Do Functionally Equivalent Representations Fail Alike? Task-Consistent Gauges under Partial Availability

Intermediate representations are often only partly available in split, adaptive, or progressive inference. If two coordinate systems implement exactly the same complete predictor, should they also fail alike when some representation blocks are missing? We show that they need not: function-preserving rotations can leave every complete prediction unchanged yet produce sharply different partial predictions. Under fixed-cardinality availability, partial logits and pairwise class margins are unbiased estimates of their complete counterparts. Their variance separates how much representation remains from how task-relevant evidence is distributed across coordinates. This explains why reducing global logit-estimation variance can still hurt classification. The nearby margins that determine the decision may become less stable. We therefore introduce BoundaryGauge, which preserves the complete predictor while selecting coordinates that stabilize those margins, without ground-truth labels or training on partial masks. At 50% availability, the same fixed Hadamard gauge changes accuracy by −13.5 points for one ResNet50 predictor but +24.9 points for another. BoundaryGauge adapts successfully to both. Across four architectures and 48 frozen-predictor cases, each optimized gauge improves mean, P05, and exact worst-subset accuracy across all three tested availability levels. Partial robustness therefore depends not only on the complete function, but on how its decision geometry is distributed across coordinates.