# Questions tagged [latent-variable]

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### What is the meaning of log p(x) in VAE math and why is it constant

I was reading the article on medium, where the author cites this equation for Variational Inference: \begin{align*} \text{KL}(q(z|x^{(i)})||p(z|x^{(i)})) &= \int_z q(z|x^{(i)})\text{log}\frac{q(z|...
1 vote
20 views

### Is it reasonable to ask for the same time-regularity of the high and low dimensional signals?

Consider we are dealing with sequential data sampled from a continuous time signal $x(t)\in \mathbb{R}^n$, so that the dataset will look like $\{x_0,x_1,…,x_n\}$, with $x_i= x(t_i)$. Assume that we ...
9 views

### How to apply Latent Diffusion for 3D Binary Voxel Data?

Suppose we have a voxel of shape (60, 36, 60) with values 0 or 1 (1-occupied, 0-empty). What is the possible architecture of latent diffusion?
1 vote
66 views

### Are diffusion models still beneficial in highly compressed latent spaces?

Consider for example the MNIST dataset. When we apply diffusion to the pixel space, the image slowly becomes more and more noisy until white noise has been reached (like below). In the last step (t=...
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1 vote
76 views

### Variational Lower Bound in VAE for Gaussian latent prior

From Bishop's recent book on Deep Learning, it says the ELBO for Gaussian latent prior can be approximated by $\frac{1}{L}\sum_{l=1}^L \ln p(x_n|z_n^l,w) + KL(q(z_n|x_n,\phi)||p(z_n))$ where $n$ are ...
• 123
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### I have n-dimensional latent representational data, with a y logit label: How do I find peaks in the data using the label?

I essentially need a "find peaks" algorithm for when the input data is n-dimensional. Specifically, in the latent space of my neural network I have have collected all the training data ...
1 vote
75 views

### Pointers to (deep) latent variable models that admit analytical approximations

I am aware that there is a plethora of deep generative models out there (e.g. variational autoencoders (VAE), GANs) that can model high-dimensional data as the images of latent variables under a non-...
• 111
115 views

### 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 ...
• 598
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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 ...
1 vote
190 views

### 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?
• 35
3k views

### 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 (...
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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-...
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1 vote
922 views

### 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 ...
1 vote
1k views

### 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 ...
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1 vote
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### What is meant by degrees of freedom of latent variables?

...Designing such a likelihood function is typically challenging; however, we observe that features like spectrogram are effective when latent variables have limited degrees of freedom. This motivates ...
• 1,141
35 views

### 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 ...
33 views

### 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 ...
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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 ...
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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 ...
• 797
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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 ...
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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 ...
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20k views

### 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" ...
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1 vote
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 ...