Training at the edge of stability causes neural network optimizers to converge on fractal attractors whose effective dimension, measured via a new sharpness dimension from the Hessian spectrum, bounds generalization error in a way not captured by prior trace or norm measures.
arXiv preprint arXiv:2507.06775 , year=
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The survey unifies extensions of PAC-Bayesian theory to data-dependent sets, geometric and topological complexity measures of optimization trajectories, and stability replacements for information terms into one template inequality with comparative evaluation.
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Generalization at the Edge of Stability
Training at the edge of stability causes neural network optimizers to converge on fractal attractors whose effective dimension, measured via a new sharpness dimension from the Hessian spectrum, bounds generalization error in a way not captured by prior trace or norm measures.
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A Survey on Data-Dependent Worst-Case Generalization Bounds
The survey unifies extensions of PAC-Bayesian theory to data-dependent sets, geometric and topological complexity measures of optimization trajectories, and stability replacements for information terms into one template inequality with comparative evaluation.