Universality in Deep Neural Networks: An approach via the Lindeberg exchange principle
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Abstract (arXiv)
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.
Key facts. Cited by 2 papers in the map (data through 14 Oct 2026). Builds on 4 of its 23 references that are in the map. First posted on arXiv 4 May 2026.
Builds on
4 of 23 references.
References · 4
- 2019Scaling Limits of Wide Neural Networks with Weight Sharing: Gaussian Process Behavior, Gradient Independence, and Neural Tangent Kernel Derivationcited by 149
- 2023Wide Deep Neural Networks with Gaussian Weights are Very Close to Gaussian Processescited by 13
- 2025Entropic bounds for conditionally Gaussian vectors and applications to neural networkscited by 7
- 2025Finite-Dimensional Gaussian Approximation for Deep Neural Networks: Universality in Random Weightscited by 5
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Citing papers per year: 2026: 2.
2 papers.