Date and time: Tuesday 16 December 2025, 10:15-11:00 CET
Speaker: Prof. Anthea Monod, Imperial College
Title: Topological Graph Kernels from Tropical Geometry
Where: Mathematics Department KTH, room 3418, KTH Campus
Host: Francesca Tombari, tombari@kth.se
Bio: Anthea Monod is a Reader (Associate Professor) in Mathematics and Machine Learning at the Department of Mathematics at Imperial College London. Her research uses theory from pure mathematics (algebraic geometry and algebraic topology) to develop computational, statistical, and machine learning methods for data that have complex topological structures.
One of her significant research areas is to advance the current understanding of deep learning and modern AI technology, which is supported by a £10M UK government-funded EPSRC Mathematical and Computational Foundations of Artificial Intelligence Hub [EP/Y028872/1]. As a Co-Director of this AI Hub, she leads in scientific and operational strategy to harness theory from algebra, geometry, and topology to understand how AI systems work and build the next generation of efficient and reliable AI.
Abstract: We introduce a new class of graph kernels for machine learning with metric graphs based on tropical geometry and the graph topologies. Unlike traditional graph kernels that are defined by graph combinatorics (nodes, edges, subgraphs), our approach considers only the geometry and topology of the underlying metric space. A key property of our construction is its invariance under edge subdivision, making the kernels intrinsically well-suited for comparing graphs that represent different underlying spaces.
Our kernels are efficient to compute and depend only on the graph genus rather than the size. In label-free settings, our kernels outperforms existing methods, which we showcase on synthetic, benchmarking, and real-world road network data. Joint work with Yueqi Cao (KTH Sweden).
