Pointed Hopf Algebras of Discrete Corepresentation Type

We classify pointed Hopf algebras of discrete corepresentation type over an algebraically closed field K with characteristic zero. For such algebras $H$, we explicitly determine the algebra structure up to isomorphism for the link indecomposable component $B$ containing the unit. It turns out that $H$ is a crossed product of $B$ and a certain group algebra.Comment: Comments are welcome

Optimizing the Electrical Energy Conversion Cycle of Dielectric Elastomer Generators

Engineering and Applied Science

Towards Trustworthy Dataset Distillation

Efficiency and trustworthiness are two eternal pursuits when applying deep learning in real-world applications. With regard to efficiency, dataset distillation (DD) endeavors to reduce training costs by distilling the large dataset into a tiny synthetic dataset. However, existing methods merely concentrate on in-distribution (InD) classification in a closed-world setting, disregarding out-of-distribution (OOD) samples. On the other hand, OOD detection aims to enhance models' trustworthiness, which is always inefficiently achieved in full-data settings. For the first time, we simultaneously consider both issues and propose a novel paradigm called Trustworthy Dataset Distillation (TrustDD). By distilling both InD samples and outliers, the condensed datasets are capable to train models competent in both InD classification and OOD detection. To alleviate the requirement of real outlier data and make OOD detection more practical, we further propose to corrupt InD samples to generate pseudo-outliers and introduce Pseudo-Outlier Exposure (POE). Comprehensive experiments on various settings demonstrate the effectiveness of TrustDD, and the proposed POE surpasses state-of-the-art method Outlier Exposure (OE). Compared with the preceding DD, TrustDD is more trustworthy and applicable to real open-world scenarios. Our code will be publicly available.Comment: 20 pages, 20 figure