Abstract
While machine learning (ML) architectures have evolved rapidly to account for complex data, loss functions like cross-entropy remain mostly structure-agnostic in many real-world applications. However, the "class-symmetric" nature of these standard losses fundamentally limits the ability of ML models to exploit structural relationships between classes, particularly when facing structured noise. We propose Conveyance, a new classification approach and associated loss function tailored to structured class spaces. It allows users to encode graph-like relations between classes without having to define complex joint distributions or manually tune utility matrices. Technically, our loss function operates by maximizing two separate margins over distinct class partitions, while preserving formal properties such as monotonicity and partial convexity. We demonstrate the versatility and effectiveness of our method by applying it to hierarchical classification, ordinal regression, and multiple instance learning. Across these tasks, Conveyance either matches or exceeds the performance of specialized baselines, thereby offering a unified solution for structured class spaces.
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Apr 30, 2026cs.LG
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May 7, 2026cs.LG
Standard cross-entropy is the default classification loss across virtually all of machine learning, yet it treats all misclassifications equally, ignoring the semantic distances that a class hierarchy encodes. We propose Hierarchy-Aware Cross-Entropy (HACE), a drop-in replacement for standard cross-entropy that incorporates a known class hierarchy directly into the loss. HACE combines two components: prediction aggregation, which propagates the model's probability mass upward through the class hierarchy to ensure that parent nodes accumulate the confidence of their children; and ancestral label smoothing, which distributes the ground-truth signal along the path from the true class to the root. We evaluate HACE on CIFAR-100, FGVC Aircraft, and NABirds in two regimes: end-to-end training across six architectures spanning convolutional and attention-based designs, and linear probing on frozen DINOv2-Large features. In end-to-end training, HACE improves accuracy over standard cross-entropy in 15 out of 18 architecture--dataset pairs, with a mean gain of 4.66%. In linear probing on frozen DINOv2-Large features, HACE outperforms all competing methods on all three datasets, with a mean improvement of 2.18% over the next best baseline.
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Jun 28, 2026cs.LG
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 bounds for CAPM and HPG, and prove exact penalty-range and conditional-target displacement bounds for APMS. Controlled five-seed experiments use Digits, Wisconsin breast cancer, and synthetic confusion and long-tail problems under clean labels, symmetric and pair-flip corruption, class imbalance, calibration evaluation, input corruption, and first-order adversarial perturbations. The candidates are close to cross-entropy on clean data and show descriptive gains in some noisy-label cells, but the five-seed comparisons are interpreted descriptively rather than as significance evidence. The selected noisy-label baselines perform better on Digits with 40% symmetric label noise, and explicit prior-adjustment methods perform better in the 30:1 synthetic long-tail experiment. Ablations do not show a consistent benefit from the candidate-specific graph, ridge, or margin components. The mathematical analysis establishes the stated properties, and the experiments delimit the empirical evidence; together they do not support a claim of general superiority.
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