Tropical Geometry and its Applications to Machine Learning

Tropical geometry is a relatively recent field in mathematics and computer science combining elements of algebraic geometry and polyhedral geometry. It has recently emerged successfully in the analysis and extension of several classes of problems and systems in both classical machine learning and deep learning. In this talk we will first summarize a few introductory ideas and tools of tropical geometry and its underlying max-plus arithmetic and matrix algebra. Then, we will focus on how this new set of tools can aid in the analysis, design and understanding of several classes of neural networks and other machine learning systems, including deep neural networks with piecewise-linear activations, morphological neural networks, neural network minimization, and nonlinear regression with piecewise-linear functions. Our coverage will include studying the representation power, training and pruning of these networks and regressors under the lens of tropical geometry and max-plus algebra. More information and related papers can be found in robotics.ntua.gr.

Biography

Petros Maragos received his Ph.D. degree from Georgia Tech, Atlanta, in 1985. Then, he joined the faculty of the Division of Applied Sciences at Harvard University, where he worked for 8 years as professor of EE affiliated with the Harvard Robotics Lab. In 1993 he joined the faculty of the School of ECE at Georgia Tech, affiliated with its Center for Signal & Image Processing. Since 1999, he has been working as professor at the NTUA, where he is currently the director of the Intelligent Robotics & Automation Lab. He has held visiting positions at MIT in 2012, at UPenn in 2016, and at USC in 2023. He is a co-founder and since 2023 the acting director of the Robotics Institute of the Athena RC. His research and teaching interests include computer vision & speech, machine learning, and robotics. He is the recipient of several awards including an NSF Presidential Young Investigator Award, Best Paper awards from IEEE journals and Computer Vision conferences, and the Technical Achievement award from EURASIP. For his research contributions he was elected a Fellow of IEEE in 1995 and a Fellow of EURASIP in 2010. He has served as IEEE Distinguished Lecturer for 2017-2018. Since 2023 he is a Life Fellow of IEEE.