Message passing receptive field

Questions
#1

I am very new to GNN but I am trying to better understand message passing and how GNN could apply to my data.

Let’s say we have a tree like bidirectional graph with a maximum depth of 20. Has an example, answered questions in an exam where the exam is structured in sections, sections contains questions.

(Exam <–> Sections <–> Questions)

If I structure the graph to have three node types, Exam, Section, Question in a tree like structure and I want to use this graph to predict the score of the next exam this student would pass. So the prediction happens at the Exam node. By using message passing, we would need several layers to be able to get the information from the bottom nodes at depth 20 to predict at the Exam node right? 20 layers basically to get from the bottom question node to the top exam node?

Or should I structure my graph otherwise and simply have all questions connect the the Exam node (Exam <–> Questions)? This way I avoid having to pass messages through all the tree, but at the same time I lose the structure of the tree.

Thank you!

#2

If I structure the graph to have three node types, Exam, Section, Question in a tree like structure and I want to use this graph to predict the score of the next exam this student would pass. So the prediction happens at the Exam node. By using message passing, we would need several layers to be able to get the information from the bottom nodes at depth 20 to predict at the Exam node right? 20 layers basically to get from the bottom question node to the top exam node?

Yes. Basically the number of layers required is the same as the length of the shortest path.

Or should I structure my graph otherwise and simply have all questions connect the the Exam node (Exam <–> Questions)? This way I avoid having to pass messages through all the tree, but at the same time I lose the structure of the tree.

  1. Is the tree structure of depth 20 really necessary? Does it capture the dependencies among questions and the one between them and the exam? Any alternative structure?
  2. You may also combine multiple structures together, e.g. combining the tree structure and the star structure.
1 Like
#3

Thank you for your response! I think I should definitely explore more structure type like you suggested and see what works best in practice.