Universality in Deep Neural Networks: An approach via the Lindeberg exchange principle
Filippo Giovagnini, Sotirios Kotitsas, Marco Romito
5/4/2026
math.PRcs.LGstat.ML
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Abstract
We consider the infinite-width limit of a fully connected deep neural network with general weights, and we prove quantitative general bounds on the $2$-Wasserstein distance between the network and its infinite-width Gaussian limit, under appropriate regularity assumptions on the activation function. Our main tool is a Lindeberg principle for Deep Neural Networks, which we use to successively replace the weights on each layer by Gaussian random variables.
