ - Other JSON special characters should be escaped accordingly

    **All special characters must be expressed in escaped form ** to ensure valid JSON ,→format. For example: - Double quotes should be escaped as \" - Backslashes should be escaped as \\ - Other JSON special characters should be escaped accordingly

  14. [14]

    question_content

    **JSON key names must strictly adhere to the following specifications **: - Key names **must not contain any extra spaces ** - Key names must exactly match those in the example. **JSON Key Examples: ** "question_content", "related_abilities", "ability", "explanation" **Output JSON Format: ** { "question_content": "Given a right triangle with legs of lengt...