Introduction to 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 tutorial we will first summarize introductory ideas and tools of tropical geometry and its underlying max-plus 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. The expected background of the audience includes students, researchers, practitioners, and university faculty from the general areas of image/video& signal processing and machine learning.