Proposes pointwise Riemannian Dimension from feature eigenvalues to derive tighter, representation-aware generalization bounds for deep networks in the nonlinear regime.
Advances in Neural Information Processing Systems , volume=
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Stochastic integer optimization has sample complexity that matches, undercuts, or exceeds the continuous case based on objective structure, with new tight bounds for nonconvex continuous problems.
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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Pointwise Generalization in Deep Neural Networks
Proposes pointwise Riemannian Dimension from feature eigenvalues to derive tighter, representation-aware generalization bounds for deep networks in the nonlinear regime.
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Sample Complexity of Stochastic Optimization with Integer Variables
Stochastic integer optimization has sample complexity that matches, undercuts, or exceeds the continuous case based on objective structure, with new tight bounds for nonconvex continuous problems.
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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.