Autoencoders: Foundations and Variants

Autoencoder definition and two-part structure

An autoencoder is an unsupervised neural network designed to learn efficient codings of unlabeled data. It consists of two main parts: an encoder that maps the input message to a latent code (a lower-dimensional representation) and a decoder that reconstructs the original message from that code. The goal is to make the reconstruction as close as possible to the input, according to a chosen reconstruction quality measure (loss function). Mathematically, an autoencoder is defined by (1) an encoded space Z and a decoded/input space X, and (2) two parameterized function families: an encoder E_φ: X → Z and a decoder D_θ: Z → X. For an input x, the latent representation is z = E_φ(x), and the reconstruction is x' = D_θ(z). Training adjusts parameters θ and ϕ to minimize the expected reconstruction loss over the data distribution, typically using gradient descent.

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Encoder and decoder function families

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