Autoencoders are neural networks that learn a compressed representation of the input in order to later reconstruct it, so they can be used for dimensionality reduction. They are composed of an encoder and a decoder (which can be separate neural networks). Dimensionality reduction can be useful in order to deal with or attenuate the issues related to the curse of dimensionality, where data becomes sparse and it is more difficult to obtain "statistical significance". So, autoencoders (and algorithms like PCA) can be used to deal with the curse of dimensionality.
Why do we care about dimensionality reduction specifically using autoencoders? Why can't we simply use PCA, if the purpose is dimensionality reduction?
Why do we need to decompress the latent representation of the input if we just want to perform dimensionality reduction, or why do we need the decoder part in an autoencoder? What are the use cases? In general, why do we need to compress the input to later decompress it? Wouldn't it be better to just use the original input (to start with)?