Item Response Theory

Multidimensional item response theory (MIRT) is a statistical test theory that precisely estimates multiple latent skills of learners from the responses in a test. Both compensatory and non-compensatory models have been proposed for MIRT: the former assumes that each skill can complement other skills, whereas the latter assumes they cannot. This non-compensatory assumption is convincing in many tests that measure multiple skills; therefore, applying non-compensatory models to such data is crucial for achieving unbiased and accurate estimation. In contrast to tests, latent skills will change over time in daily learning. To monitor the growth of skills, dynamical extensions of MIRT models have been investigated. However, most of them assumed compensatory models, and a model that can reproduce continuous latent states of skills under the non-compensatory assumption has not been proposed thus far. To enable accurate skill tracing under the non-compensatory assumption, we propose a dynamical extension of non-compensatory MIRT models by combining a linear dynamical system and a non-compensatory model. This results in a complicated posterior of skills, which we approximate with a Gaussian distribution by minimizing the Kullback-Leibler divergence between the approximated posterior and the true posterior. The learning algorithm for the model parameters is derived through Monte Carlo expectation maximization. Simulation studies verify that the proposed method is able to reproduce latent skills accurately, whereas the dynamical compensatory model suffers from significant underestimation errors. Furthermore, experiments on an actual data set demonstrate that our dynamical non-compensatory model can infer practical skill tracing and clarify differences in skill tracing between non-compensatory and compensatory models.

Although MMLU is widely adopted as a benchmark for calibrating general AI capabilities, we psychometrically demonstrate that its aggregate score primarily evaluates a model's factual retrieval capacity rather than its reasoning ability. By calibrating item difficulty for 1,000 open-weights language models over 14,042 MMLU test items using Item Response Theory, we show that evaluating both abilities via a single test is inherently flawed. Difficulty is then regressed on a deterministic, text-extractable framework of structural complexity. Applying a joint Wald test with subject-clustered covariances demonstrates that the MMLU conflates fundamentally separable constructs. The mapping from structural complexity to difficulty is not invariant across the benchmark's STEM and non-STEM partitions. This finding has practical consequences. Aggregate leaderboard ranks track non-STEM accuracy more closely than STEM accuracy, so selecting a Top-50 model on the aggregate for a reasoning-intensive deployment displaces roughly 22% of the STEM-appropriate choices. Furthermore, when controlling for the multiple-choice guessing floor natively inside the response model, we find that higher-ability models continue to degrade more steeply under increased reasoning depth. The MMLU aggregate therefore weights retrieval capacity and reasoning stability unequally, inadvertently favoring models optimized for retrieval. We release our deterministic framework as a reproducible auditing instrument and recommend disaggregated reporting.

Evaluating software engineering agents on realistic benchmarks is costly, since each task may require multi-step code exploration, modification, and test execution. Existing efficient evaluation methods select representative subsets to estimate full-benchmark performance, but are largely result-only: they fit historical pass/fail response matrices or static task semantics, discarding how agents solve problems. We propose PTA-IRT, a Privileged Trajectory-Aware Item Response Theory framework that fuses process and outcome signals. Historical execution trajectories supply process-level evidence beyond pass/fail, such as explored context, attempted edits, and solving paths, which PTA-IRT uses as privileged information for calibration subset selection and ability estimation. Under low calibration budgets, PTA-IRT consistently outperforms prior IRT baselines on score and ranking recovery across four SWE benchmarks. Code and data are publicly available at https://github.com/DeepSoftwareAnalytics/PTA-IRT.

Item-sensitivity, defined as whether a model's choice depends on the specific input rather than on its own output prior, is widely reported as evidence of task competence. We show this evidence is necessary but not sufficient using a forced-choice signalling task abstracted from the board game Deception: Murder in Hong Kong. In this environment, the reference points against which a coordinate should be judged (a fit-maximising strategy, a posterior-maximising strategy, and uniform random selection) are all computable in closed form. Across seven language models, two model families, a post-training ablation, and three independent scoring rules, every one of 21 model-by-rule cells is reliably item-sensitive. Yet 8 of those 21 cells are not statistically distinguishable from a chooser that ignores the item and selects at random, and 5 score worse than random at describing the target. Item-sensitivity and distance from random correlate at only r = 0.30. We call this consistency without alignment and argue it generalises to any evaluation that relies on item-sensitivity, permutation consistency, or self-consistency without an independent reference for the measured quantity. We further find that a literal-similarity baseline with no pragmatics outperforms most tested language models, that adding a pragmatic layer over two baseline similarity sources moves choosers toward random rather than toward the Bayesian reference, and that a standard labelled multiple-choice format carries no measurable content signal here. All results represent the model side of a pre-registered instrument; a matched human condition is designed and piloted but not yet collected.

