发表机构
Data Science Institute & Department of Civil, Construction & Environmental Engineering; University of Delaware（数据科学研究所与土木、建筑与环境工程系; 特拉华大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对序数分类中神经网络预测向中心类别对冲的问题，提出自适应边际序数损失（AMOL），通过乘性权重惩罚中心类别预测，在四个基准上取得最佳或并列最佳QWK，并引入中心对冲率（CHR）作为诊断指标。
AI 中文摘要
标准交叉熵损失会导致在序数分类任务上训练的神经网络将预测对冲至中心类别，我们将这种失败模式称为“中心类别对冲”。发生这种情况是因为预测中间类别能最小化期望对称损失，使其成为无论真实标签如何都阻力最小的路径。现有的序数损失解决了相关问题，如大误差惩罚和秩一致性，但没有一种直接根据真实标签相对于序数中心的位置来抑制中心类别对冲。我们提出了自适应边际序数损失（AMOL），这是一种应用于每类损失项的乘性权重，形式为 $m(k,y) = 1 + \alpha \cdot (1 - |k-c|/c) \cdot (|y-c|/c)$，其中 $c$ 是中心类别，$k$ 是候选类别，$y$ 是真实标签。该权重编码了一个联合条件：仅当候选类别接近中心且真实标签远离中心时权重较大，否则退化为标准行为。我们进一步引入了中心对冲率（CHR）作为直接量化这种失败模式的诊断指标。在四个序数分类基准和五个随机种子上，与交叉熵、OLL 和 SORD 基线相比，AMOL 在所有四个数据集上取得了最佳或并列最佳的二次加权卡帕（QWK）。一种非对称变体（AMOL-asym）在 Abalone 数据集上完全消除了中心类别对冲（所有五个种子的 $\text{CHR} = 0.000 \pm 0.000$，每次运行约 $n \approx 266$ 个极端类别测试样本），而标准交叉熵的 $\text{CHR} = 0.074 \pm 0.005$。
英文摘要
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 $m(k,y) = 1 + α\cdot (1 - |k-c|/c) \cdot (|y-c|/c)$, 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.
