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After a couple hours of trying to read and improve this article, I'm convinced that although it has much useful content, it is nearly unreadable because of a mixture of highly-technical jargon and informal text. |
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:I also found this incredibly confusing. As the prior on z is usually fixed and doesn't depend on any parameter. [[User:EitanPorat|EitanPorat]] ([[User talk:EitanPorat|talk]]) 00:16, 19 March 2023 (UTC)
::I see the confusion. p(z) is a probability distribution, but sometimes the same notation is used in conjunction with a parameter set to indicate that actually it is a parameterized function! The article should be cleared up. The encoder should be called q_phi everywhere and the decoder should be called p_theta. The reason is that to optimize the encoder you need gradients that only come from the KL divergence and then you take the derivative of the free energy with regard to the parameters of the encoder. Those gradients update only the encoder parameters. But the encoder also gets the reconstruction gradients from theta! [[Special:Contributions/46.199.5.20|46.199.5.20]] ([[User talk:46.199.5.20|talk]]) 19:47, 26 December 2024 (UTC)
== The image shows just a normal autoencoder, not a variational autoencoder ==
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I'm not sure that image should just be removed, or whether it make sense in the section anyway. [[User:Volker Siegel|Volker Siegel]] ([[User talk:Volker Siegel|talk]]) 14:18, 24 January 2022 (UTC)
:Just to make this point clear: The reparameterization trick is for the gradients! The trick separates the source of randomness to another node in the DAG that does not have any parameters, so that we can propagate gradients through the rest of the DAG that is now a deterministic function. [[Special:Contributions/82.102.110.228|82.102.110.228]] ([[User talk:82.102.110.228|talk]]) 18:57, 27 December 2024 (UTC)
== This is a highly technical topic ==
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The architecture section is filled with unclear phrases and undefined terms. For example, "noise distribution", "q-distributions or variational posteriors", "p-distributions", "amortized approach", "which is usually intractable" (what is intractable?), "free energy expression". None of these are defined. It is unclear if this section of the article is useful to anyone who is not already familiar with how variational autoencoders work. [[User:Joshuame13|Joshuame13]] ([[User talk:Joshuame13|talk]]) 15:14, 31 January 2023 (UTC)
:I've fixed most of those. The free energy really needs its own section. It is a lower bound that is obtained by using Jensen's inequality on the log likelihood. However, I don't think that Jenssen's inequality is within the scope of this article. [[Special:Contributions/46.199.5.20|46.199.5.20]] ([[User talk:46.199.5.20|talk]]) 19:50, 26 December 2024 (UTC)
== The ELBO section needs more derivation ==
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:I agree p_theta(z) doesn't make sense. [[User:EitanPorat|EitanPorat]] ([[User talk:EitanPorat|talk]]) 00:17, 19 March 2023 (UTC)
::Agreed. It should be p_phi(z) or even better q_phi(z). [[Special:Contributions/46.199.5.20|46.199.5.20]] ([[User talk:46.199.5.20|talk]]) 20:22, 26 December 2024 (UTC)
== Rating this article C-class ==
This article has great potential. Excellent technical content. But I just rated it "C" because it seems to have gained both content and noise over the past six months. I've tried for a couple of hours to improve the clarity of the central idea of a VAE, but I'm not satisfied with my efforts. In particular, it is still unclear to me whether both the encoder and decoder are technically random, whether any randomness should be added in the decoder, or what (beyond Z) is modeled with a multimodal Gaussian in the basic VAE. I see no reason why this article should not be accessible both to casual readers and to the technically proficient, but we are far from there yet.
In particular, the introductory figure shows x being mapped to a gaussian figure and back to x'. It would be good to explicitly state how the encoder and decoder in this figure relate to the various distributions used throughout the article, but I'm not confident on how to do so. [[User:Yoderj|Yoderj]] ([[User talk:Yoderj|talk]]) 19:25, 15 March 2024 (UTC)
I will try to make simple answers to your question. The encoder is a bad name and confuses people. In actuality, it is a gaussian distribution. It has a mean and a variance, which are each parameters given by a neural network. This network is initially random, and is trained (using gradients from the "loss function"). The decoder is also a gaussian distribution. It also has a mean and a variance, which are given by another neural network. Is the decoder technically random? It depends. If you are training, you want to make an estimate. To do the estimate, you have to take samples, which means that the result is random. When you are training, the decoder is random. On the other hand, if you are just doing inference, you can have non-randomness in the decoder. Since you are having a gaussian output, you can say I will do maximum a posteriori and only take one sample from the encoder. You may ask, hey unidentified wikipedian. If it is a gaussian decoder don't you also have to add the variance? That is a very fair question, but there are many applications where you can ignore it. Then you only take one sample out.
I hope that this clears things up. We have four variables. The mean and variance of the encoder. And the mean and variance of the decoder. These variables can be multidimensional for the multivariate Gaussian, but they are still four variables. Here are some equations to help you understand:
z = mu(x) + sigma(x)*epsilon # reparameterization trick
x' = MU(z) + SIGMA(z)*epsilon
And here is the legend:
x: input
z: sample from the latent, aka sample from the encoder, aka output of mu(x) plus output of sigma(x) with randomness
mu, sigma: encoder neural networks
MU, SIGMA: decoder neural networks
x': output
At the end of the day, people have to juggle the interaction of two probability distributions. I doubt that it can be simplified enough for the general populace at this time.
[[Special:Contributions/46.199.5.20|46.199.5.20]] ([[User talk:46.199.5.20|talk]]) 19:34, 26 December 2024 (UTC)
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