Tropical Geometric Machine Learning

Every feedforward neural network can be written in tropical geometric terms.  In this talk, I will formally present the connection between deep learning and tropical geometry, first established by Zhang et al (2018).  I will then present some recent results where we exploit the tropical geometric representation of neural networks to numerically study the evolution of their information capacity during training.  One of our contributions is a new Julia library that analyzes neural networks symbolically using their tropical representations (available here).  This is joint work with my students Paul Lezeau, Thomas Walker, Yueqi Cao, and Shiv Bhatia (preprint).