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.
Large language models (LLMs) have demonstrated a strong ability to generate syntactically correct code from natural-language specifications. In this study, we explore how LLMs can be harnessed to automatically translate a neutral graph representation of fluid system models into e…
As large language models (LLMs) continue to demonstrate exceptional capabilities across various domains, the challenge of achieving energy-efficient and accurate inference becomes increasingly critical. This work presents LightRot, a lightweight rotation scheme and dedicated hard…
While large audio-language models have achieved remarkable progress in auditory perception, they still lag behind text-based large language models in deep logical reasoning, primarily due to the scarcity of high-quality audio reasoning data. To bridge this gap, we propose X$^3$-O…
Symbolic Regression (SR) aims to discover analytical equations from observational data and plays a central role in scientific modeling. While recent Large Language Model (LLM) based approaches show promise, they face two limitations. First, they lack data analysis mechanisms for…
Cognitive impairment (CI) is a growing public health concern. Early and accurate diagnosis is critical for enabling timely intervention and improving patient outcomes. Speech-based CI detection has emerged as a promising non-invasive approach, as speech signals encode both lingui…
Resolving Design Rule Violations (DRVs) in layouts entails an iterative loop of geometric edits and verification. We present DRC-Aid, a closed-loop agentic framework that automates local DRC repair by formulating it as verification-in-the-loop search. To constrain the combinatori…