New research quantifies theory-to-practice gap in neural networks and operators

Researchers have analyzed the sampling complexity for learning with ReLU neural networks and neural operators, deriving upper bounds on convergence rates based on the number of samples. This work establishes a unified treatment of the "theory-to-practice gap" in an L^p setting, improving existing bounds and extending the concept to infinite-dimensional operator learning. The findings are applicable to various neural operator architectures, including Deep Operator Networks and Fourier neural operators, indicating convergence rates are bounded by orders of 1/p. AI

IMPACT Provides theoretical insights into the limitations of learning with neural networks and operators, potentially guiding future research and development.

RANK_REASON Academic paper detailing theoretical findings on neural networks and neural operators. [lever_c_demoted from research: ic=1 ai=1.0]

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• Deep Operator Networks
• Fourier neural operator
• Margaret Trautner
• neural operators
• ReLU neural networks

• paper
• other

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