标题： 基于身份链接的IRT用于无标签LLM评估：在TVD-MI分数中保持可加性 显示英文标题

标题： Identity-Link IRT for Label-Free LLM Evaluation: Preserving Additivity in TVD-MI Scores

摘要： 使用总变差距离互信息（TVD-MI）对大型语言模型进行成对比较，每对产生二元评判决策。 我们证明，对TVD-MI的二元试验进行平均可得到具有适合项目反应理论（IRT）的加法结构的中心概率分数，而无需非线性链接函数。 IRT的最大似然方法使用逻辑链接，但我们发现经验上这些变换会引入破坏加性的曲率：在三个领域中，恒等链接在原始数据上的中位数弯曲为0.080-0.150（P95 = [0.474, 0.580]），而probit/logit引入了明显更高的违反情况（中位数[0.245, 0.588]，P95 [0.825, 2.252]）。 我们从吉尼熵最大化推导出这个截断线性模型，得到一个处理边界饱和的箱约束最小二乘公式。 在33%的覆盖率下，我们实现了保留代理排名（Spearman $\rho = 0.972 \pm 0.015$）的保留集RMSE $0.117 \pm 0.008$，所需的评估次数仅为完整密集评估的三分之一。 法官鲁棒性分析（GPT-4o-mini与Llama3-70b）显示代理排名有很强的一致性（$\rho = 0.872$）和一致的恒等链接优势。 TVD-MI的几何结构通过恒等映射得到最佳保持，从而实现高效的LLM评估，适用于其他有限响应领域。 显示英文摘要

摘要： Pairwise comparisons of large language models using total variation distance mutual information (TVD-MI) produce binary critic decisions per pair. We show that averaging TVD-MI's binary trials yields centered-probability scores with additive structure suitable for item-response theory (IRT) without nonlinear link functions. Maximum-likelihood approaches to IRT use logistic links, but we find empirically that these transformations introduce curvature that breaks additivity: across three domains, the identity link yields median curl on raw data of 0.080-0.150 (P95 = [0.474, 0.580]), whereas probit/logit introduce substantially higher violations (median [0.245, 0.588], P95 [0.825, 2.252]). We derive this clipped-linear model from Gini entropy maximization, yielding a box-constrained least-squares formulation that handles boundary saturation. At 33% coverage, we achieve holdout RMSE $0.117 \pm 0.008$ while preserving agent rankings (Spearman $\rho = 0.972 \pm 0.015$), three times fewer evaluations than full dense. Judge robustness analysis (GPT-4o-mini vs. Llama3-70b) shows strong agreement in agent rankings ($\rho = 0.872$) and consistent identity-link advantage. TVD-MI's geometry is best preserved by identity mapping for efficient LLM evaluation, applicable to other bounded-response domains.