aiqbench analysis
This paper is about loss functions for training classifiers, a core machine learning topic, so it passes the topic gate. It proposes Linear-Core surrogates that aim to combine the differentiability of logistic-style losses with the linear consistency rates of Hinge loss. The reported gains (2.6% over Cross-Entropy on corrupted CIFAR-10, and a 23x speedup over Structured SVMs on sequence tagging) come from the authors' own experiments, so readers should check how they hold up under independent benchmarking.
Linear-Core Surrogates: Smooth Loss Functions with Linear Rates for Classification and Structured Prediction
arXiv:2604.27742v3 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. We introduce Linear-Core (LC) Surrogates, the first family of explicit convex loss functions that provably resolve this tension. By stitching a linear core to a smooth tail, we construct surrogates that are differentiable everywhere ($C^1$, and even $C^2$ under mild conditions) while retaining strict linear $H$-consistency bounds, the strongest known form of consistency guarantee. We establish these linear bounds across three increasingly complex settings: binary classification, multi-class classification, and structured prediction. To our knowledge, this is the first explicit construction to simultaneously achieve smoothness and linear $H$-consistency in any of these settings. Beyond their theoretical appeal, Linear-Core Surrogates offer practical advantages. In multi-class classification, their constant gradient profile near the decision boundary provides natural robustness to instance-dependent label noise, outperforming Cross-Entropy by 2.6% on corrupted CIFAR-10. In structured prediction, their smoothness enables an unbiased stochastic gradient estimator that bypasses the $O(|Y|^2)$ per-step complexity of exact inference, yielding a 23$\times$ speedup over Structured SVMs on large-vocabulary sequence tagging tasks.
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. We introduce Linear-Core (LC) Surrogates, the first family of explicit convex loss functions that provably resolve this tension. By stitching a linear core to a smooth tail, we construct surrogates that are differentiable everywhere ($C^1$, and even $C^2$ under mild conditions) while retaining strict linear $H$-consistency bounds, the strongest known form of consistency guarantee. We establish these linear bounds across three increasingly complex settings: binary classification, multi-class classification, and structured prediction. To our knowledge, this is the first explicit construction to simultaneously achieve smoothness and linear $H$-consistency in any of these settings. Beyond their theoretical appeal, Linear-Core Surrogates offer practical advantages. In multi-class classification, their constant gradient profile near the decision boundary provides natural robustness to instance-dependent label noise, outperforming Cross-Entropy by 2.6% on corrupted CIFAR-10. In structured prediction, their smoothness enables an unbiased stochastic gradient estimator that bypasses the $O(|Y|^2)$ per-step complexity of exact inference, yielding a 23$\times$ speedup over Structured SVMs on large-vocabulary sequence tagging tasks.
Machine Learning (cs.LG); Machine Learning (stat.ML)
arXiv:2604.27742 [cs.LG]
(or arXiv:2604.27742v3 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2604.27742 Focus to learn more arXiv-issued DOI via DataCite
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Full text under the publisher's open licence · 299 words