Random feature models including neural networks achieve universal approximation

Researchers have introduced a new framework for random feature learning, extending it to Banach spaces. This approach allows for significant reductions in computational complexity by only training a linear readout after random initialization of feature maps. The study proves a universal approximation result within the corresponding Bochner space and derives approximation rates, offering an explicit algorithm for learning elements in the Banach space. This framework encompasses random trigonometric regression and random neural networks, extending their universal approximation properties to various function spaces, including those over non-compact domains. AI

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IMPACT Extends theoretical understanding of random neural networks and their approximation capabilities.

RANK_REASON This is a research paper detailing a new theoretical framework and algorithm for random feature models and random neural networks.

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• arXiv
• Banach space
• random feature learning
• random neural networks
• Bochner space
• trigonometric regression
• Fourier regression
• feedforward neural networks
• function spaces
• weighted spaces
• L^p-spaces
• Sobolev spaces
• Philipp Schmocker

• paper
• other