Small leaderboard gaps are often interpreted as evidence that one language model is better than another, but their sign may depend on which benchmark items are included. We test this using item-level responses from five benchmarks and a family-label-free spectral approximation to multidimensional item-response theory (MIRT). In owner-disjoint folds, one owner half identifies items with low residual differential item functioning across model families (low-DIF); the resulting frozen, source- and easiness-balanced weights score models in the other half, while equally short matched-random subtests control for generic subtest variation. Full-benchmark and low-DIF rankings remain strongly correlated ($τ_b=.900$--$.948$). Yet in four of five benchmarks, 30.9--47.1% of cross-family pairs initially within one percentage point reverse order, exceeding their matched-random medians by 16.9--28.6 percentage points (all $p=.001$). The fifth benchmark shows no reliable excess ($-0.9$ points, $p=.689$). The pattern survives all pre-specified population perturbations, and residual item--family signatures replicate across owner halves; however, no family shows a consistent advantage across benchmarks. Thus, globally stable rankings can still leave individual near-tie orderings sensitive to benchmark composition, and sub-one-point leaderboard gaps should be accompanied by evidence that the implied ordering is composition-robust.

This paper studies multiple fixed points in a discrete-time hysteresis neural network. The network consists of binary hysteresis neurons characterized by the threshold parameter. Depending on the parameter, the network can have a variety of multiple binary fixed points. Stability of each fixed point is characterized by basin of attraction (BOA): the set of initial points falling into the fixed point. In order to evaluate the distribution of BOA sizes, we present entropy. In order to escape from the curse of dimensionality, we introduce a simple problem: classification of binary data set. In the classification, BOAs correspond to classes. In the problem, we clarify that the threshold parameter can control the entropy, especially, can maximize the entropy: the distribution approaches to uniform. As a concrete example, we consider an item response data set in education. Using two fundamental metrics in the item response theory, the classification results are evaluated.

We present results from reconstructing multiple-choice model (MCM) and three-parameter logistic (3PL) model curves using a fine-tuned multimodal large language model (LLM) based on Qwen3.5. The model is prompted and fine-tuned to replicate choice probabilities across a large training corpus of multiple-choice items containing both image and text stimuli, conditioned on a labeled set of student ability levels. By learning to reproduce the systematic error patterns of students across a discrete range of abilities, the LLM implicitly captures the underlying response probabilities encoded in the 3PL and MCM curves. This allows us to accurately approximate item difficulty on a held-out test set directly from the model's predicted option probabilities.

Language models differ in how safely they behave and these differences are measured by safety benchmarks. But aggregated benchmark scores are hard to trust and interpret, because benchmarks duplicate one another, correlate heavily, and models may sandbag when they detect evaluation. To address these issues, we draw on Item Response Theory (IRT), a statistical toolkit for measuring these latents from performance on items with inferred psychometric properties. We fit IRT models to eight safety benchmarks across 192 language models, the largest psychometric analysis of LLM safety evaluations to date, and contribute three results. First, we find that three interpretable factors of refusal strictness, truthfulness, and contextual harm explain most of the variance between models across benchmarks. Second, psychometrically selected items recover full benchmark scores with lower error than random subsets of the same size, and roughly ten adaptively chosen items suffice for several individual benchmarks, cutting evaluation cost by 97-99%. Third, IRT supports audits of individual models, showing that it can be used to detect naive sandbagging and changes of model behind APIs. Overall, we show IRT is a ready-made toolkit for reading, reducing, and auditing safety benchmarks, which we recommend frontier labs and evaluators adopt.

Black-box language-model reliability is commonly pursued by sampling, prompting, voting, verifying, or iteratively revising individual answers. We ask a prior question: \emph{what determines whether a collection of black-box responses is recoverable at all?} We represent responses to typed transformations of a query as a \emph{relational response field} (RRF). Edge transports encode how valid responses must change under paraphrase, scaling, decomposition, refactoring, or other task symmetries; anchors encode independently trusted evidence such as execution or a verifier. For relation operator $D$, anchor operator $A$, and at most $k$ corrupted response nodes, we identify $γ_k(D,A)$ as the intrinsic difficulty of black-box response recovery. It is positive exactly when every $k$-node corruption is identifiable; it gives a deterministic stability bound proportional to $1/γ_k$; and a matching two-point minimax lower bound shows that no estimator can improve this dependence. Thus consistency is not truth: relation-only methods are blind to null directions, including shared hallucinations. We derive sparse field-repair algorithms while separating information-theoretic identifiability from the stronger null-space conditions required by convex optimization. Controlled theorem tests and black-box mathematics/code experiments evaluate four theory-fixed consequences: consistency--truth separation, anchor phase transitions, redundancy saturation, and cross-model, cross-task prediction of repair difficulty. The results support $γ_k(D,A)$ as a measurable property of a response-recovery instance, rather than a score attached to one repair heuristic.

