Dictionary of Applied Machine Learning

autoencoder

Updated on 2026-09-18

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An autoencoder is a machine learning (ML) method that learns an encoder map $\hypothesis: \featurevec \mapsto \vz$ and a decoder map $\hypothesis^{*}: \vz \mapsto \widehat{\featurevec}$ jointly, so that the reconstruction $\hypothesis^{*}(\hypothesis(\featurevec))$ is close to the original feature vector $\featurevec$. The code $\vz$ typically has fewer entries than $\featurevec$, which makes an autoencoder a dimensionality reduction and feature learning method. Training uses empirical risk minimization (ERM) with a loss that measures the reconstruction error, and no labels are needed, so it is a form of self-supervised learning. With linear models for encoder and decoder, the learned code space coincides with that of principal component analysis (PCA); artificial neural networks (ANNs) as encoder and decoder allow nonlinear codes.

Definition

An autoencoder is a machine learning (ML) method that simultaneously learns an encoder map $\hypothesis \in \hypospace$ and a decoder map $\hypothesis^{*} \in \hypospace^{*}$. Different autoencoders use different models $\hypospace, \hypospace^{*}$, e.g., artificial neural networks (ANNs) with different architectures. The special case of an autoencoder using (vector-valued) linear models for $\hypospace, \hypospace^{*}$ results in principal component analysis (PCA).

Figure 1 of the entry autoencoder
Figure 1: Autoencoder with an encoder $\hypothesis$ mapping $\featurevec \mapsto \vz$ and a decoder $\hypothesis^*$ mapping $\vz \mapsto \hat{\featurevec}$.
The training of the encoder and decoder can be implemented via empirical risk minimization (ERM) using a loss that measures the deviation of the reconstructed feature vector $\hypothesis^{*}\big(\hypothesis\big(\featurevec \big) \big)$ from the original feature vector $\featurevec$.

See also: encoder, feature learning, dimensionality reduction.

Cite this entry

@misc{dictml_autoencoder,
  author = {Jung, Alexander and Olioumtsevits, Konstantina and Schnoor, Ekkehard},
  title = {autoencoder},
  howpublished = {Dictionary of Applied Machine Learning (course edition)},
  year = {2026},
  doi = {10.5281/zenodo.21569296},
  note = {ISBN 978-952-64-3013-3, CC BY 4.0, retrieved 2026-09-19},
  url = {https://dictionaryofml.org/terms/autoencoder.html}
}