The proliferation of Large Language Models (LLMs) necessitates valid evaluation methods to guide downstream applications and actionable future improvements. The Item Response Theory (IRT) 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 the evaluation of LLMs, we propose Latency-Response Theory (LaRT) to jointly model the response accuracy and CoT length by introducing the latent ability, latent speed, and a key correlation parameter between them. We derive an efficient estimation algorithm and establish rigorous identifiability results for the population parameters to ensure the statistical validity of estimation. Theoretical asymptotic analyses and simulation studies demonstrate LaRT's advantages over IRT in terms of higher estimation accuracy and shorter confidence intervals for latent traits. A key finding is that the asymptotic estimation precision of the latent ability under LaRT exceeds that of IRT whenever the latent ability and latent speed are correlated. We collect real responses from diverse LLMs on popular benchmark datasets. The application of LaRT reveals a strong negative correlation between the latent ability and latent speed in all benchmarks, with stronger correlation for more difficult benchmarks. This finding supports the intuition that higher reasoning ability correlates with slower speed and longer response latency. 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.

We propose a statistical framework built on latent variable modeling for scaling laws of large language models (LLMs). Our work is motivated by the rapid emergence of numerous new LLM families with distinct architectures and training strategies, evaluated on an increasing number of benchmarks. This heterogeneity makes a single global scaling curve inadequate for capturing how performance varies across families and benchmarks. To address this, we propose a latent variable modeling framework in which each LLM family is associated with a latent variable that captures the common underlying features in that family. An LLM's performance on different benchmarks is then driven by its latent skills, which are jointly determined by the latent variable and the model's own observable features. We develop an estimation procedure for this latent variable model and establish its statistical properties. We also design efficient numerical algorithms that support estimation and various downstream tasks. Empirically, we evaluate the approach on 12 widely used benchmarks from the Open LLM Leaderboard (v1/v2).

Evaluating large language models (LLMs) on comprehensive benchmarks is a cornerstone of their development, yet it's often computationally and financially prohibitive. While Item Response Theory (IRT) offers a promising path toward data-efficient evaluation by disentangling model capability from item difficulty, existing IRT -based methods are hampered by significant limitations. They are typically restricted to binary correctness metrics, failing to natively handle the continuous scores used in generative tasks, and they operate on single benchmarks, ignoring valuable structural knowledge like correlations across different metrics or benchmarks. To overcome these challenges, we introduce LEGO-IRT, a unified and flexible framework for data-efficient LLM evaluation. LEGO-IRT's novel design natively supports both binary and continuous evaluation metrics. Moreover, it introduces a factorized architecture to explicitly model and leverage structural knowledge, decomposing model ability estimates into a general component and structure-specific (e.g., per-metric or per-benchmark) components. Through extensive experiments involving 70 LLMs across 5 benchmarks, we show that LEGO-IRT achieves stable capability estimates using just 3% of the total evaluation items. We demonstrate that incorporating structural knowledge reduces estimation error by up to 10% and reveal that the latent abilities estimated by our framework may align more closely with human preferences. The evaluation of model performance is a critical component in the development process of modern large language models (LLMs) as well as a building block towards deeper understandings of LLMs.

Large Language Models (LLMs) vary in their abilities on a range of tasks. Initiatives such as the $\texttt{Open LLM Leaderboard}$ aim to quantify these differences with several large benchmarks (sets of test items to which an LLM can respond either correctly or incorrectly). However, high correlations within and between benchmark scores suggest that (1) there exists a small set of common underlying abilities that these benchmarks measure, and (2) items tap into redundant information and the benchmarks may thus be considerably compressed. We use data from $n > 5000$ LLMs to identify the most informative items of six benchmarks, ARC, GSM8K, HellaSwag, MMLU, TruthfulQA and WinoGrande (with $d=28,632$ items in total). From them we distill a sparse benchmark, $\texttt{metabench}$, that has less than $3\%$ of the original size of all six benchmarks combined. This new sparse benchmark goes beyond point scores by yielding estimators of the underlying benchmark-specific abilities. We show that these estimators (1) can be used to reconstruct each original $\textit{individual}$ benchmark score with, on average, $1.5\%$ root mean square error (RMSE), (2) reconstruct the original $\textit{total}$ score with $0.8\%$ RMSE, and (3) have a single underlying common factor whose Spearman correlation with the total score is $r = 0.93$.