LLM companions are deployed at scale in personally consequential settings, yet poorly evaluated. Existing benchmarks use hand-authored scenarios and prompted simulators, aggregate empathy into one score, and overlook judge biases such as same-family favoritism and scale drift. We introduce CompanionBench, an interactive bilingual benchmark. To our knowledge, it is the first companion benchmark to ground both its scenarios and a trained user simulator in de-identified real-world data. A hidden disclosure gate branches each persona's trajectory on the agent's own behavior, controlling the interaction state space without scripting dialogue. We operationalize ten capabilities derived from 25 theories across psychology and counseling, four of them not graded explicitly by prior work: holding ambiguity, selfobject responsiveness, positive resonance and calibrated challenge. Agents are assessed on two complementary axes: a subjective ten-capability rubric and a deterministic measure of whether deeper disclosure was earned. A cross-family panel dilutes same-family favoritism; an Item Response Theory model separates agent quality from judge severity. Theory fixes what to measure and how personas are structured; real data supply events, history, and profiles -- coverage from theory, authenticity from data. Rankings are reproducible in both languages (rho = 0.996 ZH / 0.953 EN). Evaluating 28 agents reveals capability-level differences obscured by aggregate scores. Emotion regulation and calibrated challenge remain common weaknesses; holding ambiguity discriminates most. Role-play agents rank near the bottom: immersion does not imply relational competence. Across agents, the dominant failure mode is substituting surface warmth for substantive relational support. We will release 500 Chinese-English parallel pairs and the evaluation code.

Item Response Theory (IRT) has recently been proposed as a framework for evaluating large language model (LLM) benchmarks by separating a model's latent ability from the properties of individual benchmark items. Existing neural IRT approaches, including PSN-IRT, estimate these quantities using point estimates, limiting uncertainty quantification and downstream statistical inference. We introduce Laplace-PSN-IRT, a post-hoc last-layer Laplace approximation that augments a trained PSN-IRT model with approximate Bayesian posterior inference, recovering calibrated uncertainty over model ability and item difficulty without retraining. The resulting posterior enables credible intervals, probabilistic comparisons between models, and propagation of parameter uncertainty into Fisher-information-based item selection. We show that most pairwise comparisons among 12 models on a standard LLM benchmark leaderboard are not statistically distinguishable despite differing point-estimate ranks. We further show that point-estimate Fisher information can become nearly zero for many benchmark items because it is evaluated at a single reference ability, whereas posterior-expected Fisher information remains substantially more stable across the ability range. Finally, posterior-expected Fisher information more accurately recovers full-benchmark ability rankings from small benchmark subsets in most experimental settings while matching point-estimate performance for the smallest subsets. We validate the calibration of the approximate posterior using held-out predictive coverage and find that modeling item difficulty as random while treating item discrimination as fixed produces well-calibrated uncertainty in this architecture.

Reliability assessment of large language models (LLMs) seeks to estimate the probability that a model produces correct responses under a specified operational profile. Conventional benchmark-based evaluation, often summarized by aggregate accuracy, provides a point estimate of performance but does not characterize the uncertainty associated with reliability claims. Currently, statistical inference methods for LLM reliability assessment are emerging. However, a key assumption underlying these models is that test outcomes can be treated as independent repeated trials. This assumption may be inappropriate in sequential settings, where later responses depend on earlier interactions through retained context, error propagation, or an evolving interaction state. We extend a hierarchical Bayesian framework for LLM reliability assessment by relaxing the assumption of independent task outcomes and introducing a Hidden Markov Model to capture sequential dependence in benchmark-constructed interaction sessions. In this formulation, outcomes are generated from a latent interaction state evolving according to a first-order Markov process, capturing changes in interaction context. Through experiments using Anthropic Claude and OpenAI on four datasets, we demonstrate the potential impact of sequential dependence on reliability assessment. The results suggest that ignoring sequential dependence may lead to overconfident reliability estimates.

AI benchmarks increasingly leverage item-level statistical models, particularly item response theory (IRT), to estimate model capabilities, rank systems, select informative examples, and diagnose benchmark quality. However, AI benchmark data often departs from the data regime of human testing, for which standard IRT estimation tools were originally developed: benchmarks typically involve fewer evaluated models, far more items, and capability distributions that may be skewed, clustered, or multimodal. We examine how these regime mismatches challenge the reliability of IRT modeling for AI evaluation. Using item parameters and capability distributions derived from six widely used LLM benchmarks, we simulate response matrices under three common IRT models and compare four estimation tools used in recent benchmark studies: marginal maximum likelihood, Markov chain Monte Carlo, variational inference, and a neural pseudo-Siamese estimator. Across 18,000 simulation conditions, we systematically evaluate computational feasibility, scalability, and the reliability of IRT inferences about model rankings, predicted performance, and item characteristics. Results show that classical estimators can become infeasible in large benchmark settings, whereas scalable estimators can produce unreliable item-level and ranking inferences with small or nonnormally distributed model sets. This study identifies when latent trait models reliably support or risk distorting AI benchmarking claims, and what sample sizes and diagnostics are needed for trustworthy use.

