Autoencoders
An autoencoder learns an encoder that maps an input to a code and a decoder that reconstructs the input from that code.
An autoencoder learns an encoder that maps an input to a code and a decoder that reconstructs the input from that code. An encoder can map high-dimensional inputs to low-dimensional codes. A decoder maps those codes back toward the input space.
Mean-squared error measures the difference between an output and a target. The loss can be followed in the backward direction. A denoising autoencoder can learn to map corrupted inputs to clean targets.
An autoencoder can learn a lower-dimensional code and a reconstruction function. A denoising criterion can be purely unsupervised. A wide hidden layer can learn the identity function.
An encoder compresses an input and a decoder reconstructs it.
Follow one input through a bottleneck and reconstruction.
- 1 · encodeMap the input to a hidden code.
- 2 · constrainPass information through a code with fewer dimensions than the input.
- 3 · decodeMap the code back into the input space.
- 4 · compareMeasure reconstruction error between the output and target.
- 5 · learnFollow the loss in the backward direction.
A denoising autoencoder maps a noisy image to a clean image.
| Who | What they ask | What it works with |
|---|---|---|
| Data analyst | “Can these records be represented with fewer values?” | High-dimensional feature vectors |
| Imaging team | “Can noise be removed from this image?” | Paired noisy and clean images |
| Operations team | “Which samples reconstruct unusually poorly?” | Reconstruction errors for observed samples |
- An autoencoder can learn a lower-dimensional code and a reconstruction function.
- A denoising autoencoder can reconstruct clean data from corrupted input.
- A denoising criterion can be purely unsupervised.
- A linear one-hidden-layer autoencoder with squared error learns weights spanning the principal-component subspace.
- A wide hidden layer can learn the identity function.
- Even a one-node bottleneck can overfit.
- Reconstruction alone is not sufficient for learning useful representations.
Sources used
This explainer is written in original language. The links below support its factual claims.
- paperAutoencoders, Bank, Koenigstein and Giryes · read 28 Sept 2026
- paperFrom Principal Subspaces to Principal Components with Linear Autoencoders, Elad Plaut · read 28 Sept 2026
- docsConvolutional autoencoder for image denoising, Keras · read 28 Sept 2026
- docsNeural Networks, PyTorch · read 28 Sept 2026
- paperStacked Denoising Autoencoders, Vincent et al., JMLR · read 28 Sept 2026