# Improved generalization bounds for binary linear classification via isoperimetry

arXiv: https://arxiv.org/abs/2505.16713 · HTML: https://mlsanity.com/paper/2505.16713/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 10 of its 47 references that are in the map.
- First posted on arXiv 22 May 2025.

## Builds on (most cited first, 10 of 10)

- [A modern maximum-likelihood theory for high-dimensional logistic regression](https://mlsanity.com/paper/1803.06964/) (2018)
- [The phase transition for the existence of the maximum likelihood estimate in high-dimensional logistic regression](https://mlsanity.com/paper/1804.09753/) (2018)
- [A Precise High-Dimensional Asymptotic Theory for Boosting and Minimum-ℓ1-Norm Interpolated Classifiers](https://mlsanity.com/paper/2002.01586/) (2020)
- [The Impact of Regularization on High-dimensional Logistic Regression](https://mlsanity.com/paper/1906.03761/) (2019)
- [The generalization error of max-margin linear classifiers: Benign overfitting and high dimensional asymptotics in the overparametrized regime](https://mlsanity.com/paper/1911.01544/) (2019)
- [The Likelihood Ratio Test in High-Dimensional Logistic Regression Is Asymptotically a Rescaled Chi-Square](https://mlsanity.com/paper/1706.01191/) (2017)
- [On the sample complexity of parameter estimation in logistic regression with normal design](https://mlsanity.com/paper/2307.04191/) (2023)
- [A Slightly Improved Bound for the KLS Constant](https://mlsanity.com/paper/2208.11644/) (2022)
- [The Kannan-Lov'asz-Simonovits Conjecture](https://mlsanity.com/paper/1807.03465/) (2018)
- [Dimension-free uniform concentration bound for logistic regression](https://mlsanity.com/paper/2405.18055/) (2024)

## Abstract (arXiv)

We examine the concentration of uniform generalization errors around their expectation in binary linear classification problems via an isoperimetric argument. In particular, we establish Poincar'e and log-Sobolev inequalities for the joint distribution of the output labels and the label-weighted input vectors, which we apply to derive concentration bounds. The derived results improve upon existing bounds obtained from general unbounded empirical processes, as well as that tailored specifically to logistic regression. In asymptotic analysis, we also show that almost sure convergence of uniform generalization errors to their expectation occurs in very broad settings, such as proportionally high-dimensional regimes. Using this convergence, we establish uniform laws of large numbers under dimension-free conditions.