When LLMs exhibit uneven performance across planning tasks, these gaps are often attributed to task difficulty. We argue that this explanation is incomplete, as task-level variation may reflect distinct latent planning competencies rather than differences along a single ability spectrum. We study this question on ACPBench-Hard by evaluating multiple LLM families under varying test-time reasoning budgets and applying a multidimensional item response theory model to uncover the latent competency structure underlying LLM planning. The analysis reveals two principal dimensions that shape planning performance: operational reasoning, the ability to evaluate local action applicability and immediate state transitions, and structural enumeration, the ability to reason about goal reachability and landmark structure. Operational reasoning improving under model scaling and longer reasoning traces, while structural enumeration remains comparatively insensitive. Our findings motivate competency-level evaluation of LLM planning, shifting the focus from whether models improve overall to which planning competencies improve, under what conditions, and why.

Predicting human item difficulty is central to educational assessment, where reliable estimates support fairness and effective test construction. Existing methods often depend on costly human calibration or item-level textual representations, providing limited evidence about the cognitive processes that make items difficult. We argue that difficulty should be viewed not only as a property of item text, but also as an observable consequence of the problem-solving burden an item induces. Large Reasoning Models (LRMs) offer scalable process evidence through reasoning traces, but such evidence must be structured to support interpretable modeling. To this end, we introduce Epi2Diff (Episode to Difficulty), a framework that maps LRM reasoning traces into cognitively grounded episode sequences. These episodes group trace segments into functional problem-solving states, enabling difficulty to be modeled through reasoning scale, effort allocation, and state transitions. Epi2Diff extracts compact episode-dynamic features and combines them with semantic item representations for human difficulty prediction. Experiments on four real-world human difficulty datasets show that Epi2Diff consistently outperforms strong baselines, including fine-tuned small language models, LLM in-context learning, and supervised LLM adaptation. On SAT-derived classification benchmarks, Epi2Diff achieves an 8.1% average relative gain over supervised LLM fine-tuning baselines. Further analyses show that harder items induce more effortful, iterative, and implementation-centered episode dynamics, rather than merely longer responses. These results demonstrate that cognitive episodes in LRM reasoning traces provide a predictive and interpretable process representation for human item difficulty, offering a new lens for educational measurement with reasoning models.

Standard benchmarks for multimodal large language models (MLLMs) score each item on one canonical ordering and miss whether order-irrelevant shuffling changes the answer, a baseline reliability property called for by emerging AI evaluation guidelines. We introduce Facet-Probe, a five-facet audit (option, evidence-chunk, document-rank, image-set, and mixed-modality ordering) of 18 frontier and open-weight MLLMs. A Bayesian item-response model separates ordering noise from per-facet bias, and a same-ordering control estimates the decoder-stochastic floor for observed flips. We find that none of the 18 MLLMs we audit are order-invariant: screened per-facet panel-mean flip rates span 24-50%. A Gemini same-ordering control at temperature 0 estimates a substantial ordering excess over a same-input decoder-noise floor in verified cells. Capability predicts but does not eliminate flips; the best model still flips on 13.4% of trials. In our Gemini mitigation tests, training-free prompt changes are modality-conditional and do not transfer from text to visual reasoning. These results suggest that prompt-level mitigation alone is unlikely to provide general order robustness, motivating future work on training-time and architectural approaches. We propose cross-ordering flip rate as a standard reporting axis for MLLMs.

Item discrimination is a fundamental psychometric property of educational assessment, which measures whether an item meaningfully distinguishes students with higher proficiency from students with lower proficiency. While various existing works have explored whether large language models (LLMs) can estimate item difficulty, it remains unclear whether they can capture item discrimination. In this work, we evaluate 42 proprietary and open-weight LLMs in zero-shot settings using two complementary approaches: direct discrimination prediction, where models explicitly estimate an item's discrimination value from its content, and response-based Classical Test Theory (CTT) calibration, where LLM answers are treated as synthetic student responses to compute discrimination scores. Our results show that direct prediction yields weak alignment with human-calibrated discrimination: the best-performing model reaches only a Spearman correlation of 0.152. Response-based CTT calibration provides a stronger but still limited signal, with the all-persona synthetic respondent pool reaching a Spearman correlation of 0.241. These findings highlight item discrimination as an open challenge for LLM-based psychometric evaluation: current LLMs contain non-random discrimination-relevant signal, but they do not yet reliably capture how assessment items distinguish human students.

Multilingual benchmarks are central to evaluating large language models (LLMs) across languages, but they suffer from three issues: exhaustive evaluation scales linearly with the number of languages, automatic translation introduces errors that are easily missed at scale, and some items conflate general and culture-specific knowledge. We address all three with a unified statistical framework, Multilingual-IRT, which extends Item Response Theory with per-language difficulty deviations, split discriminability separating content from language effects, and per-language ability residuals. Fitting Multilingual-IRT on 25 LLMs across 29 languages of MMLU-Pro-X, we show that its fitted parameters support three practical applications: predicting unobserved (item, LLM, language) instances with 11-16% lower binary cross-entropy than the strongest accuracy-based baseline, surfacing candidate translation errors distributed across all 28 non-English languages, whereas accuracy-based baselines concentrate detections in a few languages, and recovering culture-specific items that accuracy-based baselines miss.

