2024 Greater Bay Area Topology Conference: Topological data analysis and deep learning

November 22–24, 2024 | Southern University of Science and Technology | Shenzhen

Greater Bay Area Topology Conference

The theme of this conference is topological data analysis and deep learning. It aims to promote exchanges among experts and scholars in topology and related fields within the Guangdong–Hong Kong–Macao Greater Bay Area and across regions, provide a platform for collaboration with the industry and interdisciplinary fields, and explore the application of topology to data science and artificial intelligence.
The organizers gratefully acknowledge the support by SUSTech Department of Mathematics, National Center for Applied Mathematics Shenzhen, Shenzhen International Center for Mathematics, Guangdong Provincial Key Laboratory of Interdisciplinary Research and Application for Data Science, and National Natural Science Foundation of China.
• Poster

Invited Speakers (A–Z)


Hongwei Lin
Zhejiang University
Computer-Aided Topological Design—applications of computational topology in geometric design and processing
Computational topology is an emerging discipline developed since around 2000. It studies the determination and modeling of topological problems in computer applications, as well as the design of algorithms for topological problems. As a subject to apply computational topology to the field of data processing, topological data analysis has been developed. It has been widely used in biomedicine, drug design, financial analysis, machine learning, and other fields. The main tools in computational topology and topological data analysis are persistent homology and Mapper. Persistent homology constructs a sequence of gradually “growing” simplicial complexes in a metric space, computes the persisting homological features (generators in the persistent homology groups), and infers the importance of the features based on the life span of these homological features, thereby enabling the inference and extraction of global topological features of the discrete data set. On the other hand, Mapper extracts the main topological structure of the data set by defining a reference mapping on the data set and using data segmentation and clustering. Since almost 10 years ago, the CAGD research group of Zhejiang University has applied computational topology methods to geometric design and geometric processing, and developed a series of computer-aided topological design methods. This talk will introduce a series of work in this area, including curve and surface reconstruction technology based on topological understanding, and topological control methods in implicit curve and surface reconstruction. Furthermore, persistent homology has been applied to the field of porous structure processing, and a variety of topological descriptors have been designed for porous structure retrieval and classification; porous structure generation technology that ensures connectivity has been developed; porous thickness computation technology that preserves topological structure and porous model slicing method have been proposed in 3D printing of porous structures.


Feng Pan
Peking University Shenzhen Graduate School
Graph-theory-based exploration of structural chemistry and material genes in Li-ion batteries
Methodologies of structural chemistry have been studied to explore the material gene and structure-function relationship in Li-ion batteries. Through developing chemical methods based on graph theory as well as establishing a material big data system, we aim to incorporate artificial intelligence and investigate the fundamental questions of “what are material genes?” and “how to conduct research on material genes in lithium-ion batteries?”. In this report, several cutting-edge interdisciplinary fields will be introduced, including structural chemistry based on graph theory, big data of materials, lithium-ion battery material genes, super-exchange interaction of d-orbital spinning electrons in transitional metals, structure characterizations via large scientific facilities such as synchrotron and neutron radiation, etc. The above investigations attempt to inspire new paradigms for material research, thus advancing the development of critical materials in lithium-ion batteries.


Kelin Xia
Nanyang Technological University
Mathematical AI for Molecular Sciences
Artificial intelligence (AI) based Molecular Sciences have begun to gain momentum due to the great advancement in experimental data, computational power and learning models. However, a major issue that remains for all these AI-based learning models is the efficient molecular representations and featurization. Here we propose advanced mathematics-based molecular representations and featurization.
Molecular structures and their interactions are represented by high-order topological and algebraic models (including Rips complex, Alpha complex, Neighborhood complex, Dowker complex, Hom-complex, Tor-algebra, etc). Mathematical invariants (from persistent homology, persistent Ricci curvature, persistent spectral, R-Torsion, etc) are used as molecular descriptors for learning models. Further, we develop geometric and topological deep learning models to systematically incorporate molecular high-order, multiscale, and periodic information, and use them for analyzing molecular data from chemistry, biology, and materials.


Meng Yu
Tencent AI Lab
Advancing Speech Signal Processing: From Region-Based Audio Zooming to Near-Field Quality Transformation
Enhancing speech signals in complex acoustic environments remains a critical challenge in audio processing. Our recent work presents several innovative approaches to tackle key issues in this domain. We introduced a novel audio zooming technique based on deep learning, shifting from traditional direction-based beamforming to a user-defined, adjustable 3D region for sound capture. This advancement enables precise and flexible audio acquisition, supporting real-time applications such as remote conferencing, education, and live streaming. Building on the concept of region-based sound capture, we further aimed to transform the captured far-field audio into near-field quality. Leveraging pre-trained generative models, we designed a method to resynthesize clean speech by reducing noise and reverberation, achieving robust performance in the real-world environments. To refine this transformation, we used a two-stage framework combining predictive deep learning for initial enhancement with generative diffusion models for near-field audio generation.
By optimizing the diffusion process, we significantly reduced computational complexity while enhancing audio fidelity and reducing distortion. These advancements provide effective solutions to long-standing challenges in speech processing, enabling high-quality audio experiences in diverse applications.

Schedule

Updated Nov. 21.

