# Why Deep Learning Generalizes

arXiv: https://arxiv.org/abs/2211.09639 · HTML: https://mlsanity.com/paper/2211.09639/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 22 references that are in the map.
- First posted on arXiv 17 Nov 2022.

## Builds on (most cited first, 12 of 12)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Understanding deep learning requires rethinking generalization](https://mlsanity.com/paper/1611.03530/) (2016)
- [A Closer Look at Memorization in Deep Networks](https://mlsanity.com/paper/1706.05394/) (2017)
- [In Search of the Real Inductive Bias: On the Role of Implicit Regularization in Deep Learning](https://mlsanity.com/paper/1412.6614/) (2014)
- [On the Origin of Implicit Regularization in Stochastic Gradient Descent](https://mlsanity.com/paper/2101.12176/) (2021)
- [Implicit Gradient Regularization](https://mlsanity.com/paper/2009.11162/) (2020)
- [Implicit Regularization in Deep Learning](https://mlsanity.com/paper/1709.01953/) (2017)
- [Towards Understanding Generalization of Deep Learning: Perspective of Loss Landscapes](https://mlsanity.com/paper/1706.10239/) (2017)
- [Implicit Regularization of Stochastic Gradient Descent in Natural Language Processing: Observations and Implications](https://mlsanity.com/paper/1811.00659/) (2018)
- [Depth and Representation in Vision Models](https://mlsanity.com/paper/2211.06496/) (2022)

## Built on by (most cited first, 2 of 2)

- [Masked Mixers for Language Generation and Retrieval](https://mlsanity.com/paper/2409.01482/) (2024)
- [Adversarial Examples from Dimensional Invariance](https://mlsanity.com/paper/2304.06575/) (2023)

## Abstract (arXiv)

Very large deep learning models trained using gradient descent are remarkably resistant to memorization given their huge capacity, but are at the same time capable of fitting large datasets of pure noise. Here methods are introduced by which models may be trained to memorize datasets that normally are generalized. We find that memorization is difficult relative to generalization, but that adding noise makes memorization easier. Increasing the dataset size exaggerates the characteristics of that dataset: model access to more training samples makes overfitting easier for random data, but somewhat harder for natural images. The bias of deep learning towards generalization is explored theoretically, and we show that generalization results from a model's parameters being attracted to points of maximal stability with respect to that model's inputs during gradient descent.