Large language models (LLMs) are increasingly evaluated for bias using adaptations of human psychological paradigms, yet methodological limitations-particularly the conflation of refusal behavior with task performance-have hindered clear interpretation. Here, we adapt the Implicit Association Test (IAT) to a controlled, forced-choice framework and introduce a two-stage modeling approach that separates response compliance from task-consistent classification. Across three contemporary LLMs (Claude Sonnet-4, Gemini 2.5 Pro, and GPT-5), we evaluate associative interference, defined as reduced task-consistency in incongruent relative to congruent conditions. While compliance with the structured response format was uniformly high, interference effects varied substantially across models and domains. Claude Sonnet-4 exhibited strong interference in the Gender--Career domain (DeltaP = 0.086, 95% CrI [0.026, 0.173]) and smaller but credible effects in Gender--Science. Gemini 2.5 Pro showed attenuated interference, and GPT-5 exhibited minimal or no detectable interference across domains. These findings demonstrate that IAT-style associative asymmetries are not a universal property of LLMs, but instead depend on model-specific characteristics. By isolating interference from compliance and modeling item-level variability, this study provides a principled framework for evaluating structured response patterns in LLMs. The results highlight the importance of model-specific assessment and suggest that associative interference can be substantially mitigated in modern systems.

Large language models are increasingly used to answer culturally grounded questions across languages, yet it remains unclear whether local cultural knowledge is better accessed through English or the local language. Existing evaluations face two key limitations: many rely on parallel template-based questions that may not reflect how cultural knowledge naturally appears, and raw accuracy conflates general language proficiency with language-conditioned knowledge access. We address these issues with a controlled framework built on real-world cultural questions collected from regional benchmarks and local sources. By crossing question type (culture-agnostic vs. culture-specific) with query language (English vs. local language), and estimating ability with a shared 1PL item response theory model, we separate proficiency from localized knowledge access. Across 13 locales and roughly 80 models, we find a consistent English advantage on culture-agnostic questions, indicating stronger English proficiency. However, after accounting for this proficiency gap, local languages show a positive knowledge-access advantage in nearly all locale-model settings. This advantage is often masked in raw accuracy but becomes more visible for frontier, regionally aligned, or language-adapted models. Our results suggest that weaker local-language performance does not necessarily imply weaker cultural knowledge; rather, local cultural knowledge may be more accessible through the local language but hidden by limited language proficiency.

Scaling laws provide a fundamental framework for understanding the performance of Language Models (LMs), yet deriving them requires prohibitively expensive evaluations across thousands of checkpoints or millions of inference samples. To address this, we introduce Item Response Scaling Laws (IRSL), a unified framework that integrates Item Response Theory (IRT) within the scaling law framework. Unlike traditional approaches that treat each model-benchmark pair in isolation, IRSL disentangles latent model ability from question characteristics, factorizing the scaling law estimation for $M$ models and $N$ questions to significantly reduce parameter complexity from $O(M \times N)$ to $O(M + N)$. We instantiate IRSL with Beta-IRT, which leverages the empirical probability responses of LMs -- such as token probabilities in pre-training and pass rates in test-time sampling -- to capture richer signals than binary responses. We validate our approach across two prevalent scaling paradigms: (1) pre-training downstream scaling, using 6,612 LM checkpoints and 37,682 questions from 10 benchmarks; and (2) test-time scaling, using 12 LMs and 120 questions from 4 benchmarks with up to 2,500 samples per question. Given a one-time calibration on existing model responses, IRSL yields more reliable scaling estimates using only 50 questions per benchmark (a 99.9% reduction), achieving comparable or superior decision accuracy to traditional approaches. Furthermore, we show that the estimated latent model abilities are generalizable, enabling accurate performance forecasting across benchmarks that share the same measurement objective.

LLM benchmark labels are frozen at release and silently propagated into downstream benchmarks, errors and all. We introduce an Item Response Theory-based indicator that surfaces likely mislabels at 95% precision in the top 200 examples across seven preference and multiple-choice benchmarks using responses from 114 models, outperforming a supervised classifier. We trace these errors to mechanical labeling heuristics, upstream annotation mistakes inherited unchanged from source datasets, and fundamentally ambiguous items without a defensible single label. The same model fit reveals that reward models specialize in stylistic preference rather than factual knowledge, and identifies one frontier reward model that agrees with detected mislabels at 78% accuracy versus 38% for its peers, consistent with benchmark contamination or benchmark-specific over-optimization.

Safety benchmarks for language models are typically evaluated using static paradigms that treat all items as equally informative for all models, an assumption that is particularly problematic for adversarial, highly heterogeneous safety items. Applied in full to modern benchmark suites, the current evaluation procedures would require on the order of $10^5$ responses, most of which provide little ranking signal. We analyze a suite of widely used safety benchmarks and make three contributions toward more efficient safety evaluation. First, we show that Item Response Theory (IRT) recovers interpretable structure on safety benchmarks, with ability estimates resolving differences among models that cluster at the ceiling of raw safety metrics. Second, we show that adaptive item selection, which dynamically chooses informative items for each model based on its responses, approximates full-benchmark rankings while reducing evaluation cost by at least 80% on benchmarks where Spearman's $ρ>$90% with full-benchmark is attainable, and by up to 99.9% on AIR-Bench 2024. Third, we introduce a practical procedure for extracting a fixed, informative subset of items reusable across models, providing an alternative to adaptive selection with savings of up to 99.8% on AIR-Bench 2024. Together, these results establish that psychometric methods enable benchmark-aware reductions in evaluation costs across the safety evaluation pipeline.

