The Price of Robustness: Stable Classifiers Need Overparameterization
The relationship between overparameterization, stability, and generalization remains incompletely understood in the setting of discontinuous classifiers. We address this gap by establishing a generalization bound for finite function classes that improves inversely with class stability, defined as the expected distance to the decision boundary in the input domain (margin). Interpreting class stability as a quantifiable notion of robustness, we derive as a corollary a law of robustness for classification that extends the results of Bubeck and Sellke beyond smoothness assumptions to discontinuous functions. In particular, any interpolating model with $p \approx n$ parameters on $n$ data poin...
| Authors | Jonas von Berg, Adalbert Fono, Massimiliano Datres et al. |
|---|---|
| Primary category | cs.LG |
| Published | 3 March 2026 |
| Last updated at source | 3 March 2026 |
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