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.
By Mehryar Mohri, Yutao Zhong
arXiv:2607. 07513v1 Announce Type: new Abstract: Self-supervised learning matches supervised accuracy from a fraction of the labels, but the labeled-sample efficiency behind this has lacked a theoretical explanation.
By Adam M. Oberman
The paper develops a statistical theory for minimum‑norm interpolation in high‑dimensional regression, showing how regularization geometry and signal sparsity affect generalization. It identifies regimes where sparsity‑promoting regularizers yield exact interpolation that is far more accurate than approximate fitting, and proves a zero–one generalization law for strongly overparameterized noiseless problems. The authors also characterize training and generalization errors along ρ‑regularization paths when feature dimension and sample size are proportional, demonstrating that generalization improves with more sparsity‑promoting norms and sparser targets, and that small changes in regularization strength can cause large shifts in generalization.
whyItMatters":"The work provides a quantitative understanding of delayed generalization (grokking) and reveals a statistical instability in minimum‑norm interpolation, offering insights that could guide the design of regularizers for better generalization in overparameterized models."
By Gil Kur, Ileana Rugina, Cl\'ementine Carla Juliette Domin\'e, Marco Mondelli
arXiv:2502. 05684v5 Announce Type: replace-cross Abstract: How can we effectively remove or ``unlearn'' undesirable information, such as specific features or the influence of individual data points, from a learning outcome while minimizing utility loss and ensuring rigorous guarantees?
By Shizhou Xu, Thomas Strohmer
arXiv:2608. 09707v1 Announce Type: cross Abstract: Embedding trained neural networks as surrogates within optimisation problems is an established practice in operations research.
By Yu Liu, Jan Kronqvist, Fabricio Oliveira
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