Accurate estimates of item difficulty are essential for valid assessment and effective adaptive learning. However, for newly created tasks, response data are typically unavailable. Pretesting and expert judgement can be costly and slow, while machine learning methods often require large labelled training datasets. Recent work suggests that large language models (LLMs) may help. However, there is limited evidence on the elicitation procedures and prompt configurations used to emulate experts for difficulty estimation. This study addresses this gap by evaluating three off-the-shelf LLMs as difficulty raters for newly created items without access to response data. Using an item bank from an online learning system, the study examined 6 domains of primary-school mathematics, with empirical difficulty estimates treated as empirical reference. The study used a full factorial design crossing three factors: judgement format (absolute vs pairwise), decision type (hard decisions vs token-probability-based estimates), and prompting strategy (zero-shot vs few-shot). LLM-derived difficulty estimates were compared with empirical difficulties using Spearman rank correlations. Across domains, LLM-based estimates exhibited moderate to strong positive correlations with empirical item difficulties. For simpler arithmetic tasks, some configurations approached the upper end of the accuracy range reported for human experts in previous research. Pairwise comparison consistently outperformed absolute judgement in the absence of additional refinements. However, when token-level probabilities were incorporated and examples of items with known empirical difficulty were provided, the absolute judgement configuration likewise demonstrated moderate-to-high alignment. The study positions LLMs as a promising tool for initial item calibration and offers insights into effective workflow configuration.

Large language models exhibit safety degradation in non-English languages. Standard evaluation relies on Jailbreak Success Rate (JSR), which confounds several safety-driving factors into one, obscuring the specific cause(s) of safety failure. We introduce a latent variable model, a Multi-Group Item Response Theory (IRT) framework, that decouples safety-driving factors such as language-agnostic safety robustness ($θ$), intrinsic prompt hardness ($β$), global language processing difficulty ($γ$), and a prompt-specific cross-lingual safety gap ($τ$). Using the MultiJail dataset, we evaluate the safety robustness of 61 model configurations across 5 closed-model families and 10 languages of varying resource, aggregating a dataset of 1.9 million rows. Exploratory Factor Analysis shows safety is primarily unidimensional: models refuse different harm types mainly through a shared mechanism. Contrary to the expected trend that safety degrades largely in low-resource languages, 22 model configurations are more vulnerable in English than in low-resource languages. Low-resource languages produce more uncertain responses (high entropy) than high-resource languages. Also, high-$τ$ prompts cluster in physical harm categories like Theft and Weapons and lower-resource languages, trends validated through cross-dataset generalization. While global translation quality shows low correlation with $τ$, severe mistranslations drive high-bias outliers, as validated by native speakers. Cultural and conceptual grounding mismatches also contribute to $τ$. In predictive validation, the IRT framework achieves $\mathrm{AUC} = 0.940$, outperforming simpler baselines in predicting safe refusal of unsafe prompts. Our framework reveals concept-language vulnerabilities that aggregate metrics obscure, enabling fairer cross-lingual safety evaluation and targeted improvements in dataset construction.

Benchmark evaluation across AI and safety-critical domains overwhelmingly relies on simple averaging. We demonstrate that this practice produces substantially misleading rankings when two conditions co-occur: (1) the evaluation matrix is sparse and (2) items vary substantially in difficulty. Through controlled simulation experiments across four domains -- NLP (GLUE), clinical drug trials, autonomous vehicle safety, and cybersecurity -- we show that Spearman rank correlation $ρ$ between simple-average rankings and ground-truth rankings degrades from $ρ= 1.000$ at 100% coverage to $ρ= 0.809$ at 67% coverage with high difficulty heterogeneity (mean over 20 seeds). A standard two-parameter logistic (2PL) Item Response Theory (IRT) model maintains $ρ\geq 0.996$ across all conditions. A 150-condition grid sweep over sparsity $S \in [0, 0.70]$ and difficulty gap $D \in [0.5, 5.0]$ confirms that ranking error forms a failure surface with a strong $S \times D$ interaction ($γ_3 = +0.20$, $t = 13.05$), while IRT maintains $ρ\geq 0.993$ throughout. We discuss implications for Physical AI benchmarking, where evaluation matrices are often incomplete and difficulty gaps are extreme.

