# Uniform-in-time concentration in two-layer neural networks via transportation inequalities

arXiv: https://arxiv.org/abs/2603.01842 · HTML: https://mlsanity.com/paper/2603.01842/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 2 Mar 2026.

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

- [Propagation of Chaos in Contextual Flow Maps](https://mlsanity.com/paper/2605.16747/) (2026)
- [Fluctuations of Nonlinear Observables in Mean Field Neural Network Training](https://mlsanity.com/paper/2610.09768/) (2026)

## Abstract (arXiv)

We quantify, uniformly over time and with high probability, the discrepancy between the predictions of a two-layer neural network trained by stochastic gradient descent (SGD) and their mean-field limit, for quadratic loss and ridge regularization. As a key ingredient, we establish T p transportation inequalities (p ∈ 1, 2) for the law of the SGD parameters, with explicit constants independent of the iteration index. We then prove uniform-in-time concentration of the empirical parameter measure around its mean-field limit in the Wasserstein distance W 1 , and we translate these bounds into prediction-error estimates against a fixed test function Phi. We also derive analogous concentration bounds in the sliced-Wasserstein distance SW 1 , leading to dimension-free rates.