Homotopy Path

Homotopy path methods explore the continuous deformation of paths between two points, focusing on classifying paths based on their topological equivalence rather than their exact geometry. Current research emphasizes applications in robotics (path planning for robots and swarms, considering obstacles and topological constraints), and optimization problems (e.g., finding optimal solutions in discrete spaces like those encountered in large language models). These techniques offer improved efficiency and robustness in solving complex pathfinding and optimization problems, impacting fields ranging from automated navigation to adversarial machine learning.