DM10 - Graph Neural Networks Flashcards

Question 1

What is the primary intuition behind Graph Neural Networks (GNNs)?

Accepted Answer

They allow nodes to learn how to propagate and aggregate feature information from their local neighbors in a non-linear, trainable manner.

Question 2

How did the NetMF framework mathematically re-contextualize random-walk embeddings like DeepWalk?

Accepted Answer

It mathematically proved that DeepWalk (with infinite length random walks) is implicitly equivalent to the matrix factorization of a specific Pointwise Mutual Information (PMI) matrix.

Question 3

In the DeepWalk algorithm, how are random walks utilized to create embeddings?

Accepted Answer

Random walks are treated as sentences and nodes as words, allowing the algorithm to use NLP models like Skip-Gram to learn co-occurrence likelihoods.

Question 4

What is the core computational operation executed at every layer of a standard Graph Neural Network?

Accepted Answer

Neighborhood aggregation (or message passing), where a node updates its state by combining the embeddings of its neighbors from the previous layer.

Question 5

Why are Graph Neural Networks capable of inductive learning (generalizing to unseen nodes or entirely new graphs)?

Accepted Answer

Because instead of learning a unique, fixed embedding vector for every single node, they learn the shared weight matrices ($W$, $B$) of the aggregation functions.

Question 6

In a GNN, what does the embedding at layer zero ($z_i^0$) represent?

Accepted Answer

The raw, initial node features or attributes of node $i$.

Question 7

How does a standard Graph Convolutional Network (GCN) uniquely normalize neighbor features during aggregation?

Accepted Answer

It normalizes the message from neighbor $j$ to node $i$ using the inverse square root of their degrees: $\frac{1}{\sqrt{|N(i)||N(j)|}}$.

Question 8

Why do GCNs mathematically add the Identity matrix ($I$) to the Adjacency matrix ($A$) to create $	ilde{A}$?

Accepted Answer

To add self-loops, ensuring that a node's own feature representation from the previous layer is inherently included when computing its new embedding.

Question 9

What is the time complexity to propagate information across one layer in a sparse Graph Convolutional Network?

Accepted Answer

$\mathcal{O}(|E|)$, making it highly efficient because it scales linearly with the number of edges.

Question 10

What is the primary architectural innovation of the GraphSAGE model compared to standard GCNs?

Accepted Answer

GraphSAGE generalizes the aggregation step by allowing *any* differentiable aggregator function that maps a set of vectors to a single vector, rather than strictly using weighted averages.

Question 11

How does GraphSAGE handle a node's own previous embedding during a layer update?

Accepted Answer

Instead of just adding it, GraphSAGE explicitly *concatenates* the aggregated neighbor vector with the node's own vector from the previous layer before passing it through the non-linearity.

Question 12

What are the three primary aggregation functions proposed within the GraphSAGE framework?

Accepted Answer

1. Mean (taking the element-wise average), 2. Pool (passing neighbors through a neural net then applying max-pooling), and 3. LSTM (applying an LSTM to a random permutation of neighbors).

Question 13

What is the fundamental difference between traditional shallow graph embeddings and Graph Neural Networks?

Accepted Answer

Shallow embeddings just learn a simple lookup table ($Z$) based on structural distances, whereas GNNs use deep learning to map node attributes through neighborhood topology.

DM10 - Graph Neural Networks

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