arXiv Machine Learning By Mehryar Mohri, Yutao Zhong

Linear-Core Surrogates: Smooth Loss Functions with Linear Rates for Classification and Structured Prediction

Read the original on arXiv Machine Learning →

arXiv:2604. 27742v2 Announce Type: replace Abstract: A fundamental dichotomy in the theory of classification sets smoothness against statistical efficiency: smooth surrogate losses such as the logistic loss enable fast $O(1/T)$ optimization but yield slow square-root $H$-consistency bounds, while piecewise-linear losses like the Hinge loss achieve optimal linear $H$-consistency rates but are non-differentiable.

Machine-generated by The Flow from the publisher's headline and feed description — not written or checked by a human. The full article lives at arXiv Machine Learning.

arXiv Statistics ML
3d ago

Constrained Classification and Policy Learning

The paper investigates the consistency of surrogate loss methods for classification and policy learning when the set of admissible classifiers is constrained, such as by interpretability or fairness requirements. It shows that hinge loss is the only surrogate that preserves consistency when constraints limit only the prediction set, but consistency can fail if constraints also restrict the functional form. The authors derive conditions guaranteeing consistency for hinge-risk-minimizing classifiers and use these results to design efficient hinge-loss-based procedures for monotone classification problems.

By Toru Kitagawa, Shosei Sakaguchi, Aleksey Tetenov
arXiv Machine Learning
Sep 24

Minimal-Norm Univariate Two-Layer ReLU Classification: Exact Solutions and Global Optimality with Skip Connections

The paper investigates minimal‑norm interpolation and λ2‑regularized logistic‑loss minimization for binary classification using univariate two‑layer ReLU networks. It provides exact geometric characterizations of optimal classifiers, showing that unpenalized hidden‑layer biases yield continuous piecewise‑affine functions that tightly follow label switches, while penalized biases produce a unique, sparsest classifier with a single kink per same‑label segment. Adding a free affine skip connection does not change these function‑space solutions but guarantees that every KKT point becomes globally optimal, eliminating suboptimal KKT points that can arise without the skip connection.

By Karolina Drabik, Ben Lewis, Antoni Puch, Etienne Boursier, Piotr Hofman, Matthias Englert, Ranko Lazi\'c