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This research introduces the Latency-Response Theory (LaRT) model, a novel statistical framework that evaluates Large Language Models by jointly analyzing response accuracy and chain-of-thought length. By establishing a correlation between latent ability and processing speed, LaRT offers more precise trait estimation than traditional Item Response Theory methods, potentially reshaping how we benchmark reasoning capabilities in AI systems.
Latency-Response Theory Model: Evaluating Large Language Models via Response Accuracy and Chain-of-Thought Length
arXiv:2512.07019v4 Announce Type: replace-cross Abstract: 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
Abstract: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 this https URL
Methodology (stat.ME); Artificial Intelligence (cs.AI); Applications (stat.AP); Machine Learning (stat.ML)
arXiv:2512.07019 [stat.ME]
(or arXiv:2512.07019v4 [stat.ME] for this version)
https://doi.org/10.48550/arXiv.2512.07019 Focus to learn more arXiv-issued DOI via DataCite
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