AI RESEARCH
Linear-Core Surrogates: Smooth Loss Functions with Linear Rates for Classification and Structured Prediction
arXiv CS.LG
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ArXi:2604.27742v1 Announce Type: new The choice of loss function in classification involves a fundamental trade-off: smooth losses (like Cross-Entropy) enable fast optimization rates but yield slow square-root consistency bounds, while piecewise-linear losses (like Hinge) offer fast linear consistency rates but suffer from non-differentiability. We propose Linear-Core (LC) Surrogates, a new family of convex loss functions that resolve this tension by stitching a linear core to a smooth tail.