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Fisher information and the geometry of memorization in neural networks

NeurIPS 2026 · Label-efficient and robust learning › Noisy labels · approach: Loss correction and noise robustness theory

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Shows that projecting ResNet-20 and small transformer weights onto top Fisher eigenvectors can decouple memorized noisy samples from generalizing structure, with layer-dependent and data-dependent effects, and explains the mechanism with a linear barcode model.

Problem

How Fisher information eigenspectrum separates memorized sample-specific content from generalizing features in neural networks, and when such de-memorization by projection works across layers, data choices, and in-context tasks.

Approach

Project each layer's weights onto the top-k eigenvectors of its exact per-layer Fisher matrix (computed on clean or full training data) to suppress memorized samples while preserving generalization; analyze with participation ratios of single-sample Fishers and a closed-form linear barcode model.

Key results

• In the first layer of ResNet-20 on Gaussian-noise setting, keeping ~45 top Fisher eigenvectors gives near-maximum CIFAR-10 accuracy while memorized Gaussian samples stay around 30%.
• In the in-context regression transformer, projecting the block-2 MLP onto top Fisher subspace improves held-out task performance, closing roughly half the gap to best early-stopped performance, at the cost of memorized-task performance.
• Computing the Fisher on clean data gives cleaner separation than on the full training set; the barcode model predicts risk reduction of tr(Sigma_xi) d/(n-r-d-1), matching simulations.

Surprising findings

• Projecting out memorized-direction components in the MLP can improve held-out in-context task generalization without retraining.
• In the last layer, memorized and clean representations merge so that no selective de-memorization is possible.

Limitations

• Results are on small models (ResNet-20, 3-block transformer) and simple controlled noise; may not transfer to larger models or semantic memorization.
• Ignores cross-layer correlations; full-model analysis uses block-diagonal approximation.
• Projection is non-local in parameter space and requires BatchNorm recalibration after each projection.

Experimental setup

Datasets: CIFAR-10 synthetic Gaussian-image noise synthetic in-context linear regression tasks

Benchmarks: CIFAR-10

Metrics: accuracy participation ratio prediction risk

Baselines: K-FAC Fisher approximation SVD compression random basis projection

Builds on: Fisher-based de-memorization of language models K-FAC Fisher approximation transient in-context learning regression

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