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

Short answer Check out the paper of Shuman et al. [1], it provides some background on Graph Signal Processing, including answers to your questions in sections II.C and III.A Long Answer Question 1 Yes,...
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4 votes
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Are the authors of the VAE paper writing the PDFs as a function of the random variables?

When it comes to notation/terminology, often, people in machine learning are (a bit?) sloppy, which causes a lot of confusion, especially for newcomers to the field or people not very math-savvy. I ...
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4 votes
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What is the name of this letter $\mathcal{J}$?

It's an uppercase "J" from the math calligraphy alphabet, i.e. \mathcal{J} in latex. $\mathcal{J}$
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  • 931
3 votes
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What do the square brackets $[ ]$ and $\mid$ mean in $[G_t \mid S_t=s]$?

The square brackets are part of the expectation operator (i.e. a function of a random variable, which in this case is $G_t$). This is common notation for the expectation. So, it's not $\left[ X \right]...
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3 votes
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Where are the parentheses in the Bellman update rule?

Here's your equation with an additional couple of parenthesis that emphasizes the order of the operations (note that you had a small typo in your original equation). $$v_{\pi}(s) =\sum_a \pi(a \mid s) ...
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2 votes
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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?

The following link satisfied my inquiries: https://www.mdpi.com/1999-4907/12/2/131/htm I hope this is useful for someone else! Justin
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  • 31
2 votes

Are the authors of the VAE paper writing the PDFs as a function of the random variables?

Machine learning papers are often somewhat confused about the distinction between a distribution and its probability density. I would rewrite this The process consists of two steps: (1) a value $\...
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  • 931
2 votes
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Why $ t=τ+n-1$ instead of $t=τ+n$ in n-step TD?

The main detail that you are missing is that $t$ does not represent the "current time step" throughout the loop, but is just a variable giving a reference to a time step that you are ...
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2 votes
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What are the steps to derive the original GAN loss function from the generalized version?

There are some definitions that may cause confusion here. In the original GANs (the first formula), the output from the discriminator connects to a sigmoid activation, the second formula is the real ...
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  • 857
2 votes
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What is the equation for $\pi_*$ in terms of $q_*(s,a)$?

An optimal policy is just a greedy policy with respect to the optimal state-action value function (which is unique for a given MDP). So, $\pi_* = \text{argmax}_a q_*(s,a) $ is almost correct - it ...
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1 vote

What do we mean by the notation $\mathbf{x}_{p} \in \mathbb{R}^{N \times\left(P^{2} \cdot C\right)}$?

This itself isn't really an expression but a description of what $x_p$ looks like. Specifically, $x_p$ is a real-valued vector with the shape [N, P^2 * C]. Of ...
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  • 671
1 vote

What is the meaning of $p_{\text {data }}(y)$ in the CycleGAN?

I interpret $p_{data}(y)$ as the empirical probability of seeing an image $y$ in the training data. For example, in a typical training run, each training image is shown to the network the same number ...
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1 vote
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Does $R_{s}=E[R_{t}|S_{t}=s]$ indicate the reward we might expect on getting on average moving from any other state to $s$?

$$R_{s}=\mathbb{E}[R_{t}|S_{t}=s]$$ is the expected reward at time step $t$ given that the state at time $t$ is $s$, where $R_{t}$ and $S_t$ are random variables that represent the reward and state ...
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1 vote
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Why do we have $t$ as subscript in $V$ instead of $t+1$ in the expression of $G_{t:t+1}$?

TD-learning is based on bootstrapping. The TD target $R_{t+1} + \gamma V_t(S_{t+1})$ describes the immediate reward (random variable), $R_{t+1}$, plus the discounted estimated return (starting from ...
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  • 889
1 vote

Are the authors of the VAE paper writing the PDFs as a function of the random variables?

You can read $X=\{x^{(i)}\}_{i=1}^N$ as $X$ represents the sequence of all values of $x$ from $x_i$ to $x_N$ where $i$ is all values from 1 to $N$. To me, the notation is confusing since my experience ...
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1 vote
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Which is more popular/common way of representing a gradient in AI community: as a row or column vector?

The issue doesn't come up terribly often. If you are only dealing with vectors, everything is either a row or column vector. It makes no difference which it is. A more relevant issue is whether one ...
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1 vote
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What is the correct notation for an operation that applies to each element of an array independently?

Based on my experience, I would say that the standard notation is just to have a regular function, and specify that it applies element wise. For example, a common notation for activation functions is $...
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  • 931
1 vote

What does the notation "for t=T to 1,−1 do" in terms of time steps, in deep recurrent q network?

That notation should mean to go from time step $T$ to time step $1$ by a negative step $-1$, i.e. backward, so $T$, then $T-1$, then $T-2$, and so on until $1$. If you know Python, this should be ...
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