Functionals of infinite-width random neural networks on the sphere exhibit phase transitions in fluctuations as depth grows, converging to a limiting Gaussian field functional, a Gaussian, or a Qth Wiener chaos distribution depending on covariance fixed points.
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Extends Stein's method to symmetric matrix normal distributions with a Stein characterization, semigroup solution, and Wasserstein bound for Wishart approximation.
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Phase Transitions in the Fluctuations of Functionals of Random Neural Networks
Functionals of infinite-width random neural networks on the sphere exhibit phase transitions in fluctuations as depth grows, converging to a limiting Gaussian field functional, a Gaussian, or a Qth Wiener chaos distribution depending on covariance fixed points.
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Stein's method for the symmetric matrix normal distribution with an application to the approximation of the Wishart law
Extends Stein's method to symmetric matrix normal distributions with a Stein characterization, semigroup solution, and Wasserstein bound for Wishart approximation.