Artificial Intelligence Stack Exchange
Artificial Intelligence Stack Exchange

Questions tagged [latent-variable]

17 questions
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What is the difference between latent and embedding spaces?

In general, the word "latent" means "hidden" and "to embed" means "to incorporate". In machine learning, the expressions "hidden (or latent) space" and "embedding space" occur in several contexts. More specifically, an embedding can refer to a…
nbro
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Why is the evidence equal to the KL divergence plus the loss?

Why is the equation $$\log p_{\theta}(x^1,...,x^N)=D_{KL}(q_{\theta}(z|x^i)||p_{\phi}(z|x^i))+\mathbb{L}(\phi,\theta;x^i)$$ true, where $x^i$ are data points and $z$ are latent variables? I was reading the original variation autoencoder paper and I…
user8714896
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How to generate new data given a trained VAE - sample from the learned latent space or from multivariate Gaussian?

To generate synthetic dataset using a trained VAE, there is confusion between two approaches: Use learned latent space: z = mu + (eps * log_var) to generate (theoretically, infinite amounts of) data. Here, we are learning mu and log_var vectors…
Arun
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What are some new deep learning models for learning latent representation of data?

I know that autoencoders are one type of deep neural networks that can learn the latent representation of data. I guess there should be several other models like autoencoders. What are some new deep learning models for learning latent…
Kadaj13
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Do we also need to model a probability distribution for the decoder of a VAE?

I'm working on understanding VAEs, mostly through video lectures of Stanford cs231n, in particular lecture 13 tackles on this topic and I think I have a good theoretical grasp. However, when looking at actual code of implementations, such as this…
ytolochko
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how the GAN architecture maintain similar images close in the latent space?

I am learning about generative models, and I don't quite understand how the GAN architecture can maintain similar generated images close in the latent space. For example, an autoencoder and a variational autoencoder can map similarly generated…
Cesar Ruiz
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Clarification on the training objective of denoising diffusion models

I'm reading the Denoising Diffusion Probabilistic Models paper (Ho et al. 2020). And I am puzzled about the training objective. I understood (I think) the trick regarding the reparametrization of the variance in terms of the noise: $$\mu_\theta(x_t,…
user3903647
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Could it make any sense to choose a larger dimension for the latent space of the VAE with respect to the original input?

Could it make any sense to choose a larger dimension for the latent space of the VAE with respect to the original input? For example, we may want to learn how to reconstruct a relatively low-dimensional input (let's say $20$ dimensions), then could…
James Arten
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Why do hypercube latent spaces perform poorer than Gaussian latent spaces in generative neural networks?

I have a quick question regarding the use of different latent spaces to represent a distribution. Why is it that a Gaussian is usually used to represent the latent space of the generative model rather than say a hypercube? Is it because a Gaussian…
AlphaBetaGamma96
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Does bottleneck size matter in Disentangled Variational Autoencoders?

I suppose that picking an appropriate size for the bottleneck in Autoencoders is neither a trivial nor an intuitive task. After watching this video about VAEs, I've been wondering: Do disentangled VAEs solve this problem? After all, if the network…
fabs
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In this VAE formula, why do $p$ and $q$ have the same parameters?

In $$\log p_{\theta}(x^1,...,x^N)=D_{KL}(q_{\theta}(z|x^i)||p_{\phi}(z|x^i))+\mathbb{L}(\phi,\theta;x^i),$$ why does $p(x^1,...,x^N)$ and $q(z|x^i)$ have the same parameter $\theta?$ Given that $p$ is just the probability of the observed data and…
user8714896
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What kind of distributions can be used to model discrete latent variables?

If we take the vanilla variational auto-encoder (VAE), we $p(z)$ is a Gaussian distribution with zero mean and unit variance and we approximate $p(z|x) \approx q(z|x)$ to be a Gaussian distribution as well, for each latent variable $z$. But what if…
piccolo
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Can you extrapolate outside the latent distribution for GANs?

I was wondering what happens when you extrapolate out of the latent space distribution (noise vector) for a Generative adversarial network (GAN). Can anybody explain this?
TRM
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What is the most suitable measure of the distance between two VAE's latent spaces?

The problem I'm trying to solve is as follows. I have two separate domains, where inputs do not have the same dimensions. However, I want to create a common feature space between both domains using paired inputs (similar inputs from both…
Samuel Beaussant
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Is it possible to have a variable-length latent vector in an autoencoder?

I'm trying to have a simple autoencoder but with variable latent length (the network can produce variable latent lengths with respect to the complexity of the input), but I've not seen any related work to get idea from. Have you seen any related…
amin
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