Structured Proper Loss Geometries for Multiclass Classification: Theory and Controlled Empirical Evaluation

arXiv:2606.29471v1 Announce Type: new Abstract: Strictly proper scoring rules identify the true conditional class distribution at population level, but their curvature can alter optimization and finite-sample behavior. We study three multiclass objectives: a class-aware quadratic Bregman score (CAPM), a strongly convex generator with constrained log-cosh ridges (HPG), and an HPG objective with an annealed probability-margin penalty (APMS). CAPM is treated as a structured instance of established quadratic scoring-rule theory. We derive conditional-regret, curvature, range, and logit-gradient bo

Source: arXiv cs.LG — read the full report at the original publisher.

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