We examine the concentration of uniform generalization errors around their expectation in binary linear classification problems via an isoperimetric argument. In particular, we establish Poincaré 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 concentration bounds are sharp up to moderate multiplicative constants by those under well-balanced labels. 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.
View on arXiv@article{nakakita2025_2505.16713,
title={ Sharp concentration of uniform generalization errors in binary linear classification },
author={ Shogo Nakakita },
journal={arXiv preprint arXiv:2505.16713},
year={ 2025 }
}