a ([[function|deterministic]]) [[1991KramerNonlinearPrincipalComponent|autoencoder]] is a mapping $\text{dec}[\theta_{\text{dec}}] : x \mapsto z$ and $\text{enc}[\theta_{\text{enc}}] : z \mapsto x$ where $\dim \mathcal{Z} \ll \dim \mathcal{X}$. the task is $\max_{ \theta_{\text{enc}}, \theta_{\text{dec}} } d(x, \text{dec}(\text{enc}(x)))$ where $d$ is some [[loss function]] ie measurement of distance (eg [[metric]]). does ([[unsupervised]]) "nonlinear [[principal component]] analysis". can also be adjusted without [[backpropagation]] by using the [[recirculation algorithm]] (see [[biologically plausible]]) in [[neural gradient representation by activity differences]] framework, backpropagate activations from higher layers see [Lilian Weng's blog post](https://lilianweng.github.io/posts/2018-08-12-vae/) for more details