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

arXiv: https://arxiv.org/abs/2605.02771 · HTML: https://mlsanity.com/paper/2605.02771/

## 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 (most cited first, 4 of 4)

- [Scaling Limits of Wide Neural Networks with Weight Sharing: Gaussian Process Behavior, Gradient Independence, and Neural Tangent Kernel Derivation](https://mlsanity.com/paper/1902.04760/) (2019)
- [Wide Deep Neural Networks with Gaussian Weights are Very Close to Gaussian Processes](https://mlsanity.com/paper/2312.11737/) (2023)
- [Entropic bounds for conditionally Gaussian vectors and applications to neural networks](https://mlsanity.com/paper/2504.08335/) (2025)
- [Finite-Dimensional Gaussian Approximation for Deep Neural Networks: Universality in Random Weights](https://mlsanity.com/paper/2507.12686/) (2025)

## Built on by (most cited first, 2 of 2)

- [Quantitative Gaussian-Process limits of Tensor Programs](https://mlsanity.com/paper/2607.06290/) (2026)
- [Geometric Dyson Brownian Motions and the Free Log-Normal Limit for a Non-Square Gaussian Matrix Product](https://mlsanity.com/paper/2606.30831/) (2026)

## 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.