Universality in Deep Neural Networks: An approach via the Lindeberg exchange principle
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866910189317259264 |
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| author | Giovagnini, Filippo Kotitsas, Sotirios Romito, Marco |
| author_facet | Giovagnini, Filippo Kotitsas, Sotirios Romito, Marco |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_02771 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Universality in Deep Neural Networks: An approach via the Lindeberg exchange principle Giovagnini, Filippo Kotitsas, Sotirios Romito, Marco Probability Machine Learning 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. |
| title | Universality in Deep Neural Networks: An approach via the Lindeberg exchange principle |
| topic | Probability Machine Learning |
| url | https://arxiv.org/abs/2605.02771 |