Topological Deep Learning

The public lecture was jointly organised by IAS NTU and Institute for Mathematical Science (IMS), NUS, as part of the IAS-IMS joint public lecture series on Mathematical Artificial Intelligence (AI). It is also affiliated with the IMS conference on "Applied Topology in Frontier Sciences", July 11-22, 2022.

Data-driven sciences are widely regarded as the fourth paradigm of sciences that will fundamentally change the society and our everyday lives. Recently, the remarkable achievement of AlphaFold2 for protein folding problem has ushered in a new era of AI for sciences. Advanced mathematical tools, from algebra, topology, geometry, combinatorics, etc, have demonstrated great power in data representation, characterisation, and modelling. The interdisciplinary research area of Mathematical AI has developed very fast and demonstrated great potential in data analysis.

The speaker Prof Gunnar Carlsson from Stanford University is a world-leading mathematician specialising in topological data analysis (TDA) and its various applications. The talk focuses on topological deep learning. It covers a brief introduction of deep learning, Mapper, topological modelling, and topological deep learning. In particular, Prof Carlsson discussed the "shape of data”, i.e., using topological models to characterise the structural information of data and the combination of the shape information with deep learning. He has demonstrated that topological deep learning models are much more robust and accurate for noise-contaminated data and adversarial examples.

The webinar ended with an interactive Q&A session where Prof. Carlsson addressed different questions related to data visualization, Mapper, and advantage of topological deep learning.

Assistant Professor Kelin XIA | SPMS NTU

Figure 1 Topological modelling of hydrogen-bonding networks.