Barron Function

Barron functions, a class of high-dimensional functions representable by shallow neural networks, are a focus of current research due to their potential to overcome the curse of dimensionality in machine learning. Research efforts concentrate on developing efficient algorithms, such as inverse scale space flows, for learning sparse representations of these functions and exploring their approximation using architectures like echo state networks and sums of determinants, particularly for applications in quantum physics. These studies aim to establish theoretical guarantees for approximation and generalization capabilities, leading to improved understanding and application of Barron functions in high-dimensional problems, including classification and function approximation.