Establishes a central limit theorem for averaged Adam with n^{-1/2} convergence rate to an attracting zero and covariance determined by the algorithm at the attractor.
Mathematical Introduction to Deep Learning: Methods, Implementations, and Theory
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ADANNs design ANN architectures and initializations to mimic classical numerical algorithms for parametric PDE operator approximation and report significant outperformance over existing methods in numerical tests.
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Central limit theorem for the averaged Adam optimizer
Establishes a central limit theorem for averaged Adam with n^{-1/2} convergence rate to an attracting zero and covariance determined by the algorithm at the attractor.
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Algorithmically Designed Artificial Neural Networks (ADANNs): Higher order deep operator learning for parametric partial differential equations
ADANNs design ANN architectures and initializations to mimic classical numerical algorithms for parametric PDE operator approximation and report significant outperformance over existing methods in numerical tests.