The output of the middle layer \( \mathbf{h}_{\mathbf{i}} \) are also called a learned representation of the input observation \( \mathbf{x}_{i} \).
The encoder can reduce the number of dimensions of the input observation and create a learned representation \( \mathbf{h}_{\mathbf{i}}\mathbf{) } \) of the input that has a smaller dimension \( q < n \).
This learned representation is enough for the decoder to reconstruct the input accurately (if the autoencoder training was successful as intended).