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Suppose a Variational Autoencoder (VAE) is trained with mnist data. To sample, one draws from normal distribution. My question is: suppose I am interested in generating only 1s and no other digits. How can do I do that? do I sample until I generate a 1 and then I keep sampling from the neighborhood of that point? or is there a more controlled way to tell the VAE what digit to generate? Thanks

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The ideal encoder would take any input and generate a sample coming from $\mathcal{N}(0,1)$. If the input is 1 or 2 or 3, the samplings will all come from $\mathcal{N}(0,1)$, so, how does the decoder know if the input was 1, 2, or 3?

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    $\begingroup$ there are 2 approaches, one is sample unitll you get a 1, the other is to have some input point in latent space whose representation is close to 1. In both cases you will have to check you get indeed a 1 back $\endgroup$
    – Nikos M.
    Apr 20 at 18:01
  • $\begingroup$ about the second approach, if the encoder truly does his job, shouldn't the output of the encoder just be $\mathcal{N}(0,1)$ but it will be the same for digit 2, 3, etc. $\endgroup$
    – Schach21
    Apr 20 at 20:11
  • $\begingroup$ to my understanding "close" input points should have "close" output representations, if this is what you mean. A 3rd option is to train a VAE only with 1s $\endgroup$
    – Nikos M.
    Apr 20 at 20:16
  • $\begingroup$ I edited my question to clarify what I mean, please let me know if it's clear or I should clarify further. $\endgroup$
    – Schach21
    Apr 20 at 20:22
  • $\begingroup$ Are conditional VAEs an option? $\endgroup$
    – Sammy
    Apr 20 at 22:08
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You condition the latent variable on another variable drawn from a categorical distribution (https://wiseodd.github.io/techblog/2016/12/17/conditional-vae/).

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