Same Fit, Different Damage: Learning Order and Functional Dependence in Noisy-Label Memorization

cause very different levels of semantic damage. We show that the difference is closely related to when individual errors are learned and how their final wrong predictions are functionally realized. To study this phenomenon, we introduce relational consistency, which describes how strongly an incorrect target is supported by surrounding training examples. Using a controlled intervention that preserves the corrupted examples and class transition statistics while changing only the assignment of wrong targets, we find that highly compatible errors are learned 27.64 epochs earlier on average than random matched errors under strong augmentation. Mid-training gradient alignment further predicts this ordering. Importantly, strong augmentation does not prevent eventual memorization. When both models have fitted 98% of the incorrect labels, the strongly augmented model still achieves 23.1 percentage points higher linear-probe accuracy for the true labels. Additional controls show that errors learned later preserve stronger true-label structure at comparable levels of noise fitting. Suffix rollback experiments further reveal that these later errors depend more strongly on deep network changes formed around their learning events, and removing these changes often restores the true prediction. These patterns persist across datasets, architectures, noise rates, and human annotation noise. Our results reveal that near-identical levels of noise fitting can coexist with substantially different semantic costs, systematically linked to learning order and the functional realization of individual errors.