Polish Space

Research in "Polish spaces" focuses on extending mathematical tools and algorithms, particularly from machine learning and optimization, to handle complex, infinite-dimensional data structures. Current efforts center on developing neural network architectures capable of approximating functions on these spaces, employing methods like stochastic Halpern iteration and Fisher-Rao gradient flows for optimization tasks. This work is significant because it enables the application of powerful machine learning techniques to a broader range of problems involving functional data and complex geometric structures, with applications in areas such as reinforcement learning and graph embedding.