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Accurately quantifying uncertainty in large language models (LLMs) is crucial for their reliable deployment, especially in high-stakes applications. Current state-of-the-art methods for measuring semantic uncertainty in LLMs rely on strict…

Machine Learning · Computer Science 2024-10-31 Yashvir S. Grewal , Edwin V. Bonilla , Thang D. Bui

Considering the difficulty of interpreting generative model output, there is significant current research focused on determining meaningful evaluation metrics. Several recent approaches utilize "precision" and "recall," borrowed from the…

Machine Learning · Computer Science 2025-02-28 Alexis Fox , Samarth Swarup , Abhijin Adiga

Statistical independence and conditional independence are two fundamental concepts in statistics and machine learning. Copula Entropy is a mathematical concept defined by Ma and Sun for multivariate statistical independence measuring and…

Computation · Statistics 2021-03-30 Jian Ma

The accessibility of spatially distributed data, enabled by affordable sensors, field, and numerical experiments, has facilitated the development of data-driven solutions for scientific problems, including climate change, weather…

Machine Learning · Computer Science 2023-11-09 Vardhan Dongre , Gurpreet Singh Hora

Large language models internalize enormous parametric knowledge during pre-training. Concurrently, realistic applications necessitate external contextual knowledge to aid models on the underlying tasks. This raises a crucial dilemma known…

Artificial Intelligence · Computer Science 2024-07-29 Xiaowei Yuan , Zhao Yang , Yequan Wang , Shengping Liu , Jun Zhao , Kang Liu

Large language models (LLMs) show remarkable potential in scientific hypothesis discovery. However, existing approaches face two critical limitations: they treat divergent exploratory ideation and convergent fine-grained refinement as…

Computation and Language · Computer Science 2026-05-29 Hongran An , Zonglin Yang

The Mixture-of-Experts (MoE) architecture has enabled the creation of massive yet efficient Large Language Models (LLMs). However, the standard deterministic routing mechanism presents a significant limitation: its inherent brittleness is a…

Machine Learning · Computer Science 2025-09-30 Albus Yizhuo Li

Uncertainty quantification (UQ) is essential for assessing the reliability of Earth observation (EO) products. However, the extensive use of machine learning models in EO introduces an additional layer of complexity, as those models…

Machine Learning · Computer Science 2024-12-10 Yuanyuan Wang , Qian Song , Dawood Wasif , Muhammad Shahzad , Christoph Koller , Jonathan Bamber , Xiao Xiang Zhu

Causal discovery is a fundamental problem in statistics and has wide applications in different fields. Transfer Entropy (TE) is a important notion defined for measuring causality, which is essentially conditional Mutual Information (MI).…

Machine Learning · Computer Science 2021-03-09 Jian Ma

Due to the inherent difficulty in modeling phonetic similarities across different languages, code-switching speech recognition presents a formidable challenge. This study proposes a Collaborative-MoE, a Mixture of Experts (MoE) model that…

Computation and Language · Computer Science 2024-09-06 Hukai Huang , Jiayan Lin , Kaidi Wang , Yishuang Li , Wenhao Guan , Lin Li , Qingyang Hong

Logit-based LLM watermarking traces and verifies AI-generated content by maintaining green and red token lists and increasing the likelihood of green tokens during generation. However, it fails in low-entropy scenarios, where predictable…

Computation and Language · Computer Science 2025-05-21 Tianle Gu , Zongqi Wang , Kexin Huang , Yuanqi Yao , Xiangliang Zhang , Yujiu Yang , Xiuying Chen

Complex engineered systems require coordinated design choices across heterogeneous components under multiple conflicting objectives and uncertain specifications. Monotone co-design provides a compositional framework for such problems by…

Optimization and Control · Mathematics 2026-03-20 Yujun Huang , Gioele Zardini

Identifying differential equation governing dynamical system is an important problem with wide applications. Copula Entropy (CE) is a mathematical concept for measuring statistical independence in information theory. In this paper we…

Systems and Control · Electrical Eng. & Systems 2023-04-27 Jian Ma

We introduce a new information-theoretic formulation of quantum measurement uncertainty relations, based on the notion of relative entropy between measurement probabilities. In the case of a finite-dimensional system and for any approximate…

Mathematical Physics · Physics 2018-03-02 Alberto Barchielli , Matteo Gregoratti , Alessandro Toigo

Complex multi-step reasoning tasks, such as solving mathematical problems, remain challenging for large language models (LLMs). While outcome supervision is commonly used, process supervision via process reward models (PRMs) provides…

Computation and Language · Computer Science 2025-02-18 Zihuiwen Ye , Luckeciano Carvalho Melo , Younesse Kaddar , Phil Blunsom , Sam Staton , Yarin Gal

Concept Bottleneck Models (CBMs) predict through human-interpretable concepts, but they typically output point concept probabilities that conflate epistemic uncertainty (reducible model underspecification) with aleatoric uncertainty…

Artificial Intelligence · Computer Science 2026-04-28 Tanmoy Mukherjee , Thomas Bailleux , Pierre Marquis , Zied Bouraoui

Mixture-of-Experts (MoE) is a flexible framework that combines multiple specialized submodels (``experts''), by assigning covariate-dependent weights (``gating functions'') to each expert, and have been commonly used for analyzing…

Methodology · Statistics 2026-01-06 Qicheng Zhao , Celia M. T. Greenwood , Qihuang Zhang

Class imbalance remains a major challenge in machine learning, especially for high-dimensional biomedical data where nonlinear manifold structures dominate. Traditional oversampling methods such as SMOTE rely on local linear interpolation,…

Self-evolving large language models (LLMs) learn by generating their own training tasks and solutions, reducing reliance on human-curated supervision. However, in many reasoning domains, the model must also validate generated tasks and…

Artificial Intelligence · Computer Science 2026-05-28 Bowen Wei , Nan Wang , Yuqing Zhou , Jinhao Pan , Ziwei Zhu

Uncertainty quantification in automated image analysis is highly desired in many applications. Typically, machine learning models in classification or segmentation are only developed to provide binary answers; however, quantifying the…

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