A Survey on Data-Dependent Worst-Case Generalization Bounds
Deep neural networks generalize well despite being heavily overparameterized, in apparent contradiction with classical learning theory based on uniform convergence over fixed hypothesis spaces. Uniform bounds over the entire parameter space are vacuous in this regime, and recent work has shown that non-vacuous guarantees can be recovered by restricting attention to the part of parameter space that the algorithm actually visits. This survey paper organizes this line of work around three steps: extending PAC-Bayesian theory to random, data-dependent hypothesis sets (arXiv:2404.17442); refining the complexity term with geometric and topological descriptors of the optimization trajectory, inc...
| Authors | Hubert Leroux, Jean Marcus, Julien Roger |
|---|---|
| Primary category | stat.ML |
| Published | 13 May 2026 |
| Last updated at source | 13 May 2026 |
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