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Feedforward neural networks trained to reconstruct their own input. Usually one of the hidden layers is a "bottleneck", leading to encoder->decoder interpretation.
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Help Understanding Reconstruction Loss In Variational Autoencoder
Typically in VAE implementations, the output of the decoder is actually the mean $\mu_{x|z}$ which I will just call $\mu$, and people assumes a unitary covariance. So in that case we have:
$logP(x|z)= …