Researchers have established central and non-central limit theorems for functionals derived from infinitely-wide random neural networks on a d-dimensional sphere. The study reveals that the asymptotic behavior of these functionals, as network depth increases, is critically dependent on the fixed points of the covariance function. This dependency leads to three distinct limiting regimes: convergence to a functional of a limiting Gaussian field, convergence to a Gaussian distribution, or convergence to a distribution within the Qth Wiener chaos. AI
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IMPACT Provides theoretical insights into the behavior of deep neural networks, potentially informing future architectural designs.
RANK_REASON Academic paper on theoretical aspects of random neural networks.
