Depth Separation

Depth separation in neural networks investigates the fundamental advantage of deeper architectures over shallower ones in representing and learning complex functions. Current research focuses on understanding this advantage through theoretical analyses of sample complexity and approximation capabilities, often employing ReLU networks and exploring the impact of weight constraints and architectural modifications like intra-layer connections. These studies aim to clarify the role of depth versus width in network expressivity and optimization efficiency, with implications for both theoretical understanding of deep learning and the design of more efficient and effective neural network architectures for various applications. The ultimate goal is to provide a rigorous theoretical foundation for the empirical success of deep learning.