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This paper addresses the challenge of uncertainty quantification in large language models (LLMs) by introducing a novel framework for calibrating the eigenvalues of semantic embeddings. By interpreting LLMs with semantic embeddings as density matrix predictors, the authors apply temperature scaling to eigenvalues, establishing a central calibration inequality and proving that this method optimizes calibration by minimizing proper score risks. Experimental results reveal that existing LLMs exhibit systematic overconfidence, validating the theoretical advancements made in uncertainty quantification for semantic embeddings.
Current large language models are overconfident, but a new calibration method for eigenvalues could significantly enhance their reliability in real-world applications.
Uncertainty quantification is central to the reliable deployment of large language models (LLMs), and eigenvalues of semantic embeddings have recently emerged as a key tool in state-of-the-art methods. However, conventional calibration results developed for classification probabilities cannot be directly transferred to eigenvalues. We address this gap by proposing a novel framework for calibrating the eigenvalues of semantic embeddings. We interpret LLMs combined with semantic embeddings of their generated answers as density matrix predictors, and we propose a novel approach to calibrate density matrix predictors by applying temperature scaling to their eigenvalues. We establish entropy-risk equivalence under calibration, derive a central calibration inequality specific to eigenvalues, and prove that temperature-scaled eigenvalues optimize calibration when minimizing proper score risks. Experiments on a variety of real-world settings show that current LLMs are systematically overconfident, and validate our theoretical findings. Together, these results advance the foundations and practice of uncertainty quantification for semantic embeddings.
