Hilbert Schmidt

Hilbert-Schmidt methods focus on measuring distances and similarities between objects residing in Hilbert spaces, infinite-dimensional vector spaces with an inner product, finding applications in diverse fields like machine learning and quantum computing. Current research emphasizes developing efficient algorithms for computing Hilbert-Schmidt distances, particularly between probability distributions and operators, often employing techniques like kernel methods, Riemannian geometry, and neural networks (e.g., Deep Operator Networks). These advancements enable improved performance in tasks such as distribution comparison, operator learning, and dimensionality reduction, impacting areas ranging from data analysis to quantum algorithms.