# Mean-field Analysis of Generalization Errors

arXiv: https://arxiv.org/abs/2306.11623 · HTML: https://mlsanity.com/paper/2306.11623/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 20 Jun 2023.

## Built on by (most cited first, 5 of 5)

- [Generalization Error of Graph Neural Networks in the Mean-field Regime](https://mlsanity.com/paper/2402.07025/) (2024)
- [Generalization and Robustness of the Tilted Empirical Risk](https://mlsanity.com/paper/2409.19431/) (2024)
- [Which Algorithms Have Tight Generalization Bounds?](https://mlsanity.com/paper/2410.01969/) (2024)
- [Understanding Transfer Learning via Mean-field Analysis](https://mlsanity.com/paper/2410.17128/) (2024)
- [Mean-Field Generalisation Bounds for Learning Controls in Stochastic Environments](https://mlsanity.com/paper/2508.16001/) (2025)

## Abstract (arXiv)

We propose a novel framework for exploring weak and L2 generalization errors of algorithms through the lens of differential calculus on the space of probability measures. Specifically, we consider the KL-regularized empirical risk minimization problem and establish generic conditions under which the generalization error convergence rate, when training on a sample of size n, is O(1/n). In the context of supervised learning with a one-hidden layer neural network in the mean-field regime, these conditions are reflected in suitable integrability and regularity assumptions on the loss and activation functions.