New theory explains shallow neural network approximation in mixed Sobolev spaces

Researchers have developed a new theoretical framework for understanding how shallow neural networks approximate functions within mixed Sobolev spaces. This framework establishes an activation-independent Fourier-block principle, which dictates that the approximation rate is dependent on the target function's mixed smoothness and the activation function's univariate approximation order. The study also introduces a structured univariate approximation condition to verify this principle for specific activation functions like ReLU^k, ELU, and cosine, providing insights into their optimal approximation exponents. AI

IMPACT Provides a theoretical foundation for understanding the approximation capabilities of shallow neural networks, potentially guiding future model design.

RANK_REASON The cluster contains a new academic paper detailing theoretical advancements in neural network approximation. [lever_c_demoted from research: ic=1 ai=1.0]

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• arXiv
• cosine
• ELU
• Fourier-block principle
• mixed Sobolev spaces
• shallow neural network

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