# Memorization in Overparameterized Autoencoders

arXiv: https://arxiv.org/abs/1810.10333 · HTML: https://mlsanity.com/paper/1810.10333/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 16 Oct 2018.

## Built on by (most cited first, 3 of 3)

- [Analysis of feature learning in weight-tied autoencoders via the mean field lens](https://mlsanity.com/paper/2102.08373/) (2021)
- [How Much Training Data is Memorized in Overparameterized Autoencoders? An Inverse Problem Perspective on Memorization Evaluation](https://mlsanity.com/paper/2310.02897/) (2023)
- [Geometric instability of out of distribution data across autoencoder architecture](https://mlsanity.com/paper/2201.11902/) (2022)

## Abstract (arXiv)

The ability of deep neural networks to generalize well in the overparameterized regime has become a subject of significant research interest. We show that overparameterized autoencoders exhibit memorization, a form of inductive bias that constrains the functions learned through the optimization process to concentrate around the training examples, although the network could in principle represent a much larger function class. In particular, we prove that single-layer fully-connected autoencoders project data onto the (nonlinear) span of the training examples. In addition, we show that deep fully-connected autoencoders learn a map that is locally contractive at the training examples, and hence iterating the autoencoder results in convergence to the training examples. Finally, we prove that depth is necessary and provide empirical evidence that it is also sufficient for memorization in convolutional autoencoders. Understanding this inductive bias may shed light on the generalization properties of overparametrized deep neural networks that are currently unexplained by classical statistical theory.