When Does Perturbation Consistency Add Information Beyond Softmax Confidence? Theory and Evidence for the Decision Consistency Framework
Perturbation consistency scores judge whether a prediction survives small input changes. The Decision Consistency Framework (DCF) scores each image by label stability (LS) and confidence deviation (CD) under six mild operators, combines them into a consistency score (CS), and summarises a model by the gap between accuracy and mean consistency (CAG). We ask when these scores carry information that the clean softmax output lacks. Across 201 evaluations with three seeds per configuration, CS detected misclassifications on clean data less well than the maximum softmax probability (MSP) in every model family. For frozen CNNs, the deficit was 0.057 in area under the ROC curve (AUROC; 95% CI 0.043 to 0.073), at 8 to 15 times the compute. A label flip requires the logit margin to be at most the square root of two times the logit displacement, and at a fixed margin, the displacement predicted errors at AUROC 0.515. The same inequality gives a label-free split-conformal no-flip certificate, never violated in 84 runs. Consistency did add information where confidence is misled: under noise corruptions of CIFAR-10-C, it beat the margin, and under projected gradient attacks, it separated clean from attacked inputs with AUROC 0.83 against 0.37 for MSP at a budget of 2/255, as pre-specified. The gain under noise did not transfer to unseen shift families. The large negative CAG on OCTMNIST persists under full fine-tuning and in-domain training and is partly a class-prior effect: correcting the prior recovers about 40% of the gap.