Tropical Geometry

Tropical geometry, a combinatorial variant of algebraic geometry, is increasingly used to analyze and understand the behavior of neural networks, particularly those with piecewise linear activation functions like ReLU. Current research focuses on leveraging tropical geometry's tools to characterize neural network expressivity, analyze decision boundaries, and develop novel algorithms for network simplification and optimization, often employing techniques like tropical polynomial division and Markov chain Monte Carlo sampling. This interdisciplinary approach offers valuable insights into the structure and performance of neural networks, potentially leading to improved model design and more efficient training methods.