The Shapes of Knowledge: Topological and Geometric Methods for Learning on Complex Networks

Speaker: Dr. Claudio Battiloro, Harvard T.H. Chan School of Public Health

Abstract: Current frontiers in machine learning, data science, and, more broadly, artificial intelligence reveal the limits of purely predictive systems and motivate a shift toward decentralized, scalable, and causal systems. Many such systems imply processing and learning on complex networks. These networks are becoming larger and more sophisticated, making them increasingly hard to understand, operate, and design. A promising modern toolbox, loosely known as Topological Deep Learning (TDL), aims to design deep architectures that integrate and synergize ideas from algebraic topology, non-Euclidean geometry, and category theory to address this complexity. In TDL, the basic units of a network are cells, which generalize graph nodes. A cell may represent, for example, a single agent or a group of agents in an agentic AI system, a neuron or a brain region in a neural circuit, or a sensor or sensor type in an environmental monitoring network. Cells can be organized hierarchically and exhibit rich intra- and inter-cell interaction patterns.In this seminar, Dr. Battiloro will (1) present core principles of TDL, (2) show how to reveal sophisticated higher-order hierarchical interactions in data by inferring latent cell complexes describing them, and (3) introduce the concept of cellular sheaves of (relative) causal knowledge, useful to jointly model the causal structure of each cell and communication between cells.

Biography: Dr. Battiloro is a postdoctoral fellow at the Harvard T.H. Chan School of Public Health in the NSAPH group supervised by Prof. Francesca Dominici. He is part of the Harvard Data Science Initiative. He is a former Visiting Associate at the University of Pennsylvania School of Engineering and Applied Science in the AleLab group supervised by Prof. Alejandro Ribeiro. He received a M.Sc. cum laude (and recognized as a top 1.5% student) in Data Science and a Ph.D. cum laude in Information and Communication Technologies, both from Sapienza University of Rome, and both under the supervision of Prof. Paolo Di Lorenzo. Claudio’s research interests include theory and methods for topological signal processing and deep learning, AI for healthy climate adaptation, and distributed stochastic optimization. He has over 40 publications, including papers published in top-tier journals (e.g., IEEE Transactions on Signal Processing, Journal of Machine Learning Research, IEEE Transactions on IoT, and IEEE Transactions on Green Communications and Networking) and conferences (e.g., ICLR, ICML, ICASSP, NeurIPS, and IJCNN). Claudio received different awards, such as the IEEE SPS Italian Chapter Best M.Sc. Thesis Award (2020), the GTTI Best Ph.D. Thesis Award (2024), and the "Elio Di Claudio" Best Ph.D. Thesis Award (2025).

Host: Prof. Cesare Alippi