Fisher Rank Inflation: A Spectral Signature of Memorization under Label Noise

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Original abstract

Deep networks trained with label noise often learn clean structure before memorizing corrupted labels. We show that this transition leaves a spectral signature in the centered scatter of per-example last-layer gradients. Its effective rank transiently expands during memorization and contracts after corrupted labels are fit. We call this phenomenon Fisher Rank Inflation. Corrupted labels increase effective rank by injecting spectral mass into low-energy or previously unused eigendirections, increasing the entropy of the gradient spectrum. We derive a first-order leave-one-out attribution formula, identify conditions under which corrupted examples contribute more strongly than clean examples, and explain why attribution signals weaken once the normalized Fisher-gradient spectrum stabilizes. We test these predictions on CIFAR-10, CIFAR-100, and CIFAR-10N using SmallCNN, ResNet18, and Vision Transformers. Across settings, Fisher effective rank exhibits a consistent inflation--collapse trajectory aligned with memorization. At peak-rank checkpoints, corrupted examples are enriched among the highest rank-contributing samples, with top-100 noisy fractions from \(69.2\%\) to \(96.2\%\) across five-seed synthetic-corruption experiments and \(94.4\%\pm1.9\%\) on CIFAR-10N. First-order spectral attribution closely matches exact leave-one-out contributions in convolutional models and remains enriched in the Vision Transformer. Peak effective rank increases monotonically with corruption severity, from \(28.88\pm1.95\) under clean training to \(97.09\pm1.78\) at \(60\%\) corruption. In several settings, the retrospectively identified onset of rank inflation precedes observable test degradation. These results establish Fisher Rank Inflation as a spectral signature connecting corrupted-example enrichment, corruption severity, and the transition from structure learning to memorization.

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