<p>From my understanding of the paper, <span class="math-container">$Z^{pres}$</span> keeps track of the objects in the scene. For every step of the sequential inference, <span class="math-container">$z^{pres,i}$</span> takes either a 0 or a 1. A 1 represents that an object is present and it has to be explained by the remaining latent variables. 0 indicates that all the objects have been explained and inference is complete.</p>

CC BY-SA 4.0
2020-10-05T16:08:24.333Z
2020-10-05T16:08:24.333Z
Niranjan Kumar
<p>I've been reading the <a href="https://arxiv.org/abs/1806.01794" rel="nofollow noreferrer">SQAIR paper</a> lately, and the mathematics involved seems a bit complicated.</p>
<p>Some background, about the paper: <em>SQAIR stands for Sequential Attend, Infer, Repeat</em> - the paper does generative modelling of moving objects. The idea of <em>Attend, Infer, Repeat</em> is to decompose a static scene into constituent objects, where each object is represented by continuous latent variables. The latent variables, <span class="math-container">$z^{what}$</span>,<span class="math-container">$z^{where}$</span> and <span class="math-container">$z^{pres}$</span> encode the appearance, position and presence of an object.</p>
<p>Here's a screenshot of the first of many things I'm unable to understand -</p>
<p><a href="https://i.sstatic.net/6dRLa.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/6dRLa.png" alt="enter image description here" /></a></p>
<p>Why is <span class="math-container">$z^{pres,1:n+1}$</span> a random vector of <span class="math-container">$n$</span> ones followed by a zero? Why do we need the zero? How does it help?</p>
<p>Furthermore, an explanation of equation <span class="math-container">$(2)$</span> as in the image above, would be great.</p>
<p>P.S. I hope you all find the paper interesting. I'll ask other questions from the paper in separate posts, so as to not crowd one post with too many queries.</p>

<computer-vision><papers><generative-model><random-variable>
Why is this variable in equation 2 of the SQAIR paper a random vector of $n$ ones followed by a zero?
stoic-santiago
# Why is this variable in equation 2 of the SQAIR paper a random vector of $n$ ones followed by a zero?

(Asked by: username_0 on 2020-04-30)

I've been reading the [SQAIR paper](https://arxiv.org/abs/1806.01794) lately, and the mathematics involved seems a bit complicated.

Some background, about the paper: *SQAIR stands for Sequential Attend, Infer, Repeat* - the paper does generative modelling of moving objects. The idea of *Attend, Infer, Repeat* is to decompose a static scene into constituent objects, where each object is represented by continuous latent variables. The latent variables, $z^{what}$,$z^{where}$ and $z^{pres}$ encode the appearance, position and presence of an object.

Here's a screenshot of the first of many things I'm unable to understand -

[![enter image description here](https://i.sstatic.net/6dRLa.png)](https://i.sstatic.net/6dRLa.png)

Why is $z^{pres,1:n+1}$ a random vector of $n$ ones followed by a zero? Why do we need the zero? How does it help?

Furthermore, an explanation of equation $(2)$ as in the image above, would be great.

P.S. I hope you all find the paper interesting. I'll ask other questions from the paper in separate posts, so as to not crowd one post with too many queries.

**Tags:** computer-vision, papers, generative-model, random-variable


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## 1 answers

### Answer by username_1 on 2020-10-05. Score: 0

From my understanding of the paper, $Z^{pres}$ keeps track of the objects in the scene. For every step of the sequential inference, $z^{pres,i}$ takes either a 0 or a 1. A 1 represents that an object is present and it has to be explained by the remaining latent variables. 0 indicates that all the objects have been explained and inference is complete.


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