Universality in Deep Neural Networks: An approach via the Lindeberg exchange principle

Filippo Giovagnini; Sotirios Kotitsas; Marco Romito

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arXiv · 2605.02771

Universality in Deep Neural Networks: An approach via the Lindeberg exchange principle

Filippo Giovagnini·Sotirios Kotitsas·Marco Romito

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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.

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Filippo Giovagnini, Sotirios Kotitsas, Marco Romito. 2026-05-04. Universality in Deep Neural Networks: An approach via the Lindeberg exchange principle. https://arxiv.org/abs/2605.02771

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