Wat is Autoencoder, conditional autoencoder?

An autoencoder is a network trained to reproduce its input through a lower-dimensional bottleneck: an encoder maps $x$ to a code $h$, a decoder maps $h$ back to $\hat x$, and the loss is the reconstruction error. A conditional autoencoder reconstructs the cross-section of returns $r_{t+1}$ as $\beta(z_{it})^\top f_{t+1}$, where the code $f_{t+1}$ ($K$ factors) is a linear map of characteristic-managed portfolios $Z_t^\top r_{t+1}/n$ and the betas are a network of the characteristics (Gu, Kelly and Xiu, 2021).