01·Autoencoders: encoder, decoder, and the latent space

Introduction

An autoencoder is a network trained to reconstruct its own input through a bottleneck — it compresses x into a representation z = f(x) and then reconstructs x̂ = g(z). This lesson dissects classical AEs, denoising AEs (Vincent et al. 2008), sparse AEs, contractive AEs, undercomplete vs overcomplete variants, and the difference between AEs and PCA. It explains what the latent space actually represents, why a vanilla AE is NOT a generative model, and the typical pitfalls (identity mapping, manifold collapse).