报告人：庄晓生

报告人简介：Prof. Zhuang Xiaosheng received his bachelor's and master's degrees in mathematics from Sun Yat-sen (Zhongshan) University, China, in 2003 and 2005 respectively. He received his PhD in Applied Mathematics from the University of Alberta, Canada, in 2010. He was a Postdoctoral Fellow at Universität Osnabrück in 2011 and Technische Universität Berlin in 2012. He joined the Department of Mathematics of City University of Hong Kong in 2012 and served as the department Associate Head from 2018 to 2021. He is a Professor in the Department of Mathematics, City University of Hong Kong. Prof. Zhuang Xiaosheng's research is mainly on applied and computational harmonic analysis, wavelet and framelet analysis, signal and image processing, deep and machine learning, etc. He has published more than 40 academic papers in international journals, including Applied and Computational Harmonic Analysis (ACHA), SIAM Journal on Imaging Sciences (SIIMS), Mathematics of Computation, ICML, JMLR, IEEE TNNLS, IEEE TIP, Neural Networks, Pattern Recognition, etc.

报告一：Directional Haar Tight Framelets on Bounded Domains

内容简介：In this talk, motivated by the development of directional Haar framelet systems on Rd as well as wavelet-like systems for graph signal processing, we focus on the development of directional multiscale representation systems for signals defined on digraphs. We investigate two main problems: 1) How to construct directional Haar tight framelets on bounded domains with adaptivity? 2) How to efficiently represent digraph signals? Based on hierarchical partitions, we provide the construction of Haar-type tight framelets on any compact set in Rd. In particular, on the unit block [0, 1]d, such tight framelets can be built to be with adaptivity and directionality. We show that the adaptive directional Haar tight framelet systems can be used for efficient digraph signal representation.

时  间：2025年5月9日（周五）下午18:00开始

地  点：南海楼124

报告二：Framelets on Spheres and Graphs: Construction and Applications

内容简介：Deep learning has revolutionized modern society and people’s daily lives during the past decade, ranging from automated driving, online shopping, and AI assistants to intelligent surveillance systems, medical diagnosis, drug discovery, and so on. Spherical neural networks (SNNs) and Graph neural networks (GNNs) are powerful deep learning methods for machine learning tasks on non-Euclidian data, e.g., CMB data, social networks, and citation networks. Framelet systems, like the traditional wavelet systems for Euclidean data (signals, images, videos, etc.), provide a powerful tool for multiresolution analysis of such data. Based on a general framework for the construction of framelets on compact sets, we establish Haar framelet systems on various domains and demonstrate how to build Haar framelet systems that can be efficiently and effectively utilized for the design of deep neural network architecture. We demonstrate state-of-the-art performances of the framelet neural networks in some deep learning tasks.

时  间：2025年5月10日（周六）上午8:00开始

地  点：南海楼124

报告三：Permutation Equivariant Graph Framelets for Heterophilous Graph Learning

内容简介：The nature of heterophilous graphs is significantly different from that of homophilous graphs, which causes difficulties in early graph neural network models and suggests aggregations beyond the 1-hop neighborhood. In this talk, we discuss a new way to implement multi-scale extraction via constructing Haar-type graph framelets with desired properties of permutation equivariance, efficiency, and sparsity, for deep learning tasks on graphs. We design a graph framelet neural network model PEGFAN (Permutation Equivariant Graph Framelet Augmented Network) based on our constructed graph framelets. The experiments are conducted on a synthetic dataset and 9 benchmark datasets to compare performance with other state-of-the-art models. The result shows that our model can achieve the best performance on certain datasets of heterophilous graphs (including the majority of heterophilous datasets with relatively larger sizes and denser connections) and competitive performance on the remaining.

时  间：2025年5月10日（周六）上午10:00开始

地  点：南海楼124

报告四：Spherical Framelets from Spherical Designs

内容简介：In this talk, we discuss the structures of the variational characterization of the spherical t-design, its gradient, and its Hessian in terms of fast spherical harmonic transforms. Moreover, we propose solving the minimization problem of the spherical t-design using the trust-region method to provide spherical t-designs with large values of t. Based on the obtained spherical t-designs, we develop (semi-discrete) spherical tight framelets as well as their truncated systems and their fast spherical framelet transforms for practical spherical signal/image processing. Thanks to the large spherical t-designs and localization property of our spherical framelets, we are able to provide signal/image denoising using local thresholding techniques based on a fine-tuned spherical cap restriction. Many numerical experiments are conducted to demonstrate the efficiency and effectiveness of our spherical framelets and spherical designs, including Wendland function approximation, ETOPO data processing, and spherical image denoising.

时  间：2025年5月10日（周六）下午14:00开始

地  点：石牌校区南海楼124会议室

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信息科学技术学院

2025年5月6日