Polynomial System

Polynomial systems are mathematical structures representing sets of polynomial equations, with research focusing on efficiently finding their solutions and leveraging them in various applications. Current research emphasizes developing novel algorithms for solving polynomial systems, particularly within machine learning contexts, including the design of polynomial neural networks, polynomial-augmented neural networks, and the use of polynomials as basis functions in other architectures. These advancements are significant because efficient polynomial system solving underpins progress in diverse fields such as robotics, computer vision, and machine learning, enabling more robust and accurate models for complex tasks.