The problem of predicting unobserved entries in a binary matrix, known as 1-bit matrix completion, has found diverse applications in fields such as recommendation systems. In this study, we develop an empirical Bayes method for 1-bit matrix completion motivated by the Efron--Morris estimator, a matrix generalization of the James--Stein estimator that shrinks singular values toward zero. The proposed method exploits the underlying low-rank structure of binary matrices, drawing parallels with multidimensional item response theory. Simulation studies and real-data applications demonstrate that the proposed method achieves a superior balance of predictive accuracy, calibration reliability (uncertainty quantification), and computational efficiency compared to existing methods.

Multiple-choice reasoning benchmarks face dual challenges: rapid saturation from advancing models and data contamination that undermines static evaluations. Ad-hoc hardening methods (paraphrasing, perturbation) attempt to increase difficulty but sacrifice logical validity for surface complexity, falling short to challenge advanced reasoning models. We present LogiHard, a formal framework that deterministically transforms 0-order selection into 2-order logical judgment, which significantly increases the thinking overhead and reasoning steps. The framework integrates Item Response Theory (IRT) for computerized adaptive testing (CAT), enabling precise difficulty control with fewer questions than static benchmarks. We instantiate LogiHard-2k, a logical reasoning dataset constructed by cognitively ranking high-stakes examination questions via 9-dimensional analysis of model thinking traces, followed by combinatorial transformation of high-difficulty items. Evaluation across twelve state-of-the-art models reveals an accuracy degradation ranging from 31% to 56% on combinatorially hardened questions. LLMs suffer from the multi-select failure and early exit bias, which are not shared by human testees. Zero-shot transfer to MMLU demonstrates 47% accuracy degradation (89.84% to 42.86%), confirming applicability across domains with provable validity preservation. The consistent aggregate degeneration is domain-agnostic and stems not from knowledge deficits but from a combinatorial reasoning gap, reflecting a training-induced completeness-verification deficit.

Evaluation of large language models (LLMs) is increasingly critical, yet standard benchmarking methods rely on average accuracy, overlooking both the inherent stochasticity of LLM outputs and the heterogeneity of benchmark items. Item Response Theory (IRT) offers a principled framework for modeling latent model abilities and item characteristics, but conventional methods are computationally expensive and numerically unstable, limiting large-scale implementations. To address these challenges, we propose an interpretable and scalable framework for LLM evaluation based on the majorization-minimization principle. Our approach reformulates the problem as a sequence of constrained matrix factorization subproblems, enabling stable and efficient parameter estimation with theoretical guarantees for identifiability and convergence. Experiments on synthetic and real-world datasets, including MATH-500 and six Open LLM Leaderboard benchmarks, demonstrate that our method achieves superior scalability and interpretability. It delivers orders-of-magnitude speedups over competing methods while maintaining comparable or even higher estimation accuracy. Our results align with established scaling laws and offer insights into item difficulty and discrimination, informing more principled benchmark design.

Recent advances in large language models (LLMs) have led to the development of AI-powered tutoring systems that provide interactive support via dialogue. To enable these tutoring systems to provide personalized support, it is essential to assess student performance at each turn, motivating knowledge tracing (KT) in dialogue settings. However, existing dialogue-based KT approaches often ignore question difficulty modeling and rely on opaque latent representations from LLMs, hindering accurate and interpretable prediction. In this work, we propose an interpretable difficulty-aware conversational KT framework built upon LLMs, which explicitly models students' abilities and the difficulty of tutor-posed tasks at each turn. The framework incorporates the original textual question and the next tutor-posed task to estimate the student's knowledge state and the difficulty of the upcoming turn. Furthermore, it integrates Item Response Theory to map LLM's outputs into student ability and question difficulty parameters, enabling interpretable prediction of student performance grounded in cognitive theories of learning. We evaluate the framework on two tutor-student dialogue datasets. Both quantitative and qualitative results show that our framework outperforms existing KT baselines, meanwhile generating interpretable outputs consistent with cognitive theory.

Automated short answer grading (ASAG) with large language models (LLMs) is commonly evaluated with aggregate metrics such as macro-F1 and Cohen's kappa. However, these metrics provide limited insight into how grading performance varies across student responses of differing grading difficulty. We introduce an evaluation framework for LLM-based ASAG based on item response theory (IRT), which models grading correctness as a function of latent grader ability and response grading difficulty. This formulation enables response-level analysis of where LLM graders succeed or fail and reveals robustness differences that are not visible from aggregate scores alone. We apply the framework to 17 open-weight LLMs on the SciEntsBank and Beetle benchmarks. The results show that even models with similar overall performance differ substantially in how sharply their grading accuracy declines as response difficulty increases. In addition, confusion patterns show that errors on difficult responses concentrate disproportionately on the \texttt{partially_correct_incomplete} label, indicating a tendency toward intermediate-label collapse under ambiguity. To characterize difficult responses, we further analyze semantic and linguistic correlates of estimated difficulty. Across both datasets, higher difficulty is associated with weaker semantic alignment to the reference answer, stronger contradiction signals, and greater semantic isolation in embedding space. Overall, these results show that item response theory offers a useful framework for evaluating LLM-based ASAG beyond aggregate performance measures.

