Quantifying and Auditing LLM Evaluation via Positive--Unlabeled Learning

2026-06-17

AI Summary

This work addresses the misalignment between LLM-as-a-Judge systems and human judgments of semantic quality, which often arises from biases such as verbosity. Human annotations are costly and typically yield only partially reliable positive samples, leaving a large pool of unlabeled outputs with mixed quality. The paper formulates LLM evaluation as a positive–unlabeled learning problem and introduces a geometry-aware auditing framework based on biased optimal transport. This framework aligns the reliably human-verified positive samples with a trustworthy subset of unlabeled outputs within a fixed embedding space. Without requiring retraining, the method corrects biased evaluators, recovers human-aligned preferences, and provides interpretable confidence estimates. Experiments demonstrate that the approach significantly improves agreement with human preferences and enhances robustness to presentation bias, establishing a scalable and statistically principled paradigm for LLM evaluation.

Abstract

Large Language Models (LLMs) are increasingly used as judges for scalable evaluation, yet such LLM--as--a--Judge systems exhibit systematic biases that are decoupled from semantic quality, most notably verbosity bias. Meanwhile, human supervision is costly and typically selective, yielding reliable positive judgments but leaving most outputs unlabelled and potentially mixed in quality. We formulate LLM evaluation under selective human supervision as a positive--unlabelled learning problem and propose a geometric auditing framework based on Partial Optimal Transport. By aligning a small set of human--verified positives with a reliable subset of unlabelled outputs in a fixed embedding space, our method identifies human--consistent preferences and corrects biased judges without retraining. Experiments demonstrate improved alignment with human preferences, increased robustness to presentation biases, and interpretable confidence estimates, offering a scalable and statistically grounded alternative to existing LLM--as--a--judge pipelines.

Problem

• LLM-as-a-Judge
• verbosity bias
• positive-unlabeled learning
• human supervision
• evaluation bias

Innovation

• Positive-Unlabeled Learning
• Partial Optimal Transport
• LLM-as-a-Judge
• Evaluation Bias Correction
• Geometric Auditing