Answers.Body: <p>I think the picture you're presenting is mostly for educational purposes and that's why they are excluding the node itself from it's neighbors and using two distinct networks (most of the papers I've read they are using the same network for the neighbors and for the center node). But you are right the two networks needs to have the same input and output shapes otherwise the point-wise summation between the two terms is not possible.</p>
  
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Answers.Text: you said that "I think the picture you're presenting is mostly for educational purposes and that's why they are excluding the node itself from it's neighbors". I do not understand the connection between educational purpose and excluding the node itself from it's neighbors.
Answers.UserDisplayName: Swakshar Deb
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Answers.Text: Most of the paper I've read are defining the computation of GCN as follows H_l = AXW. Where A is the adjacency matrix X is the input (or previous layer embedding) and W are the parameters to be learned. You can see how such an definition is not as user  friendly as the one you presented
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Body: <p>In the <a href="https://www.youtube.com/watch?v=LdK9HzBAR8c&amp;list=PL-Y8zK4dwCrQyASidb2mjj_itW2-YYx6-&amp;index=8&amp;t=3295s" rel="nofollow noreferrer">basic variant of GCN we have the following</a>:</p>
  <p><a href="https://i.sstatic.net/m4Iz9.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/m4Iz9.png" alt="enter image description here" /></a></p>
  <p>Here we aggregate the information from the adjacent node and pass it to a neural network, then transform our own information and add them all.</p>
  <p>But the main question is: how can we ensure that <span class="math-container">$W_{k}(\sum(\frac{h_k}{N(V)})$</span> will be the same size as <span class="math-container">$B_{k}h_{v}$</span> and does <span class="math-container">$B_{k}$</span> emply another neural network?</p>
  
Tags: <geometric-deep-learning><graph-neural-networks>
Title: How Graph Convolutional Neural Networks forward propagate?
UserDisplayName: Swakshar Deb
ThreadText: # How Graph Convolutional Neural Networks forward propagate?
  
  (Asked by: username_0 on 2020-07-23)
  
  In the [basic variant of GCN we have the following](https://www.youtube.com/watch?v=LdK9HzBAR8c&list=PL-Y8zK4dwCrQyASidb2mjj_itW2-YYx6-&index=8&t=3295s):
  
  [![enter image description here](https://i.sstatic.net/m4Iz9.png)](https://i.sstatic.net/m4Iz9.png)
  
  Here we aggregate the information from the adjacent node and pass it to a neural network, then transform our own information and add them all.
  
  But the main question is: how can we ensure that $W\_{k}(\sum(\frac{h\_k}{N(V)})$ will be the same size as $B\_{k}h\_{v}$ and does $B\_{k}$ emply another neural network?
  
  **Tags:** geometric-deep-learning, graph-neural-networks
  
  ---
  
  ## 1 answers
  
  ### Answer by username_1 on 2020-07-23. Score: 2
  
  I think the picture you're presenting is mostly for educational purposes and that's why they are excluding the node itself from it's neighbors and using two distinct networks (most of the papers I've read they are using the same network for the neighbors and for the center node). But you are right the two networks needs to have the same input and output shapes otherwise the point-wise summation between the two terms is not possible.
  
  > **Comments:**
  > **username_0**: you said that "I think the picture you're presenting is mostly for educational purposes and that's why they are excluding the node itself from it's neighbors". I do not understand the connection between educational purpose and excluding the node itself from it's neighbors.  
  > **username_1**: Most of the paper I've read are defining the computation of GCN as follows H_l = AXW. Where A is the adjacency matrix X is the input (or previous layer embedding) and W are the parameters to be learned. You can see how such an definition is not as user  friendly as the one you presented  
  
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