给大模型语义嵌入的特征值做校准，让信心预测更靠谱。
Eigenvalue Calibration for Semantic Embeddings of Large Language Models
- 把语义嵌入特征值看作密度矩阵预测，用温度缩放校准。
- 实验发现当前大模型普遍过度自信，校准后误差显著下降。
- 理论严谨，适合关注模型置信度可靠性的研究者。
不确定性量化是大语言模型可靠部署的核心，而语义嵌入的特征值近年来已成为先进方法的关键工具。然而，传统针对分类概率的校准方法无法直接适用于特征值。本文提出一种新框架，将结合语义嵌入的大模型生成答案视为密度矩阵预测器，并通过对其特征值应用温度缩放来校准。我们建立了校准下的熵-风险等价关系，推导出专属于特征值的中心校准不等式，并证明在最小化合理评分风险时，温度缩放的特征值能实现最优校准。在多种真实场景下的实验表明，当前大模型系统性地过度自信，验证了理论发现。这些成果推动了语义嵌入不确定性量化的理论与实践发展。
原文摘要 · Abstract (English)
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.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。