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From the paper on VQ-VAE, it said that the vector quantized variational autoencoder (VQ-VAE), differs from VAEs in two key ways:

  1. the encoder network output discrete, rather than continuous, codecs
  2. the prior is learnt rather than static

The paper further says, using the VQ method allows the model to circumvent issues of "posterior collapse".

So can anybody explain the main use of vector quantization in VQ-VAE, and how does it improve the VAE model in a mathematical or some kind of rigorous way so that I can understand it?

Also explain points 1, 2, and "posterior collapse" in detail with mathematical notions if possible.

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