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I am currently reading paper on Variational Autoencoders by Dr. Kingma and Dr. Welling, and am having a few confusions.

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Question 1: What is a spherical Gaussian latent space? How do we interpret it

Question 2: In equation 1.15, does the Roman I in standard deviation mean 1 or does it have a different meaning?

Could anyone please provide me some information on these?

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  1. A spherical gaussian distribution is a multivariate normal distribution that has diagonal covariance and equal variances in all directions. A "spherical gaussian latent space" means that the latent space is a random variable with a spherical gaussian distribution.

  2. $I$ is the identity matrix.

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  • $\begingroup$ Thank you @Sycorax! I have added a confusion in the description. It would be great if you could please help me understand it. $\endgroup$
    – Curious
    Commented May 11, 2022 at 12:26
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    $\begingroup$ Sycorax answered the question you posted. If you have another, please post it as a separate question instead of editing it into the previous one. If you take advantage of the opportunity to do that, I encourage you to specify where the newly added figures are taken from. They’re not comparable to each other. $\endgroup$
    – Arya McCarthy
    Commented May 11, 2022 at 12:44
  • $\begingroup$ @Curious Arya is correct — if you have a follow-up question, you should ask a new question $\endgroup$
    – Sycorax ♦
    Commented May 11, 2022 at 12:45
  • $\begingroup$ Sure, will add a new question. Thanks! Edit removed. $\endgroup$
    – Curious
    Commented May 11, 2022 at 12:52

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