Variation Space

Variation spaces are function spaces used to analyze the representational capacity of neural networks, particularly focusing on how well these networks can approximate complex functions. Current research emphasizes the development of novel variation spaces tailored to specific network architectures (like ReLU networks) and learning objectives (like multi-task learning), often leveraging tools from functional analysis such as Bochner integrals and reproducing kernel Hilbert spaces. This work aims to provide a deeper theoretical understanding of neural network behavior, leading to improved network design, compression techniques, and more efficient training algorithms. The resulting insights have implications for both theoretical machine learning and practical applications involving large-scale neural network training and deployment.