Barron Space

Barron spaces are function spaces particularly relevant for understanding the approximation capabilities of shallow neural networks, with current research focusing on their properties in various contexts, including graph convolutional networks and the solutions of partial differential equations. A key area of investigation involves establishing embeddings between different Barron spaces defined by varying activation functions and smoothness parameters, aiming to clarify their relationships and approximation power. This research contributes to a deeper understanding of neural network expressivity and generalization, with implications for both theoretical machine learning and the efficient solution of complex scientific problems.