Learning to Space and Score Ordinal Labels Across Vision and Touch

Ordinal labels specify class order, but not the distances between classes. Yet ordinal soft supervision must choose both how target probability is distributed across neighboring classes and how the resulting ordered distributions are scored. We make these two choices explicit. First, we formulate cumulative ordinal training as proper scoring over nested threshold events, connecting the commonly used squared cumulative objective (${\mathrm{EMD}}^2$/RPS-type scoring) to cumulative Brier scoring and CDF-CE to cumulative logarithmic scoring. We prove cumulative strict propriety, derive their distinct cross-boundary gradient scaling, and show that soft and hard cumulative targets induce different probability-matching geometries. Second, we replace fixed equal spacing with a lightweight learnable supervision geometry in which positive gaps define strictly ordered, fixed-span class positions $z$, optionally with a single global softness parameter $\tau$. Across five benchmarks spanning vision and touch, Gaussian soft targets improve the mean task-primary metric over hard targets for every dataset under CE, ${\mathrm{EMD}}^2$, and CDF-CE. Under Gaussian supervision, CDF-CE improves over ${\mathrm{EMD}}^2$ on all five tasks, whereas the ordering reverses on four of five under hard targets. Learning the target geometry further improves AADB, HCI, and PHAC-2, while the physically grounded equal spacing of Whisker remains preferable. Across the controlled target-and-scoring variants, a fixed or adaptive CDF-CE model achieves the best mean primary result on every benchmark. Together, these results show that ordinal soft supervision depends jointly on target construction and scoring.