Adaptive Margin Ordinal Loss: Penalizing Center-Class Hedging in Ordinal Classification

Researchers proposed the Adaptive Margin Ordinal Loss (AMOL), a multiplicative per-class weighting scheme that suppresses "center-class hedging" in ordinal classification, according to an arXiv paper (arXiv:2609.10752v1). Across four ordinal classification benchmarks and five random seeds, AMOL achieved the best or tied-best Quadratic Weighted Kappa on all four datasets versus cross-entropy, OLL, and SORD baselines, and an asymmetric variant (AMOL-asym) eliminated center-class hedging entirely on the Abalone dataset with a Center-Hedging Rate of 0.000 ± 0.000 across all five seeds (n ≈ 266 extreme-class test samples per run), compared to 0.074 ± 0.005 for standard cross-entropy.

arXiv:2609.10752v1 Announce Type: new Abstract: Standard cross-entropy loss causes neural networks trained on ordinal classification tasks to hedge predictions toward center classes, a failure mode we term \emph{center-class hedging}. This occurs because predicting the middle class minimizes expected symmetric loss, making it the path of least resistance regardless of the true label. Existing ordinal losses address related problems such as large-error penalization and rank consistency, but none directly suppresses center-class hedging as a function of where the true label lies relative to the ordinal center. We propose the Adaptive Margin Ordinal Loss AMOL , a multiplicative weight applied to per-class loss terms of the form $m k,y = 1 + \alpha \cdot 1 - |k-c|/c \cdot |y-c|/c $, where $c$ is the center class, $k$ is the candidate class, and $y$ is the true label. The weight encodes a joint condition: it is large only when the candidate class is near center and the true label is far from center, collapsing to standard behavior otherwise. We further introduce the Center-Hedging Rate CHR as a diagnostic metric that directly quantifies this failure mode. Across four ordinal classification benchmarks and five random seeds, AMOL achieves the best or tied-best Quadratic Weighted Kappa QWK on all four datasets compared to cross-entropy, OLL, and SORD baselines. An asymmetric variant AMOL-asym eliminates center-class hedging entirely on the Abalone dataset $\text{CHR} = 0.000 \pm 0.000$ across all five seeds, $n \approx 266$ extreme-class test samples per run , compared to $0.074 \pm 0.005$ for standard cross-entropy.