Logarithmic-Free Moment and Generalization Bounds for Uniformly Stable Algorithms

What the math gives to ML

The paper proves a logarithmic-free high-moment inequality for sums of weakly interacting functions of independent examples. Its transferable asset is the explicit separation between cross-example sensitivity beta and single-example fluctuation M, yielding a bound that scales as 16 p beta plus M sqrt(2p/n) for an averaged quantity rather than carrying an additional log n factor. A practical neural-network use is an empirical stability certificate for checkpoint selection, optimizer comparison, and stability regularization. The certificate should be treated as an approximate diagnostic unless the learning decomposition satisfies the theorem's conditional-centering and bounded-difference assumptions.