Item Response Theory

Computerized Adaptive Testing (CAT) has proven effective for efficient LLM evaluation on multiple-choice benchmarks, but modern LLM evaluation increasingly relies on generation tasks where outputs are scored continuously rather than marked correct/incorrect. We present a principled extension of IRT-based adaptive testing to continuous bounded scores (ROUGE, BLEU, LLM-as-a-Judge) by replacing the Bernoulli response distribution with a heteroskedastic normal distribution. Building on this, we introduce an uncertainty aware ranker with adaptive stopping criteria that achieves reliable model ranking while testing as few items and as cheaply as possible. We validate our method on five benchmarks spanning n-gram-based, embedding-based, and LLM-as-judge metrics. Our method improves ranking correlation by 0.13 $τ$ over random sampling and has 99% accuracy on confident predictions while using 2% of the items after a one-time calibration step.

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 Latency-Response Theory (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.