Paper

How abundant are good interpolators?

arXiv:2606.06469v1 Announce Type: cross Abstract: Let $S$ be the set of unit norm linear classifiers $\theta \in \mathbb{R}^d$ which correctly classify every point of a labeled dataset $(X_i,y_i)_{i=1}^n$, $X_i \in \mathbb{R}^d$, $y_i \in \{-1,+1\}$, with a possibly negative margin $\kappa$ fixed in advance. Under two natural data-generating distributions of the $(X,y)$ pairs -- a Gaussian mixture model and a logistic model with Gaussian features -- and in the proportional regime $n/d \to \alpha$ with small enough $\alpha$, we establish a large deviation principle on the event that a point $\…

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