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

arXiv: https://arxiv.org/abs/2607.12438 · HTML: https://mlsanity.com/paper/2607.12438/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 37 of its 40 references that are in the map.
- First posted on arXiv 14 Jul 2026.

## Builds on (most cited first, 30 of 37)

- [Neural Tangent Kernel: Convergence and Generalization in Neural Networks](https://mlsanity.com/paper/1806.07572/) (2018)
- [Understanding Black-box Predictions via Influence Functions](https://mlsanity.com/paper/1703.04730/) (2017)
- [Understanding deep learning requires rethinking generalization](https://mlsanity.com/paper/1611.03530/) (2016)
- [On the Spectral Bias of Neural Networks](https://mlsanity.com/paper/1806.08734/) (2018)
- [Co-teaching: Robust Training of Deep Neural Networks with Extremely Noisy Labels](https://mlsanity.com/paper/1804.06872/) (2018)
- [A Closer Look at Memorization in Deep Networks](https://mlsanity.com/paper/1706.05394/) (2017)
- [Reconciling modern machine learning practice and the bias-variance trade-off](https://mlsanity.com/paper/1812.11118/) (2018)
- [Optimizing Neural Networks with Kronecker-factored Approximate Curvature](https://mlsanity.com/paper/1503.05671/) (2015)
- [A Convergence Theory for Deep Learning via Over-Parameterization](https://mlsanity.com/paper/1811.03962/) (2018)
- [Prevalence of Neural Collapse during the terminal phase of deep learning training](https://mlsanity.com/paper/2008.08186/) (2020)
- [DivideMix: Learning with Noisy Labels as Semi-supervised Learning](https://mlsanity.com/paper/2002.07394/) (2020)
- [An Empirical Study of Example Forgetting during Deep Neural Network Learning](https://mlsanity.com/paper/1812.05159/) (2018)
- [Deep Double Descent: Where Bigger Models and More Data Hurt](https://mlsanity.com/paper/1912.02292/) (2019)
- [Making Deep Neural Networks Robust to Label Noise: a Loss Correction Approach](https://mlsanity.com/paper/1609.03683/) (2016)
- [Data Shapley: Equitable Valuation of Data for Machine Learning](https://mlsanity.com/paper/1904.02868/) (2019)
- [Estimating Training Data Influence by Tracing Gradient Descent](https://mlsanity.com/paper/2002.08484/) (2020)
- [Symmetric Cross Entropy for Robust Learning with Noisy Labels](https://mlsanity.com/paper/1908.06112/) (2019)
- [What Neural Networks Memorize and Why: Discovering the Long Tail via Influence Estimation](https://mlsanity.com/paper/2008.03703/) (2020)
- [Does Learning Require Memorization? A Short Tale about a Long Tail](https://mlsanity.com/paper/1906.05271/) (2019)
- [Early-Learning Regularization Prevents Memorization of Noisy Labels](https://mlsanity.com/paper/2007.00151/) (2020)
- [Confident Learning: Estimating Uncertainty in Dataset Labels](https://mlsanity.com/paper/1911.00068/) (2019)
- [How does Disagreement Help Generalization against Label Corruption?](https://mlsanity.com/paper/1901.04215/) (2019)
- [Unsupervised Label Noise Modeling and Loss Correction](https://mlsanity.com/paper/1904.11238/) (2019)
- [Training Deep Neural Networks on Noisy Labels with Bootstrapping](https://mlsanity.com/paper/1412.6596/) (2014)
- [Empirical Analysis of the Hessian of Over-Parametrized Neural Networks](https://mlsanity.com/paper/1706.04454/) (2017)
- [Combating noisy labels by agreement: A joint training method with co-regularization](https://mlsanity.com/paper/2003.02752/) (2020)
- [Identifying Mislabeled Data using the Area Under the Margin Ranking](https://mlsanity.com/paper/2001.10528/) (2020)
- [Influence Functions in Deep Learning Are Fragile](https://mlsanity.com/paper/2006.14651/) (2020)
- [Representer Point Selection for Explaining Deep Neural Networks](https://mlsanity.com/paper/1811.09720/) (2018)
- [CleanNet: Transfer Learning for Scalable Image Classifier Training with Label Noise](https://mlsanity.com/paper/1711.07131/) (2017)

## Abstract (arXiv)

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%±1.9%) 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±1.95) under clean training to (97.09±1.78) 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.