With a foundational understanding of neural networks and dimensionality reduction from our previous discussions, we now focus on autoencoders. These are a specific type of neural network architecture primarily used for unsupervised learning of efficient data codings. The core idea is to learn a compressed representation (encoding) of the input data, and then from this representation, reconstruct the original input (decoding) as closely as possible.

This chapter introduces the fundamental building blocks and operational principles of autoencoders. You will learn about:

• The encoder: The part of the network that compresses the input into a lower-dimensional latent space representation.
• The bottleneck layer: The layer that contains the compressed representation, often referred to as the latent space or code.
• The decoder: The part of the network that reconstructs the input from the latent space representation.

We will also cover the training process for autoencoders, emphasizing the role of the reconstruction loss function. For instance, with continuous input data, a common loss function is Mean Squared Error (MSE), defined as: $MSE = \frac{1}{N} \sum_{i=1}^{N} (x_i - \hat{x}_i)^2$ where $x_i$ represents an original input sample and $\hat{x}_i$ is its reconstructed version. You will also be introduced to concepts like undercomplete and overcomplete autoencoders, and begin to see how these networks can discover meaningful features from data. The chapter includes a practical session where you'll build a basic autoencoder.