---
title: "What Neural Networks Memorize and Why: Discovering the Long"
description: "The authors instead define subsampled versions: models are trained on random subsets of the data… 34 references, cited by 83 papers here."
authors: ["Vitaly Feldman", "Chiyuan Zhang"]
year: 2020
venue: "arXiv:2008.03703"
source: "https://arxiv.org/abs/2008.03703"
doi: "10.48550/arxiv.2008.03703"
arxiv: "2008.03703"
licence: "arXiv — non-exclusive license to distribute"
licence_url: "http://arxiv.org/licenses/nonexclusive-distrib/1.0/"
summary_licence: "Elamur Cosmic License"
canonical: "https://research.elamur.ai/free/en/papers/feldman-2020-neural-networks-memorize-why-discovering/"
---
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# What Neural Networks Memorize and Why: Discovering the Long Tail via Influence Estimation

**Authors:** Vitaly Feldman and [Chiyuan Zhang](https://md.research.elamur.ai/free/en/authors/chiyuan-zhang/) · **Year:** 2020 · **Venue:** arXiv:2008.03703 · **Licence:** [arXiv — non-exclusive license to distribute](http://arxiv.org/licenses/nonexclusive-distrib/1.0/)

**Links:** [Publisher's page](https://arxiv.org/abs/2008.03703) · [PDF](https://arxiv.org/pdf/2008.03703) · [DOI 10.48550/arxiv.2008.03703](https://doi.org/10.48550/arxiv.2008.03703) · [arXiv 2008.03703](https://arxiv.org/abs/2008.03703) · [OpenAlex](https://openalex.org/W3100352836)

**Citations:** 110 citations (OpenAlex, 2026-10-14) · [83](https://md.research.elamur.ai/free/en/papers/feldman-2020-neural-networks-memorize-why-discovering/cited-by/) in our library, of the 149,439 papers whose bibliographies we read

## Summary
Deep networks routinely fit outliers and mislabeled training points. Classical generalization theory treats this as harmful overfitting, so it cannot explain why it happens. Feldman's earlier "long tail theory" argued that memorization is needed for near-optimal accuracy when data contain many rare subpopulations, but it lacked empirical support. This paper tests that theory on MNIST, CIFAR-100 and ImageNet.

Exact leave-one-out memorization and influence scores would need millions of training runs. The authors instead define subsampled versions: models are trained on random subsets of the data, and each example's effect is estimated by comparing models that did or did not see it. This yields estimates for all examples at once from a few thousand runs, and the method works with any model.

On the two larger datasets, many training examples turn out to be strongly memorized. Removing them hurts test accuracy more than removing a random set of equal size. Many test images depend on a single, visually similar training image. These results suggest that limiting memorization, for example through compression or differential privacy, may disproportionately harm under-represented groups.

## Key points
- **Estimator cost:** Exact estimation needs a number of runs that grows with dataset size n (Ω(n/σ²)). The subsampled estimator needs only O(1/σ²) runs to cover every example together.
- **ImageNet memorization:** About 32% of training examples have memorization estimates ≥ 0.3. Removing them lowers test accuracy by roughly 3.4%, compared with about 2.6% for a random subset of the same size.
- **High-influence pairs:** Pairs were selected with thresholds of 0.25 (memorization) and 0.15 (influence). ImageNet yielded 1641 such pairs covering 1462 test images (2.92% of the test set), and 1298 of those images rely on just one training example.
- **Architecture and retraining checks (CIFAR-100):**
  - ResNet50, ResNet18, Inception and DenseNet100 produce strongly correlated sets of memorized examples and high-influence pairs.
  - Retraining only the last layer on fixed representations finds just 38 memorized examples, versus 18,099 with full ResNet50 training. This indicates that memorization mostly lives in the learned representations.
- **Released resource:** The computed memorization and influence values for CIFAR-100 and ImageNet are publicly available [FZ20].

*Our summary of the paper, in our own words — not its text. The work belongs to its authors; read it at the links above.*

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## Cite

Cite as: Vitaly Feldman and Chiyuan Zhang. 2020. What Neural Networks Memorize and Why: Discovering the Long Tail via Influence Estimation. arXiv:2008.03703.

The paper itself, not this page. BibTeX from the library's record of the work.

```bibtex
@misc{feldman2020what,
  title = {{What Neural Networks Memorize and Why: Discovering the Long Tail via Influence Estimation}},
  author = {Vitaly Feldman and Chiyuan Zhang},
  year = {2020},
  doi = {10.48550/arxiv.2008.03703},
  eprint = {2008.03703},
  archivePrefix = {arXiv},
  url = {https://doi.org/10.48550/arxiv.2008.03703}
}
```

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*Updated 2 November 2026*