# Questions tagged [notation]

For questions related to notation (in general).

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• 194
1 vote
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### What do the square brackets $[ ]$ and $\mid$ mean in $[G_t \mid S_t=s]$?

Here is the formula of state-value function in Reinforcement Learning. What do the square brackets $[ ]$ and $\mid$ mean in $[G_t \mid S_t=s]$? Why use square brackets? Why use $\mid$? Why do ...
• 113
237 views

### Where are the parentheses in the Bellman update rule?

I'm not having a lot of intuition about the equation. I have this Bellman update rule: $$v_{\pi}(s) =\sum_a \pi(a|s)\sum_{s',r} p(s',r|s,a)[r+ \gamma v_{k}(s')]$$ But where are the parenthesis? Is the ...
• 155
1 vote
46 views

### What does the complexity equation constitute exactly in “Why Should I Trust You?” LIME paper

I've recently been reading this paper on LIME, an algorithm to interpret ANY machine learning model. I encountered this equation (in red) on page 4 and have just been having a hard time deciphering ...
1 vote
32 views

### Why do we use $q_{\phi}(z \mid x^{(i)})$ in the objective function of amortized variational inference, while sometimes we use $q(z)$?

In page 21 here, it states: General Idea of Amortization: if same inference problem needs to be solved many times, can we parameterize a neural network to solve it? Our case: for all $x^{(i)}$ we ...
• 203
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### Are the authors of the VAE paper writing the PDFs as a function of the random variables?

Usually, I see the conventions: discrete random variable is denoted as $X$, the pmf is written as $P(X=x)$ or $p(X=x)$ or $p_{X}(x)$ or $p(x)$, where $x$ is an instance of $X$ a continuous random ...
• 203
32 views

### Which is more popular/common way of representing a gradient in AI community: as a row or column vector?

Consider the following remark about writing gradients from the chapter named Vector Calculus from the test book titled Mathematics for Machine Learning by Marc Peter Deisenroth et al. Remark (...
• 2,977
1 vote
67 views

### What is the name of this letter $\mathcal{J}$?

What is the name of this letter $\mathcal{J}$ in the following deep learning equation? And what alphabet it is from? $$\mathcal{J} = \frac{1}{m} \sum_{i=1}^m \mathcal{L}^{(i)}$$
• 113
1 vote
134 views

### What is a filter in the context of graph convolutional networks?

In Section 2.1 of the research paper titled Semi-Supervised Classification with Graph Convolutional Networks by Thomas N. Kipf et al., Spectral convolution on graphs defined as The multiplication of ...
• 115
42 views

### In this example of fuzzy c-means, what is the difference between "sigma" and "center" for the clusters?

In this example, what exactly do "Cluster" and "Sigma" mean? (They chose random coordinates for the three centroids of the groups) Centers: Cluster centers, returned as a ...
• 129
40 views

### Why using negative integers (as dimensions?) in tensor shapes rather than natural numbers?

Consider the following paragraph from A.1 MULTI-MNIST AND CLEVR of A IMPLEMENTATION DETAILS from the research paper titled ...
• 2,977
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### What, exactly, do mlp(64,64) and mlp(64,128,1024) mean in PointNet, and how many input neurons does 1 (x,y,z) point have?

I couldn't find out how to interpret the multilayer perceptron notation given in PointNet. Specifically, I am looking to find out what the numbers inside the parentheses of ...
• 21
35 views

### Is there any difference between input and conditional input incase of neural networks?

In the research paper titled Conditional Generative Adversarial Nets by Mehdi Mirza and Simon Osindero, there is a notion of conditioning a neural network on class label. It has been mentioned in <...
• 2,977
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### Does generator in conditonal GAN obey probability laws?

In probability, we have two types of probability functions: unconditional probability $p(x)$ and conditional probability $p(x | y)$. Both are fundamentally different and the latter can be obtained by ...
• 2,977
1 vote
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• 107
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### What is the meaning of these equations in Noise2Noise paper?

I am trying to understand what is meant by following equations in the Noise2Noise paper by Nvidia. What is meant by the equation in this image? What is $\mathbb{E}_y\{y\}$? And how should I try to ...
• 31
1 vote
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• 21
1 vote
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### What is the purpose of the arrow $\leftarrow$ in this formula?

What is the purpose of the arrow $\leftarrow$ in the formula below? $$V(S_t) \leftarrow V(S_t) + \alpha \left[ G_t - V(S_t) \right]$$ I presume it's not the same as 'equals'.
• 573
1 vote
164 views

### Why is exp used in encoder of VAE instead of using the value of standard deviation alone?

There's one VAE example here: https://towardsdatascience.com/teaching-a-variational-autoencoder-vae-to-draw-mnist-characters-978675c95776. And the source code of encoder can be found at the ...
• 1,133
91 views

### How to understand the average l2 loss?

In the snippet below, the highlighted part is the average norm, but since $1/|p_i|$ is outside the summation, it is very confusing to understand. is $|p_i|$ l2-norm(as per wolfram) or l1-norm or ...
97 views

### What is the difference between the notations $\|x\|_1, \|x\|_2$ and $|x|$?

What is the difference between the notations $\|x\|_1, \|x\|_2$ and $|x|$? I think $|x|$ is the magnitude of $x$.
80 views

### What does the notation sup dist mean in distributional RL?

I'm trying to understand distributional RL, based on this article. In one of the equations, there is a symbol $\operatorname{sup dist}$. \begin{align} \operatorname{sup dist}_{s, a} (R(s, a) + \...
877 views

### What is a probability distribution in machine learning?

If we were learning or working in the machine learning field, then we frequently come across the term "probability distribution". I know what probability, conditional probability, and ...
• 936
71 views

### What do the subscripts mean in $N_{t,n,\sigma,L}$?

A neural network can apparently be denoted as $N_{t,n,\sigma,L}$. What do these subscripts $t, n, \sigma$ and $L$ mean? Could you link me to a paper, article or webpage with an explanation for this?
• 143
### Sutton & Barto's notation $V_{t+n}$ in Chapter 7: $n$-step Bootstrapping
Until Chapter 6 of Sutton & Barto's book on Reinforcement Learning, the authors use $V$ for the current estimate of a state value. Equation (6.1), for example, shows:  V(S_t) \leftarrow V(S_t) +...