In the wide-width limit under Gaussian likelihood, the posterior of the network output is identified when the random covariance matrix is positive definite, with mild conditions ensuring invertibility and order-independent sequential limits.
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Quantitative 2-Wasserstein bounds are established between finite-width deep neural networks and their infinite-width Gaussian limits using a Lindeberg principle for successive Gaussian replacement of weights.
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Posterior Bayesian Neural Networks with Dependent Weights
In the wide-width limit under Gaussian likelihood, the posterior of the network output is identified when the random covariance matrix is positive definite, with mild conditions ensuring invertibility and order-independent sequential limits.
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Universality in Deep Neural Networks: An approach via the Lindeberg exchange principle
Quantitative 2-Wasserstein bounds are established between finite-width deep neural networks and their infinite-width Gaussian limits using a Lindeberg principle for successive Gaussian replacement of weights.