We are excited to host Ginestra Bianconi (QMUL) in the BeyondTheEdge Seminar series:
The Topological Dirac operator: theory and applications in Artificial Intelligence
The dynamics of a network is not only encoded in node variables but also in edge variables, like currents and fluxes. The graph Laplacian has been extensively used in Machine Learning and Artificial Intelligence to process node signals, however the graph Laplacian and its higher-order versions (the Hodge Laplacians) can only process separately nodes, edge signals and topological signals of higher dimension. The Topological Dirac operator [1] allows cross-talk of the topological signals, on nodes, edges, triangles and so on, encoded in the topological spinor, and is able to jointly treat and process them. The Topological Dirac operator is currently attracting growing attention in AI and Network Science applications. In this talk we will provide an overview of the theory beyond the Topological Dirac operator and their applications in AI focusing in particular on Dirac signal processing [2] and its physics-inspired generalizations [3].
[1] Bianconi, G., 2021. The topological Dirac equation of networks and simplicial complexes. Journal of Physics: Complexity, 2(3), p.035022.
[2] Calmon, L., Schaub, M.T. and Bianconi, G., 2023. Dirac signal processing of higher-order topological signals. New Journal of Physics, 25(9), p.093013.
[3] Wang, R., Tian Y., Lio, P. and Bianconi,, 2024. Dirac-Equation Signal Processing: Physics Boosts Topological Machine Learning. arXiv preprint arXiv:2412.05132.
About the speaker
Ginestra Bianconi is a mathematical physicist with expertise in network theory. She is a Professor of Applied Mathematics in the School of Mathematical Sciences at Queen Mary University of London and a member of the European Academy of Sciences. She currently serves as the Chief Editor of JPhys Complexity and is also an editor for PLOS ONE and Scientific Reports. Her honors include being named an APS Fellow, a Network Science Fellow, and holding the Franqui Chair for 2023.
Meeting information
https://zoom.us/j/95485471819?pwd=h2xoNm0fbo90glcmX0F4pRoEdM2YoZ.1
Zoom Meeting ID: 954 8547 1819, Passcode: 447968