Fri. Nov. 22

There will be a Departmental Tea at 16:00 in M712, College of Science. All are welcome. The Mathematics Colloquium / opening talk takes place in M1001:

16:30 Prof. Hongwei Lin, Computer-Aided Topological Design—applications of computational topology in geometric design and processing Computational topology is an emerging discipline developed since around 2000. It studies the determination and modeling of topological problems in computer applications, as well as the design of algorithms for topological problems. As a subject to apply computational topology to the field of data processing, topological data analysis has been developed. It has been widely used in biomedicine, drug design, financial analysis, machine learning, and other fields. The main tools in computational topology and topological data analysis are persistent homology and Mapper. Persistent homology constructs a sequence of gradually “growing” simplicial complexes in a metric space, computes the persisting homological features (generators in the persistent homology groups), and infers the importance of the features based on the life span of these homological features, thereby enabling the inference and extraction of global topological features of the discrete data set. On the other hand, Mapper extracts the main topological structure of the data set by defining a reference mapping on the data set and using data segmentation and clustering. Since almost 10 years ago, the CAGD research group of Zhejiang University has applied computational topology methods to geometric design and geometric processing, and developed a series of computer-aided topological design methods. This talk will introduce a series of work in this area, including curve and surface reconstruction technology based on topological understanding, and topological control methods in implicit curve and surface reconstruction. Furthermore, persistent homology has been applied to the field of porous structure processing, and a variety of topological descriptors have been designed for porous structure retrieval and classification; porous structure generation technology that ensures connectivity has been developed; porous thickness computation technology that preserves topological structure and porous model slicing method have been proposed in 3D printing of porous structures.

Sat. Nov. 23

The morning session takes place in M1001, College of Science. The afternoon session takes place in Room 240A, Taizhou Hall (International Center for Mathematics Lecture Hall).

8:30 Prof. Feng Pan, Graph theory based exploration of structural chemistry and material genes in Li-ion batteries Methodologies of structural chemistry have been studied to explore the material gene and structure-function relationship in Li-ion batteries. Through developing chemical methods based on graph theory as well as establishing a material big data system, we aim to incorporate artificial intelligence and investigate the fundamental questions of “what are material genes?” and “how to conduct research on material genes in lithium-ion batteries?”. In this report, several cutting-edge interdisciplinary fields will be introduced, including structural chemistry based on graph theory, big data of materials, lithium-ion battery material genes, super-exchange interaction of d-orbital spinning electrons in transitional metals, structure characterizations via large scientific facilities such as synchrotron and neutron radiation, etc. The above investigations attempt to inspire new paradigms for material research, thus advancing the development of critical materials in lithium-ion batteries.
9:30 Break
10:00 Prof. Kelin Xia, Mathematical AI for Molecular Sciences Artificial intelligence (AI) based Molecular Sciences have begun to gain momentum due to the great advancement in experimental data, computational power and learning models. However, a major issue that remains for all these AI-based learning models is the efficient molecular representations and featurization. Here we propose advanced mathematics-based molecular representations and featurization. Molecular structures and their interactions are represented by high-order topological and algebraic models (including Rips complex, Alpha complex, Neighborhood complex, Dowker complex, Hom-complex, Tor-algebra, etc). Mathematical invariants (from persistent homology, persistent Ricci curvature, persistent spectral, R-Torsion, etc) are used as molecular descriptors for learning models. Further, we develop geometric and topological deep learning models to systematically incorporate molecular high-order, multiscale, and periodic information, and use them for analyzing molecular data from chemistry, biology, and materials.
11:00 Lunch
14:00 Dr. Meng Yu, Advancing Speech Signal Processing: From Region-Based Audio Zooming to Near-Field Quality Transformation Enhancing speech signals in complex acoustic environments remains a critical challenge in audio processing. Our recent work presents several innovative approaches to tackle key issues in this domain. We introduced a novel audio zooming technique based on deep learning, shifting from traditional direction-based beamforming to a user-defined, adjustable 3D region for sound capture. This advancement enables precise and flexible audio acquisition, supporting real-time applications such as remote conferencing, education, and live streaming. Building on the concept of region-based sound capture, we further aimed to transform the captured far-field audio into near-field quality. Leveraging pre-trained generative models, we designed a method to resynthesize clean speech by reducing noise and reverberation, achieving robust performance in the real-world environments. To refine this transformation, we used a two-stage framework combining predictive deep learning for initial enhancement with generative diffusion models for near-field audio generation. By optimizing the diffusion process, we significantly reduced computational complexity while enhancing audio fidelity and reducing distortion. These advancements provide effective solutions to long-standing challenges in speech processing, enabling high-quality audio experiences in diverse applications.
15:00 Break
15:30 Panel discussion (panelists: Fengchun Lei, Jingyan Li, Hongwei Lin, and Kelin Xia, with Yifei Zhu as moderator), Research in applied topology and collaboration across disciplines: Challenges and opportunities This will be a moderated conversation between the audience and the invited panelists, based on their experiences and practices.
17:30 Dinner at 老广新意（留仙大道宝能环球汇A馆3楼3009-D号）

Sun. Nov. 24

Free discussion.

Local information

Information on travel, lodging, etc. can be found here (updated Nov. 21).

Organizers

Assistant: Leyuan Shen, Southern University of Science and Technology

If you have any questions, comments or suggestions, please contact us at gba.topology@outlook.com

Participants

Updated Nov. 20.