{"ID":6267161,"CreatedAt":"2026-07-10T01:11:38.759438437Z","UpdatedAt":"2026-07-13T01:02:08.706470581Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2607.08377","arxiv_id":"2607.08377","title":"Eigenvalue Calibration for Semantic Embeddings of Large Language Models","abstract":"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.","short_abstract":"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...","url_abs":"https://arxiv.org/abs/2607.08377","url_pdf":"https://arxiv.org/pdf/2607.08377v1","authors":"[\"Sebastian G. Gruber\",\"Nassim Walha\",\"Francis Bach\",\"Florian Buettner\"]","published":"2026-07-09T11:54:53Z","proceeding":"cs.LG","tasks":"[\"cs.LG\"]","methods":"[\"Large Language Model\",\"Language Model\"]","has_code":false}