arXiv:2604.03257v1 Announce Type: cross Abstract: The ability to rigorously estimate the failure rates of large language models (LLMs) is a prerequisite for their safe deployment. Currently, however, practitioners often face a tradeoff between expensive human gold standards and potentially severely-biased automatic annotation schemes such as "LLM-as-a-Judge" labeling. In this paper, we propose a new, practical, and efficient approach to LLM failure rate estimation based on constrained maximum-likelihood estimation (MLE). Our method integrates three distinct signal sources: (i) a small, high-quality human-labeled calibration set, (ii) a large corpus of LLM-judge annotations, and, most importantly, (iii) additional side information via domain-specific constraints derived from known bounds on judge performance statistics. We validate our approach through a comprehensive empirical study, benchmarking it against state-of-the-art baselines like Prediction-Powered Inference (PPI). Across diverse experimental regimes -- spanning varying judge accuracies, calibration set sizes, and LLM failure rates -- our constrained MLE consistently delivers more accurate and lower-variance estimates than existing methods. By moving beyond the "black-box" use of automated judges to a flexible framework, we provide a principled, interpretable, and scalable pathway towards LLM failure-rate certification.

arXiv:2603.02029v2 Announce Type: replace Abstract: Moving beyond evaluations that collapse performance across heterogeneous prompts toward fine-grained evaluation at the prompt level, or within relatively homogeneous subsets, is necessary to diagnose generative models' strengths and weaknesses. Such fine-grained evaluations, however, suffer from a data bottleneck: human gold-standard labels are too costly at this scale, while automated ratings are often misaligned with human judgment. To resolve this challenge, we propose a novel statistical model based on tensor factorization that merges cheap autorater data with a limited set of human gold-standard labels. Specifically, our approach uses autorater scores to pretrain latent representations of prompts and generative models, and then aligns those pretrained representations to human preferences using a small calibration set. This sample-efficient methodology is robust to autorater quality, more accurately predicts human preferences on a per-prompt basis than standard baselines, and provides tight confidence intervals for key statistical parameters of interest. We also showcase the practical utility of our method by constructing granular leaderboards based on prompt qualities and by estimating model performance solely from autorater scores, eliminating the need for additional human annotations.