How abundant are good interpolators?

Large deviation analysis shows most interpolating classifiers share the same generalization performance

A new arXiv preprint establishes a large deviation principle characterizing the generalization performance of interpolating linear classifiers in the overparameterized regime (n/d → α, small α). The key result is a concentration phenomenon: all but an exponentially small fraction of interpolators achieve approximately the same generalization error, determined by a unique rate-function maximizer. Empirically, gradient descent and a natural linear program both outperform this typical interpolator, providing theoretical grounding for benign overfitting in overparameterized models.