  In this article, we will look at autoencoders. This article covers the
mathematics and the fundamental concepts of autoencoders. We will discuss what
they are, what the limitations are, the typical use cases, and we will look at
some examples. We will start with a general introduction to autoencoders, and
we will discuss the role of the activation function in the output layer and the
loss function. We will then discuss what the reconstruction error is. Finally,
we will look at typical applications as dimensionality reduction,
classification, denoising, and anomaly detection. This paper contains the notes
of a PhD-level lecture on autoencoders given in 2021.