Automated essay scoring (AES) is commonly evaluated on public benchmarks using quadratic weighted kappa (QWK). However, because benchmark labels are assigned by human raters and inevitably contain scoring errors, it remains unclear both what QWK is theoretically attainable and what level is practically sufficient for deployment. We therefore derive two dataset-specific QWK ceilings based on the reliability concept in classical test theory, which can be estimated from standard two-rater benchmarks without additional annotation. The first is the theoretical ceiling: the maximum QWK that an ideal AES model that perfectly predicts latent true scores can achieve under label noise. The second is the human-like ceiling: the QWK attainable by an AES model with human-level scoring error, providing a practical target when AES is intended to replace a single human rater. We further show that human--human QWK, often used as a ceiling reference, can underestimate the true ceiling. Simulation experiments validate the proposed ceilings, and experiments on real benchmarks illustrate how they clarify the current performance and remaining headroom of modern AES models.

Generative Agents, owing to their precise modeling and simulation capabilities of human behavior, have become a pivotal tool in the field of Artificial Intelligence in Education (AIEd) for uncovering complex cognitive processes of learners. However, existing educational agents predominantly rely on static personas to simulate student learning behaviors, neglecting the decisive role of deep cognitive capabilities in learning outcomes during practice interactions. Furthermore, they struggle to characterize the dynamic fluidity of knowledge internalization, transfer, and cognitive state transitions. To overcome this bottleneck, this paper proposes a human-like educational agent capable of simulating student cognitive evolution: CogEvolution. Specifically, we first construct a cognitive depth perceptron based on the Interactive, Constructive, Active, Passive (ICAP) taxonomy from cognitive psychology, achieving precise quantification of learner cognitive engagement. Subsequently, we propose a memory retrieval method based on Item Response Theory (IRT) to simulate the connection and assimilation of new and prior knowledge. Finally, we design a dynamic cognitive update mechanism based on evolutionary algorithms to simulate the real-time integration of student learning behaviors and cognitive evolution processes. Comprehensive evaluations demonstrate that CogEvolution not only significantly outperforms baseline models in behavioral fidelity and learning curve fitting but also uniquely reproduces plausible and robust cognitive evolutionary paths consistent with educational psychology expectations, providing a novel paradigm for constructing highly interpretable educational agents.

The proliferation of Large Language Models (LLMs) necessitates valid evaluation methods to provide guidance for both downstream applications and actionable future improvements. The Item Response Theory (IRT) model with Computerized Adaptive Testing has recently emerged as a promising framework for evaluating LLMs via their response accuracy. Beyond simple response accuracy, LLMs' chain of thought (CoT) lengths serve as a vital indicator of their reasoning ability. To leverage the CoT length information to assist LLM evaluation, we propose the \textbf{La}tency-\textbf{R}esponse \textbf{T}heory (LaRT) model, which jointly models both the response accuracy and CoT length by introducing a key correlation parameter between the latent ability and the latent speed. We derive an efficient stochastic approximation Expectation-Maximization algorithm for parameter estimation. We establish rigorous identifiability results for the latent ability and latent speed parameters to ensure the statistical validity of their estimation. Through both theoretical asymptotic analyses and simulation studies, we demonstrate LaRT's advantages over IRT in terms of superior estimation accuracy and shorter confidence intervals for latent trait estimation. To evaluate LaRT in real data, we collect responses from diverse LLMs on popular benchmark datasets. We find that LaRT yields different LLM rankings than IRT and outperforms IRT across multiple key evaluation metrics including predictive power, item efficiency, ranking validity, and LLM evaluation efficiency. Code and data are available at https://github.com/Toby-X/Latency-Response-Theory-Model

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.

Agentic AI evaluation pipelines produce benchmark scores that justify deployment decisions, safety certifications, and regulatory compliance claims. No formal framework has yet characterized how validity degrades across the stages of these pipelines. We present a three-layer compounding validity model, $V_{total} \leq V_1 \times V_2 \times V_3$, that captures multiplicative degradation across task generation ($V_1$), human-simulator calibration ($V_2$), and automated judgment ($V_3$). Under empirically grounded estimates, a pipeline retaining 70% validity at each stage is at most 34% valid against the intended construct (range 0.17-0.54 across the empirical estimate bounds). We examine the model's predictions against a structured survey of 55 published agentic evaluation papers, finding that approximately 82% of papers in this purposive sample apply structurally mismatched, incomplete, or absent inter-rater reliability (IRR) metrics, a pattern consistent with systematic $V_3$ collapse. We further identify empirical evidence of $V_1$ failures (task validity flaws in 7 of 10 popular benchmarks) and $V_2$ miscalibration (up to 9 percentage points inter-simulator variance, with systematic demographic disparities for non-Standard American English speakers). We derive eight prescriptions grounded in psychometric science and domain-stratified reliability thresholds (ICC $\geq$ 0.70; $\alpha \geq$ 0.67/0.70/0.80 by consequence level) that practitioners and benchmark authors can apply immediately. The framework provides a tractable knowledge-based tool for diagnosing and correcting evaluation pipeline validity before deployment decisions are made.