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Noise Stability Optimization for Flat Minima with Tight Rates
April 22, 2024, 4:42 a.m. | Haotian Ju, Dongyue Li, Hongyang R. Zhang
cs.LG updates on arXiv.org arxiv.org
Abstract: We consider minimizing a perturbed function $F(W) = \mathbb{E}_{U}[f(W + U)]$, given a function $f: \mathbb{R}^d \rightarrow \mathbb{R}$ and a random sample $U$ from a distribution $\mathcal{P}$ with mean zero. When $\mathcal{P}$ is the isotropic Gaussian, $F(W)$ is roughly equal to $f(W)$ plus a penalty on the trace of $\nabla^2 f(W)$, scaled by the variance of $\mathcal{P}$. This penalty on the Hessian has the benefit of improving generalization, through PAC-Bayes analysis. It is useful in …
abstract arxiv cs.ds cs.lg distribution equal flat function math.oc mean noise optimization random sample stability stat.ml type
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